arXiv subjects

Abicumaran Uthamacumaran

Publications and source records attributed to Abicumaran Uthamacumaran.

At least 19 recordsLinked to original sources

arXiv2026

Large Language Models are Shannon Lossy Compressors Not Solomonoff Induction Estimators: Self-improvement and Singularity Are Not Near Without Symbolic Model Synthesis

We connect two questions in Algorithmic Information Theory (AIT), Machine Learning (ML) and Artificial General Intelligence (AGI): whether LLMs estimate Solomonoff induction, and whether they can self-improve towards an AI Singularity. We provide theoretical, methodological and empirical answers in the negative but show how limits can be circumvented. Cross-entropy, negative log-likelihood and related next-token objectives cannot alone implement Solomonoff induction: they fit supplied conditionals rather than a program-weighted universal mixture. More computation can improve fit within a fixed objective but cannot change its inductive principle without external hyperparameter or architectural tuning; they alone do not deliver Solomonoff-Levin optimal prediction. For finite learners and observers, theoretical boundaries become less decisive and approaches diverge. Resource-bounded estimators are finite mechanism-search tools whose divergence does not violate algorithmic information conservation. All 26 served language-model checkpoints across five pre-training families, 0.8-35 billion parameters and 1.9-8.5 bits per weight, evaluated at their commitments over a closed alphabet, violate the dominance guarantee defining a universal mixture. Against a 3.32-bit bound attained by a genuine mixture, the best model trails a Krichevsky-Trofimov code by 4.5 bits, the median by 36 and the worst by 128; excess grows to every stream's end rather than settling to a constant. Served conditionals fail to form a mixture over the declared class in 79 of 91 checkpoint-designs; neither scale nor post-training closes the gap. Frontier developers adopt neurosymbolic approaches, including Fable and Astra, incorporating model synthesis via neurosymbolic computation. They are no longer purely statistical LLMs, making them better, though still limited, candidates for higher forms of induction & model synthesis.

cs.IT↗

arXiv2026

Algorithmic Information Dynamics of Learning: A Certified, Differentiable Complexity Controller for Grokking

Algorithmic Information Dynamics (AID) studies systems by perturbing them and measuring changes in algorithmic complexity, but its usual estimator, the Block Decomposition Method, is piecewise constant, restricting the calculus to finite differences. We use $K^{\mathrm{CDM}}_{\mathrm{s}F}$, a certified, differentiable estimator, to bring the calculus into learning dynamics: grokking, where a complexity order parameter is known but has not been made to act. As a transient loss kick, the estimator becomes a controller that accelerates grokking in Levin's description-length--versus-time sense, within a data-dependent Occam boundary whose finite-size trend, $f_c\sim\ln p/p$, is consistent with a coupon-collector interpretation. Ablations show that a complexity gate matches a train-loss gate in rescuing failing seeds with $27\%$ less intervention; among the tested signals, only map complexity marks the transition's completion; the certified prior and the per-parameter $\nabla K$ attribution are both fungible (a uniform-prior sensor makes bit-identical gate decisions, and random supports match $\nabla K$-selected ones above a sparsity threshold); and direct field perturbation shows a nucleation-like response to the Occam field (no linear regime is resolved over the probed amplitudes, so these measurements do not justify a fluctuation--dissipation surrogate), with a finite-field response growing by orders of magnitude toward the phase-transition. These measurements account for the empirically tuned staircase: bang--bang pulses, stall-fired and released on yield, whose iteration plausibly builds the response it exploits. The kick transfers to sparse parity and to a transformer; a sustained weight-space loss fails. The algorithmic estimator's distinct contribution is timing (when to fire and when to release), not attribution.

cs.LG↗

arXiv2026

Enhancing Clinical Decision Support and Differential Diagnosis with Knowledge Graphs, and Retrieval Augmented Generation in Generative AI

