Abstract: Functional information measures how rare functional configurations are. Wong and colleagues argue that selection should drive a law of increasing functional information. This is often read as a claim that complexity must increase. We give a cleaner interpretation, which is that survivors tend to be the systems that did not overcommit. We model a system as a policy π, meaning a bundle of commitments expressed in a finite embodied vocabulary. New selection pressures arrive as a set of future requirements drawn from the unobserved outcome set U. A currently viable policy leaves an unobserved buffer B_π ⊆ U of outcomes it still permits. Under a maximally ignorant novelty model, the survival probability of π is exactly 2^|B_π|−|U|. Under any exchangeable novelty prior, survival remains monotone in |B_π|. So persistence favours weaker constraints on function, where weakness counts the compatible completions left open. We define degree of function as survival probability and functional information as Hazen and Szostak rarity among currently viable policies. Conditioning on persistence reweights the population toward larger buffers, hence higher functional information. This yields a formal version of Wong’s law under explicit assumptions. In fully enumerated toy worlds, weakness maximisation improves mean log survival probability by 1.674 bits relative to random choice. Weakness and simplicity are not the same thing. Weakness helps a system persist under novelty, because it keeps more futures compatible. Simplicity can help a system persist because there is less to break. That obviates the need for repair. Complexity requires self-repair to persist, increasing weakness. Life is persistent complexity. In between complex life and simple nonlife is the void of the unviable; complexity which is not alive.

Abstract: Understanding how lifestyle factors influence the dynamic organization of intrinsic brain networks in young adulthood is critical for identifying mechanisms that support cognitive health during a formative developmental period. In this study, we examined whether an 8-week physical activity and cognitive training intervention altered dynamic functional network connectivity (dFNC) patterns in undergraduate students and how these neural dynamics related to physical activity levels, sedentary behavior, and cognitive performance. Resting-state fMRI data were decomposed using a constrained ICA framework to extract 53 intrinsic connectivity networks, from which 10 dynamic connectivity states were identified and individualized via constrained dynamic double functional independent primitives (c-ddFIPs). We quantified state occupancy, convergence, and divergence to characterize network flexibility. Occupancy analyses showed modest but consistent associations linking greater physical activity with increased time in integrative, higher-order states (especially states 6 and 7) and reduced time in segregated or sensory-weighted states. Convergence and divergence analyses further revealed that physically active individuals demonstrated stronger differentiation between integrative and low-engagement states, whereas sedentary behavior corresponded to greater similarity among segregated configurations. Cognitive measures—particularly working memory—showed parallel relationships, aligning improved performance with more flexible and well-differentiated dynamic patterns. Together, these findings suggest that physical activity in young adults is associated with enhanced neural flexibility, characterized by greater engagement and differentiation of integrative connectivity states that support executive and other cognitive functions.

Abstract: Accurate in-vivo brain tumor detection using hyperspectral imaging (HSI), a non-invasive technique that captures spectral information beyond the visible range, is challenging due to the complexity of biological tissues and the difficulty in distinguishing malignant from healthy areas. Conventional neural network-based methods often misclassify tumor tissue as blood vessels, largely due to high vascularization and the scarcity of annotated data. To address this issue, this work proposes an underexplored approach that decomposes the problem into two tasks: (1) segmentation of the brain cortical surface and its blood vessels, and (2) segmentation of biological tissues within the segmented craniotomy site. The cortical segmentation task is addressed independently of the segmentation model used in the second stage. To achieve this, a set of pseudo-labels is generated from RGB and HSI captures acquired during in-vivo brain surgeries. These pseudo-labels support a multimodal training strategy that leverages both imaging domains, yielding a model capable of segmenting the craniotomy site and the blood vessels contained in it. The model is further refined on HSI using weakly supervised fine-tuning with sparse ground truth annotations. The final segmentation map combines cortical and tissue segmentation outputs, considering only cortex pixels not overlapped by vessels as potential tumor regions. This simplifies the HSI tissue segmentation task, reframing it as a binary segmentation of healthy vs. other tissues, while still enabling a comprehensive multiclass output. The proposed method achieves up to a 15.48\% increase in F1 score for the tumor class, while segmenting the brain cortex with a mean Dice Similarity Coefficient (DSC) of 92.08\% and accurately detecting 95.42\% of labeled blood vessel samples in the HSI dataset.

Abstract: The rugged morphology and dispersed settlements of the Calabrian region pose long-standing barriers to timely and equitable access to healthcare, particularly for elderly and fragile populations living in mountainous areas. In this paper, we present a telemedicine ecosystem specifically designed for Calabria that integrates certified wearable wristbands, secure communication infrastructure, and intelligent back-end services to enable continuous home monitoring and rapid clinical intervention. Building on the SidlyCare platform, the system acquires real-time physiological signals (heart rate and oxygen saturation), streams them to a central server through encrypted channels, and applies machine learning and deep learning-based anomaly detection models to identify both acute and insidious deteriorations in patient status. Alerts are propagated via a multi-stakeholder workflow involving patients, family caregivers, general practitioners, non-profit organizations, and local health authorities, who interact with the platform through role-specific dashboards that support longitudinal visualization, risk stratification, and integration with existing electronic health record infrastructures. A pilot case study in a tele-home care programme for elderly patients in Calabria demonstrates the feasibility and potential of this architecture to improve safety, foster patient engagement, and strengthen continuity of care in geographically isolated communities, offering a scalable blueprint for territorial telemedicine in similar rural and mountainous contexts.

Abstract: The pharmaceutical industry is undergoing a transformative revolution driven by artificial intelligence, fundamentally reshaping drug discovery and early development processes. This comprehensive review examines how AI technologies from machine learning to deep neural networks are enhancing predictive accuracy and operational efficiency across the entire development pipeline. By analyzing complex biological data, these computational approaches enable unprecedented precision in target identification, lead optimization, and preclinical assessment, significantly accelerating therapeutic development. However, substantial challenges persist in implementation, including data harmonization issues, model interpretability constraints, and integration barriers within existing regulatory frameworks. This analysis critically evaluates both the transformative potential and practical limitations of AI applications, highlighting their capacity to not only streamline development pipelines but also pioneer innovative approaches in personalized medicine and novel therapeutic solutions for complex diseases, while addressing the critical hurdles that must be overcome for successful integration into pharmaceutical research and development.

Abstract: The origin of life's rapid emergence (~10⁹ years) and universal biochemical features (homochirality, conserved metabolic pathways) present a fundamental puzzle: random chemical search in configuration space predicts timescales exceeding 10¹²³ years, rendering biogenesis essentially impossible within cosmic history. We present a comprehensive theoretical framework unifying Penrose's Conformal Cyclic Cosmology (CCC) with sheaf-theoretic descriptions of prebiotic chemical organization. We suggest that biological information from extinct systems in the previous cosmic Aeon (Aeonn) can survive the conformal boundary transition (ℐ⁺n → ℐ⁻(n+1)) through squeezed quantum states with squeezing parameter r ~ 10⁸⁶, which suppress decoherence over timescales approaching 10⁹⁷ years. This information, encoded in photonic field correlations, establishes topological attractors in the chemical configuration space of the subsequent Aeon (Aeon(n+1)) via modified Casimir forces. Using formal concept analysis and sheaf theory, we show that microenvironmental integration satisfying locality and gluing conditions enables coherent assembly of inherited structural motifs, reducing effective search space by ~10⁶⁴ orders of magnitude. The framework makes seven falsifiable predictions including universal homochirality (enantiomeric excess ~0.2% from photonic bias amplified by autocatalysis), convergent metabolic network topology across independent biogenesis events, and specific cosmic microwave background non-Gaussian signatures at ℓ ~ 1000-3000. Numerical simulations of molecular dynamics in squeezed electromagnetic vacua demonstrate biogenesis timescales of τbio ~ 10⁹ years, consistent with terrestrial observations. This work provides the first physically viable mechanism for trans-Aeon biological information transfer, resolving the combinatorial impossibility problem and suggesting life is an iteratively optimized feature of cosmic evolution rather than a contingent chemical accident.

Abstract: Cancer represents a dynamic and evolving ecosystem driven by complex interactions among genetically and phenotypically diverse cell populations. Within the tumor microenvironment, cells engage in both competitive and cooperative behaviors that determine their collective evolutionary fate. To capture these dynamics, we employ evolutionary game theory to investigate the coexistence and adaptation of four representative tumor phenotypes: proliferative (P), invasive (I), resistant (R), and cooperative (C). Using a four-strategy evolutionary game-theoretic framework, we show that explicitly including a cooperative phenotype qualitatively expands the range of polymorphic and noise-sustained coexistence regimes observed in the model, enabling coexistence regimes that cannot arise in reduced three-strategy models. Numerical simulations reveal that frequency-dependent selection promotes stable polymorphisms or oscillatory coexistence among phenotypes, explaining persistent intratumoral heterogeneity. Incorporating stochastic replicator equations further demonstrates that random fluctuations can sustain rare phenotypes, induce transient dominance shifts, and generate noise-driven evolutionary transitions. To explore environmental modulation, we extend the model to analyze tumor evolution under acidic microenvironmental conditions and under pH-buffered therapeutic interventions. Acidity enhances the fitness of invasive and resistant cells, driving the system toward aggressive, therapy-tolerant equilibria. In contrast, buffering restores cooperative and proliferative dominance, illustrating that ecological control of the tumor microenvironment can redirect evolutionary trajectories. Collectively, this work unifies deterministic and stochastic evolutionary game theory approaches to show how tumor heterogeneity arises from eco-evolutionary feedbacks, stochastic fluctuations, and environmental pressures. The results suggest that evolution-informed, microenvironment-modulating interventions may influence selective pressures in ways that favor less aggressive evolutionary outcomes, providing a conceptual basis for adaptive therapeutic strategies.