Diagnostic error carries a burden, while unconstrained large language models (LLMs) remain vulnerable to hallucination and weak integration of quantitative laboratory dynamics. We developed a decision-support pipeline combining disease-specific biomarker correlation graphs, ordinary differential equations (ODEs), deep sequence classification, and retrieval-augmented generation (RAG). For 103 disease classes from a full blood count (FBC) repository, biomarker networks were used as coupling matrices to generate 30 trajectories per disease (3,090 total). A one-dimensional convolutional neural network (CNN) and long short-term memory (LSTM) network classified disease trajectories and six dynamical clusters. A constrained GPT-4o-mini RAG layer used a 19-pattern BMJ Best Practice/NICE corpus to generate differential diagnoses evaluated for diagnostic suitability, evidential grounding, and clinical plausibility. Across five random-seed runs, disease-level accuracy was $0.940 \pm 0.006$ for the CNN (95\% CI 0.933--0.948) and $0.852 \pm 0.019$ for the LSTM (95\% CI 0.828--0.875); the CNN advantage was 8.87 percentage points (95\% CI 6.47--11.27; $t(4)=10.26$, $p=5.1\times10^{-4}$; Hedges' $g=3.67$). Among 100 sampled RAG cases, 96 parsed successfully; evidence was cited in 97.9\%, the true diagnosis was mentioned in 71.9\%, and the composite score was 3.82/5 with a 47.9\% strict pass rate. The central finding was a decoupling between grounding and diagnostic correctness: classifier-correct versus classifier-wrong outputs differed in diagnostic suitability but not evidential grounding. Post-hoc analysis confirmed a 1.02-point diagnostic-score difference (Mann--Whitney $p=0.0024$; Hedges' $g=0.72$), whereas grounding differed by only $-0.02$ points ($p=0.839$; $g=-0.04$).

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arXiv2026

Similarity Analysis of Blood Count Reference Intervals Across Continents Reveals No Reproducible Population or Geography-Linked Structure and Supports Personalised Values

Blood reference intervals (RIs) underpin diagnostic interpretation and therapeutic monitoring worldwide. However, many widely used RI systems originate from limited historical cohorts and have been propagated across health systems without harmonised derivation protocols, shared metadata, or cross-population validation. Consequently, the global RI landscape reflects a heterogeneous mixture of legacy standards and local laboratory practices rather than a biologically grounded framework. Here we examine published Complete Blood Count (CBC) reference intervals, one of the most commonly used laboratory panels worldwide. We compiled CBC RI data from 28 countries and analysed their similarity using variability mapping, hierarchical clustering, information-theoretic distances, cohesion benchmarking, and nonlinear manifold visualisation. Body mass index (BMI) served as a methodological positive benchmark and exhibited clear continent-level clustering (mean cohesion approximately 0.78-0.81). In contrast, CBC reference intervals showed no reproducible geography-linked clustering across methods, with uniformly high cohesion scores (mean approximately 1.27-1.30). Weak signals in red-cell indices (MCV, HGB) were unstable across sexes and distance metrics. This absence of structure should not be interpreted as evidence that current CBC reference intervals represent universal biological standards. Rather, it is more consistent with the fragmented and historically inherited nature of the global RI landscape. These findings indicate that published CBC reference intervals do not encode coherent global structure and provide limited support for universal population-based diagnostic thresholds. Instead, they support a transition toward recalibrated and personalised reference frameworks based on longitudinal individual baselines and harmonised derivation standards.

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arXiv2026

Multi-omic Enriched Blood-Derived Digital Signatures Reveal Mechanistic and Confounding Disease Clusters for Differential Diagnosis

Understanding disease relationships through blood biomarkers offers a pathway toward data-driven taxonomy and precision medicine. In this study, we constructed a digital blood twin, a computational model derived from 103 disease signatures comprising longitudinal hematological and biochemical analytes. Profiles were standardized into a unified disease-analyte matrix, and pairwise Pearson correlations were computed to assess similarity across conditions. Hierarchical clustering revealed consistent grouping of hematopoietic disorders, while metabolic, endocrine, and respiratory diseases were more heterogeneous, reflecting weaker internal cohesion. To evaluate cluster structure, the tree was partitioned at a stringent distance threshold, yielding 16 groups. Enrichment analysis of the largest and most heterogeneous cluster demonstrated convergence on cytokine-signaling pathways, indicating shared inflammatory mechanisms that transcend conventional clinical boundaries. PCA and UMAP corroborated the correlation-based results, consistently separating hematological diseases as a distinct cluster. Random Forest feature selection identified neutrophils, mean corpuscular volume, red blood cell count, and platelet count as the most discriminative analytes, reinforcing the role of hematopoietic markers as key drivers of disease stratification. Collectively, these findings show that blood-derived digital signatures can recover clinically meaningful disease clusters while uncovering mechanistic overlaps across categories. This network physiology framework highlights the potential of integrating routine laboratory data with computational methods to refine disease ontology, map comorbidities, and advance precision diagnostics.

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arXiv2026

Patterns in Individual Blood Count Trajectories in the UK Biobank Characterise Disease-Specific Signatures and Anticipate Pan-Cancer Risk

We investigate the longitudinal behaviour of blood markers from common haematological tests as a marker of disease and as a function of disease progression in a variety of conditions including cancer, cardiovascular disease, and infections. We study confounding and non-confounding factors to allow for the earlier detection of disease and conditions based on their longitudinal signatures from biomarker patterns commonly measured in popular and scalable common blood tests across routine clinical tests, in particular the Complete Blood Count (CBC or FBC). Our analysis with normalised temporal profiles and machine learning techniques even before any symptoms appear demonstrates that analyte-group patterns found in blood testing are disease sensitive and disease specific. We demonstrate that CBC markers contribute to the majority of the predictive signal, while biochemistry and other blood panels provide only a modest additional gain mostly associated to very the individual disease for which the test was designed (e.g. CRP, liver enzymes, blood sugar). Our results demonstrate how regular monitoring, computational intelligence, and machine learning applied to longitudinal CBC data can converge to uncover disease patterns, advancing the potential for precision healthcare and predictive medicine on a mass scale leveraging an existing and pervasive blood test.

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arXiv2026

Integrative Adaptive Indexes from Noisy Routine Haematological Markers can Predict and Discriminate Health Status and Biological Age

For more than two decades, advances in personalised medicine and precision healthcare have largely been based on genomics and other omics data. These strategies aim to tailor interventions to individual patient profiles, promising greater treatment efficacy and more efficient allocation of healthcare resources. Here, we show that widely collected common haematologic markers can reliably predict and discriminate individual chronological age and health status from even noisy sources. Our analysis includes synthetic and real retrospective patient data, including medically relevant and extreme cases, and draws on more than 100\,000 complete blood count records over 13 years from the United States Centers for Disease Control and Prevention's National Health and Nutrition Examination Survey (CDC NHANES). We combine fully explainable risk assessment scores with machine and deep learning techniques to focus on clinically significant patterns and characteristics without functioning purely as a ''black-box model allowing interpretation and control. We validated the results with the UK Biobank, a larger cohort independent of the CDC NHANES and with very different collection techniques, the former a survey and the second a longitudinal study. Unlike current biological ageing indicators, this approach may offer rapid, and scalable implementations of personalised, precision and predictive approaches to healthcare and medicine without or before requiring other specialised, uncommon or costly tests.