Abstract: The antibiotic pipeline has stalled: most recent approvals reflect incremental modifications of existing scaffolds, while antimicrobial resistance continues to outpace discovery. Antimicrobial peptides (AMPs) offer a compelling alternative because of rapid, multi-modal activity, but clinical translation has been limited by toxicity, serum instability, and the prohibitive cost of synthesizing and testing large libraries. Recent progress in protein language models (pLMs) changes the computational landscape by providing embeddings that capture sequence context and biophysical regularities from massive unlabeled datasets. However, pLMs alone are not a design solution. We propose a technique coupling pLM-derived representations to diffusion or discrete flow-based generative models that can explore non-homologous regions of peptide space while being steered by multi-objective guidance. This framework supports direct optimization for potency, selectivity, and developability during generation, compressing hit discovery and early optimization into a single in silico loop. Conditioning generation on target and safety predictors could shift AMPs from membrane-lytic ‘blunt instruments’ toward more selective, target-aware therapeutics.

Abstract: Antiretroviral agents for HIV prevention are typically evaluated in terms of trial efficacyand programmatic coverage, but rarely in terms of whether they admit a true mathematicalsolution to prevention. Here we introduce the Prevention Theorem, which formalizesprevention for a given exposure e as the condition R0(e) = 0, meaning that the probability of establishing a productive, transmissible infection is exactly zero. Within this framework,post-exposure prophylaxis (PEP) is not delayed treatment but a time-dependent operatoracting on within-host infection establishment dynamics. Using a mechanistic model of reservoirseeding and proviral integration, we derive the PEP Window Corollary: PEP can enforce R0(e) = 0 only when initiated within a finite biological window prior to irreversible integrationand initial reservoir establishment. Beyond this window, all reachable system statessatisfy R0(e) > 0 and are irreducible by post-exposure intervention. Parameterization usingvirological data indicates that this window extends to approximately 72 hours for mucosalexposures but is compressed to roughly 12–24 hours for parenteral exposures due to bypass ofearly immune bottlenecks. As an applied example, we show that structural access delays inhigh-risk populations—such as people who inject drugs—frequently exceed this compressedparenteral window. Consequently, for such exposures the condition R0(e) = 0 is mathematicallyand biologically unreachable before access is even attempted, rendering the failure ofpost-exposure prevention a consequence of violated biological boundary conditions ratherthan pharmacological efficacy.

Abstract: Background: Major depressive disorder (MDD) is increasingly viewed through a neuroplasticity lens, with developmental synaptic pruning emerging as a potential core liability. Genetic evidence implicates pruning pathways, while rapid-acting antidepressants like ketamine promote synaptogenesis, suggesting that excessive early elimination leaves circuits vulnerable to later stress. Few computational models, however, capture the specific MDD pattern of latent fragility collapsing under perturbation, followed by recovery via limited plasticity enhancement.Methods: An overparameterized feed-forward neural network (∼396,000 parameters) was trained on a noisy four-class Gaussian cluster task to represent dense early connectivity. Excessive pruning (95% magnitude-based weight removal, per-layer) simulated adolescent over-elimination. Fragility was assessed under input perturbations and internal neural noise (post-activation Gaussian injections at varying intensities) modeling neuromodulatory disruption. Recovery involved gradient-guided regrowth (50% of pruned connections, prioritized by loss-reduction potential) followed by fine-tuning. Comparisons included random regrowth and a sparsity sweep to identify thresholds.Results: The intact network showed robust performance across conditions. Pruning induced sharp collapse (clean accuracy ∼51%, standard noisy ∼43%), with pronounced sensitivity to internal noise (moderate stress accuracy ∼31%) exceeding input noise effects. Gradient-guided regrowth plus fine-tuning restored near-baseline accuracy (clean/standard ∼100%) and robustness (combined stress ∼97%) despite ∼47% persistent sparsity. Targeted regrowth slightly outperformed random under high stress. A critical threshold emerged around 93% sparsity, beyond which combined-stress performance dropped abruptly (>44 percentage points).Conclusions: Excessive pruning generates threshold-like intrinsic fragility consistent with stress-triggered MDD relapse, while targeted, limited synaptogenesis efficiently compensates without full density restoration. These findings support a pruning-mediated plasticity deficit as a mechanistic framework for MDD vulnerability and highlight the therapeutic potential of activity-dependent plasticity enhancement. The model provides a testable scaffold for linking polygenic pruning risk to circuit-level decompensation and rapid treatment response.