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arXiv2025

Systematic Reconstruction of Disease Networks from Longitudinal Blood Data for Causal Discovery and Intervention Analysis

We explore the hyperparameters and introduce a methodological framework to convert disease patterns from time series data of blood test results into correlation graphs for causal hypothesis exploration. The networks represent hypotheses that can then be validated or rejected both for causal discovery and causal analysis (under intervention). We synthetically recreated a repository of 105 typical disease longitudinal patterns extracted from medical guidance and research literature of common blood markers to build a systematic pipeline to translate multidimensional clinical data into intervenable disease networks for causal discovery and causal analysis. This study demonstrates that knowledge graphical models reconstructed from longitudinal data can transform routine medical data into clinically interpretable structures. By integrating multiple thresholding strategies and causal graph design, the framework has the purpose to move beyond statistical correlation toward clinically and testable inference networks. These results highlight a practical pathway for more transparent, explainable, and scalable tools in clinical decision support for AI training, precision healthcare and predictive medicine, offering interpretable, clinically actionable outputs that support safer use of AI in differential diagnosis.

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arXiv2025

XGBoost-Powered Digital Twins Leverage Routine Blood Tests for Early Detection of Cancer and Cardiovascular Disease

Early detection of cancer and cardiovascular diseases is fundamental to improving patient outcomes and reducing healthcare expenditure. Current cancer screening programs are targeted towards specific cancers and are often inaccessible to large parts of the population, particularly in remote regions. This project aimed to develop digital blood twins: machine learning models that leverage routinely collected blood test data, demographics, comorbidities, and prescribed medications, for scalable and cost-effective disease screening. Digital blood twins were constructed using the UK Biobank dataset (n = 373,269). Using age, sex, comorbidities, medication profiles, and blood test z-scores, three iterations of XGBoost classifiers were trained for broad cancer, colorectal cancer, and cardiovascular disease prediction. Model interpretability was achieved through SHAP and dimensionality reduction analyses (UMAP, t-SNE). Broad-category cancer models achieved ROC-AUC = 0.607-0.706. Colorectal cancer prediction demonstrated excellent discrimination (ROC-AUC = 0.816-0.993), and cardiovascular models showed clinical utility, notably for hypertension (ROC-AUC = 0.813, F1 = 0.861). SHAP revealed consistent importance of age, sex, basophil count, and cystatin C. Immune digital blood twins as an agnostic tool demonstrate proof-of-concept feasibility for accessible, low-cost, and scalable screening of cancer and cardiovascular diseases, supporting future integration into predictive and preventive healthcare.

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arXiv2025

A High-Fidelity Neurosurgical Training Platform for Bimanual Procedures: A Feasibility Study

Background. Bimanual psychomotor proficiency is fundamental to neurosurgical procedures, yet it remains difficult for trainees to acquire and for educators to objectively evaluate performance. In this study, we investigate the feasibility of a neurosurgical simulation platform that integrates an anatomically realistic brain model with surgical instrument tracking to support training and objective assessment of bimanual tasks in the context of subpial corticectomy. Methods. We developed and evaluated a neurosurgical simulation platform based on an ex-vivo calf brain model and a multi-camera tracking system capable of simultaneously capturing the motion of surgical instruments in both hands, including collection of real-time instrument trajectories and synchronized video recordings. These enabled extraction of motion-based, time-based, and bimanual coordination metrics. We conducted a case series involving 47 participants across four training levels: medical students, junior residents, senior residents, and neurosurgeons. Results. The tracking system successfully captured instrument motion during 81% of the periods when instruments were actively used throughout the simulation procedure. Several extracted metrics were able to significantly differentiate between levels of surgical expertise. In particular, instrument usage duration and custom-defined bimanual coordination metrics such as instrument tip separation distance and simultaneous usage time, show potential as features to identify participant expertise levels with different instruments. Conclusions. We demonstrated the feasibility of tracking surgical instruments during complex bimanual tasks in an ex-vivo brain simulation platform. The metrics developed provide a foundation for objective performance assessment and highlight the potential of motion analysis to improve neurosurgical training and evaluation.

cs.CE↗

arXiv2025

Exhaustive Investigation of CBC-Derived Biomarker Ratios for Clinical Outcome Prediction: The RDW-to-MCHC Ratio as a Novel Mortality Predictor in Critical Care

Ratios of common biomarkers and blood analytes are well established for early detection and predictive purposes. Early risk stratification in critical care is often limited by the delayed availability of complex severity scores. Complete blood count (CBC) parameters, available within hours of admission, may enable rapid prognostication. We conducted an exhaustive and systematic evaluation of CBC-derived ratios for mortality prediction to identify robust, accessible, and generalizable biomarkers. We generated all feasible two-parameter CBC ratios with unit checks and plausibility filters on more than 90,000 ICU admissions (MIMIC-IV). Discrimination was assessed via cross-validated and external AUC, calibration via isotonic regression, and clinical utility with decision-curve analysis. Retrospective validation was performed on eICU-CRD (n = 156530) participants. The ratio of Red Cell Distribution Width (RDW) to Mean Corpuscular Hemoglobin Concentration (MCHC), denoted RDW:MCHC, emerged as the top biomarker (AUC = 0.699 discovery; 0.662 validation), outperforming RDW and NLR. It achieved near-universal availability (99.9\% vs.\ 35.0\% for NLR), excellent calibration (Hosmer--Lemeshow $p = 1.0$; $\mathrm{ECE} < 0.001$), and preserved performance across diagnostic groups, with only modest attenuation in respiratory cases. Expressed as a logistic odds ratio, each one standard deviation increase in RDW:MCHC nearly quadrupled 30-day mortality odds (OR = 3.81, 95\% CI [3.70, 3.95]). Decision-curve analysis showed positive net benefit at high-risk triage thresholds. A simple, widely available CBC-derived feature (RDW:MCHC) provides consistent, externally validated signal for early mortality risk. While not a substitute for multivariable scores, it offers a pragmatic adjunct for rapid triage when full scoring is impractical.

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arXiv2025

Assembly Theory Reduced to Shannon Entropy and Rendered Redundant by Naive Statistical Algorithms

Assembly Theory (AT) and its central measure, the assembly index (Ai), represent an invaluable opportunity to address some of the most persistent and widespread conflations and misconceptions about computability and complexity theory in science. The AT defence embodies several common concurrent misconceptions that pile on each other: the belief that Turing machines impose artefactual constraints, the mischaracterisation of Kolmogorov complexity as inapplicable, and the claims around Ai as different from Shannon entropy or compression algorithms. Here we show that the new arguments advanced by the AT group in their defence, are based on misleading and incomplete experiments that, when completed, show the extent of the correlations and overlapping with popular statistical compression algorithms, conforming with the mathematical equivalence to Shannon entropy previously mathematically proved and reported, which remains undisputed. Through theoretical and empirical analysis, we show that Ai does not offer a path towards fundamental novel causal or informational insights beyond what existing statistical frameworks already offer. Rather than offering a unifying theory of life as the AT authors suggest, we argue that AT obfuscates the field and provides a cautionary example of how the accumulation of conceptual mistakes can lead to a misleading theory. Finally, we show that Ai is a particular limited case of another complexity metric based on algorithmic (Kolmogorov) complexity, consisting of decomposing an object into its causal blocks that goes beyond, and outperforms, AT.

cs.IT↗

arXiv2025

Complexity-Informed Causal Modeling of Neurodevelopmental Trajectories in Pediatric High-Grade Gliomas: Divergences from Neural Stem Cell Signatures