Abstract: Resistant mechanisms to venetoclax, a selective BCL-2 inhibitor approved for hematological malignancies, are frequently mediated by the G101V mutation in BCL-2. Sonrotoclax illustrates superior potency against both wild-type and G101V-mutated BCL-2, yet the mechanistic basis remains unclear. This study employed computational methods to investigate the binding dynamics of both inhibitors. Structures were predicted with AlphaFold, refined via molecular dynamics simulations (MDS), and ligands were docked with AutoDock Vina. Four systems were subjected to triplicate 200 ns MDS, with analyses including RMSD, RMSF, buried surface area, protein-ligand interaction fingerprint, and MM/GBSA binding free energies. Results indicate venetoclax exhibits progressive dissociation from G101V BCL-2, with elevated RMSD, reduced buried surface area, and increased unbound states. In contrast, Sonrotoclax maintains a steady correlation, shows persistence with entropy-enthalpy compensation, displays negligible unbound time, higher binding free energies, and constant van der Waals anchors. Having all these results in mind, a "Dynamic Blockade" hypothesis is proposed, where Sonrotoclax's flexibility enables sustained BH3 groove occupancy, blocking pro-apoptotic BH3-only proteins and overcoming allosteric perturbations induced by G101V. This mechanistic perspective proposes the optimal approach for designing resilient inhibitors to accelerate drug repurposing and development in oncology.

Abstract:

We devised a quantitative scoring function to assess the cumulative effects of nonsynonymous single nucleotide variants (SNVs) on protein-coding genes in patients with ovarian cancer (OvCa) and thyroid cancer (ThCa). The goal is to find novel candidate cancer-related genes for downstream bioinformatics analyses and wet-lab studies. With Genomic Data Commons as primary data resource, SNV information was extracted from whole-exome sequencing data from patients with these cancers. A cumulative variant scoring function, Q(G) was developed to sum up the deleterious effects of the individual SNVs on the gene G. While Q(G) can be computed using any popular functional effect analyzers such as FATHMM-XF, SIFT, PolyPhen, and CADD, we have also established an integrative scoring function iQ(G) that combines the deleterious assessments from different analyzers and demonstrated that iQ(G) is a more effective method for identifying likely cancer-related genes. Based on the iQ(G) rankings, the top three novel genes for OvCa are AHNAK2, UNC13A, and PCDHB4; and those for ThCA are PLEC, HECTD4, and CES1. Furthermore, the top 1% genes with highest iQ(G) scores for each cancer were submitted for KEGG pathway analysis. The results revealed that several genes of the CACNA1 family within the type II diabetes mellitus pathway are likely related to both OvCa and ThCa and suggested other molecular interactions that should be further studied in connection with OvCa prognosis and ThCa treatment.

Abstract: Cells adapt their phenotypes in noisy microenvironments while maintaining robust decision-making. We develop a coarse-grained theoretical framework in which cellular phenotypic adaptation is described as Bayesian decision-making coupled to replication and diffusion. This leads to an effective Fokker--Planck equation with an emergent fitness landscape governing phenotypic dynamics. We identify distinct phenotypic regimes—homeostatic fixation, bistable decision-making, critical switching, and runaway explosion—and propose a biological interpretation in which homeostatic and bistable landscapes correspond to healthy differentiated cell states, whereas explosive landscapes capture stem-like or cancer-like behaviour. In the Gaussian setting, the correlation $\rho$ between intrinsic and extrinsic states directly encodes mutual information and acts as a bifurcation parameter: high correlation produces shallow or explosive landscapes associated with phenotypic plasticity, while reduced correlation stabilises differentiated fates by deepening potential wells. We further show that proliferation reshapes these landscapes in a nontrivial manner. Proliferation conditionally may stabilises local homeostasis without altering global confinement, or cooperate with biased environmental sensing to eliminate homeostasis/bistability and drive cancer-like phenotypic explosion even at high phenotypic fidelity. Finally, we show that negative intrinsic–extrinsic correlations suppress explosive dynamics but also reduce bistable plasticity, suggesting a robustness-plasticity trade-off. Together, our results suggest that development, tissue homeostasis, and carcinogenesis can be understood as information-driven deformations of a Bayesian phenotypic fitness landscape.