Pediatric high grade gliomas are lethal evolutionary disorders with stalled developmental trajectories and disrupted differentiation hierarchies. We integrate transcriptional and algorithmic network complexity based perturbation analysis to elucidate gene expression patterns and molecular divergence between Diffuse Midline Gliomas and glioblastoma, revealing shared developmental programs steering cell fate decision making. Our complex systems approach supports the emerging paradigm that pediatric high grade gliomas are neurodevelopmental disorders with hybrid lineage identities and disrupted patterning. We identify dysregulated neurodevelopmental and morphogenetic signatures, alongside bioelectric and neurotransmitter signaling programs that alter synaptic organization, neuronal fate commitment, and phenotypic plasticity, regulating glioma phenotypic switching. Causal drivers and regulators of plasticity were predicted as both biomarkers and therapeutic targets, reinforcing the view that pediatric gliomas are disorders of cell fate decisions and collective cellular identity. Decoded plasticity signatures indicate a teleonomic bias toward neural progenitor or neuron like identities, while synaptic transmission gene enrichment supports neuron glioma interactions shaping fate trajectories. These findings advance differentiation therapy as a systems medicine strategy, discovering plasticity regulators to reprogram malignant fates toward stable lineages, offering complex systems based targets for cancer reversion and predictive, preventive, precision oncology.

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arXiv2025

Neurosymbolic Learning for Predicting Cell Fate Decisions from Longitudinal Single Cell Transcriptomics in Paediatric Acute Myeloid Leukemia

Paediatric Acute Myeloid Leukemia is a complex adaptive ecosystem with high morbidity. Current trajectory inference algorithms struggle to predict causal dynamics in AML progression, including relapse and recurrence risk. We propose a symbolic AI and deep learning framework grounded in complexity science, integrating Recurrent Neural Networks, Transformers, and Algorithmic Information Dynamics to model longitudinal single cell transcriptomics and infer complex state transitions in paediatric AML. We identify key plasticity markers as predictive signatures regulating developmental trajectories. These were derived by integrating deep learning with complex systems based network perturbation analysis and dynamical systems theory to infer high dimensional state space attractors steering AML evolution. Findings reveal dysregulated epigenetic and developmental patterning, with AML cells in maladaptive, reprogrammable plastic states, i.e., developmental arrest blocking terminal differentiation. Predictions forecast neurodevelopmental and morphogenetic signatures guiding AML cell fate bifurcations, suggesting ectoderm mesoderm crosstalk during disrupted differentiation. Neuroplasticity and neurotransmission related transcriptional signals implicate a brain immune hematopoietic axis in AML cell fate cybernetics. This is the first study combining RNNs and AID to predict and decipher longitudinal patterns of cell fate transition trajectories in AML. Our complex systems approach enables causal discovery of predictive biomarkers and therapeutic targets for ecosystem engineering, cancer reversion, precision gene editing, and differentiation therapy, with strong translational potential for precision oncology and patient centered care.

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arXiv2025

AI-Driven Hybrid Ecological Model for Predicting Oncolytic Viral Therapy Dynamics

Oncolytic viral therapy (OVT) is an emerging precision therapy for aggressive and recurrent cancers. However, its clinical efficacy is hindered by the complexity of tumor-virus-immune interactions and the lack of predictive models for personalized treatment. This study develops a data-driven, AI-powered computational model combining time-delayed Generalized Lotka-Volterra equations with advanced optimization algorithms, including Genetic Algorithms, Differential Evolution, and Reinforcement Learning, to optimize OVT oscillations' growth and damping. We hypothesize that the model can provide accurate, real-time predictions of OVT responses while identifying key biomarkers to enhance therapeutic efficacy. The model demonstrates strong predictive accuracy, achieving mean squared error (MSE) < 0.02 and R-squared > 0.82. It also identifies experimentally validated biomarkers such as TNF, NFkB, CD81, TRAF2, IL18, and BID, among other inflammatory cytokines and extracellular matrix reconstruction factors, despite being causally agnostic and unaware of specific experimental conditions or therapeutic combinations. Gene set enrichment analysis confirmed these biosignatures as critical predictors of tumor progression and indicated that photodynamic therapy activates immune responses similar to those elicited by combined OVT and immune checkpoint inhibitors. This hybrid model represents a significant step toward precision oncology and computational medicine, enabling longitudinal, adaptive treatment regimens and developing targeted immunotherapies based on molecular signatures, potentially improving patient outcomes.

q-bio.QM↗

arXiv2025

Deep Learning-based Feature Discovery for Decoding Phenotypic Plasticity in Pediatric High-Grade Gliomas Single-Cell Transcriptomics

By use of complex network dynamics and graph-based machine learning, we identified critical determinants of lineage-specific plasticity across the single-cell transcriptomics of pediatric high-grade glioma (pHGGs) subtypes: IDHWT glioblastoma and K27M-mutant glioma. Our study identified network interactions regulating glioma morphogenesis via the tumor-immune microenvironment, including neurodevelopmental programs, calcium dynamics, iron metabolism, metabolic reprogramming, and feedback loops between MAPK/ERK and WNT signaling. These relationships highlight the emergence of a hybrid spectrum of cellular states navigating a disrupted neuro-differentiation hierarchy. We identified transition genes such as DKK3, NOTCH2, GATAD1, GFAP, and SEZ6L in IDHWT glioblastoma, and H3F3A, ANXA6, HES6/7, SIRT2, FXYD6, PTPRZ1, MEIS1, CXXC5, and NDUFAB1 in K27M subtypes. We also identified MTRNR2L1, GAPDH, IGF2, FKBP variants, and FXYD7 as transition genes that influence cell fate decision-making across both subsystems. Our findings suggest pHGGs are developmentally trapped in states exhibiting maladaptive behaviors, and hybrid cellular identities. In effect, tumor heterogeneity (metastability) and plasticity emerge as stress-response patterns to immune-inflammatory microenvironments and oxidative stress. Furthermore, we show that pHGGs are steered by developmental trajectories from radial glia predominantly favoring neocortical cell fates, in telencephalon and prefrontal cortex (PFC) differentiation. By addressing underlying patterning processes and plasticity networks as therapeutic vulnerabilities, our findings provide precision medicine strategies aimed at modulating glioma cell fates and overcoming therapeutic resistance. We suggest transition therapy toward neuronal-like lineage differentiation as a potential therapy to help stabilize pHGG plasticity and aggressivity.

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arXiv2024

On the Salient Limitations of the Methods of Assembly Theory and their Classification of Molecular Biosignatures

We demonstrate that the assembly pathway method underlying assembly theory (AT) is an encoding scheme widely used by popular statistical compression algorithms. We show that in all cases (synthetic or natural) AT performs similarly to other simple coding schemes and underperforms compared to system-related indexes based upon algorithmic probability that take into account statistical repetitions but also the likelihood of other computable patterns. Our results imply that the assembly index does not offer substantial improvements over existing methods, including traditional statistical ones, and imply that the separation between living and non-living compounds following these methods has been reported before.

cs.IT↗

arXiv2022

A Review of Mathematical and Computational Methods in Cancer Dynamics

Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires the integration of information dynamics across multidimensional spatiotemporal scales, including genetic, transcriptional, metabolic, proteomic, epigenetic, and multi-cellular networks. However, the time-series analysis of these complex networks remains vastly absent in cancer research. With longitudinal screening and time-series analysis of cellular dynamics, universally observed causal patterns pertaining to dynamical systems, may self-organize in the signaling or gene expression state-space of cancer triggering processes. A class of these patterns, strange attractors, may be mathematical biomarkers of cancer progression. The emergence of intracellular chaos and chaotic cell population dynamics remains a new paradigm in systems oncology. As such, chaotic and complex dynamics are discussed as mathematical hallmarks of cancer cell fate dynamics herein. Given the assumption that time-resolved single-cell datasets are made available, a survey of interdisciplinary tools and algorithms from complexity theory, are hereby reviewed to investigate critical phenomena and chaotic dynamics in cancer ecosystems. To conclude, the perspective cultivates an intuition for computational systems oncology in terms of nonlinear dynamics, information theory, inverse problems and complexity. We highlight the limitations we see in the area of statistical machine learning but the opportunity at combining it with the symbolic computational power offered by the mathematical tools explored.

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