Abstract: The generation of synthetic human genomic data offers immense potential for biomedical research and data sharing, while theoretically safeguarding individual privacy. However, existing methods, including deep generative models, struggle to achieve a robust balance between data utility and privacy protection. State-of-the-art evaluations like PRISM-G reveal vulnerabilities such as proximity, kinship replay, and trait-linked leakage. This paper introduces GenProtect-V, an end-to-end privacy-preserving synthetic human genomic data generation framework based on a Variational Autoencoder architecture. GenProtect-V integrates multi-layered privacy mechanisms: a Differentially Private Encoder to mitigate Proximity Leakage, Decoupled Latent Space Learning to address Kinship Replay, and a Rare Variant Smoother to counter Trait-linked Leakage. Through extensive experiments on the 1000 Genomes Project dataset, we demonstrate that GenProtect-V consistently achieves significantly lower PRISM-G composite scores compared to state-of-the-art baselines. Crucially, GenProtect-V simultaneously maintains or improves key utility metrics, including Allele Frequency fidelity, Population Structure preservation, and GWAS reproducibility. An ablation study further confirms the independent and significant contributions of its privacy mechanisms. GenProtect-V establishes a new benchmark for balancing privacy and utility, offering a more secure and practical paradigm for synthetic genomic data generation.

Abstract: The rapid diffusion of high-throughput sequencing technologies has generated a vast repertoire of protein-coding se- quences whose biological roles remain unknown. This discrepancy between sequence availability and functional under- standing has led to the definition of the dark proteome, comprising proteins or protein regions that lack experimentally resolved structures and reliable functional annotations. Classical sequence-based approaches often fail to characterize these targets due to extreme sequence divergence, intrinsic disorder, or membrane localization. Here, we present an inte- grated, structure-centric computational framework that leverages recent advances in artificial intelligence to enable func- tional inference in the human dark proteome. By combining deep learning–based protein structure prediction, large-scale structural alignment, and machine learning–driven surface pocket analysis, we uncover remote evolutionary relationships and conserved functional features that remain invisible to traditional bioinformatics pipelines. Our results demonstrate that artificial intelligence provides a powerful strategy to bridge the gap between genomic information and biological function, opening new avenues for systematic exploration of uncharacterized regions of the human proteome.

Abstract: Amid COVID-19-related in-person school closures in 2021, an agent-based simulation grounded in social impact theory was implemented and documeted to investigate the effects of in-person school closure on nonmedical prescription opioid use among adolescents in Ontario, Canada. The results of model simulations forecasted an alarming rebound effect in the opioid use prevalence after the lifting of in-person school closures and identified secure medication storage in households as an effective strategy for mitigating associated risks. This study evaluates this result by comparing the baseline projection from the previously published study with newly released 2023 data from the Ontario Student Drug Use and Health Survey. Furthermore, it employs the developed agent-based model to simulate the projection through 2030 and assesses the efficacy of secure medication storage in households for the coming years. The study confirms that the previously published simulation projection for 2023 closely aligns with observed data, showing nonmedical prescription opioid use prevalence among Ontario adolescents nearly doubling from 2021 to 2023. Additionally, the results show that nonmedical prescription opioid use prevalence among youth is projected to remain at these elevated levels. Critically, the findings suggest that the temporal window for effective secure medication storage interventions has elapsed, and these interventions are now expected to have minimal impact on reducing this increase, even when applied extensively. The agreement between reported predictions and observed data demonstrates that a simulation model with relevant conceptual foundation can accurately predict future trends and provide sufficient lead time for policymakers to implement interventions within critical time-sensitive windows to alter undesirable trajectories before public health crises escalate.

Abstract: Following Livadiotis G. and McComas D. J. (2023) [1], we propose a new type of DNA frameshift mutations that occur spontaneously due to information exchange between the DNA sequence of length bases (n) and the mutation sequence of length bases (m), and respect the kappa-addition symbol ⊕κ. We call these proposed mutations Kappa-Frameshift Background (KFB) mutations. We find entropy defects originate in the interdependence of the information length systems (or their interconnectedness, that is, the state in which systems with a significant number of constituents (information length bases) depend on, or are connected with each) by the proposed KFB-mutation). We also quantify the correlation among DNA information length bases (n) and (m) due to information exchange. In the presence of entropy defects, the Landauer’s bound and minimal metabolic rate for a biological system are modified. We observe that the different n and κ scales are manifested in the double evolutionary emergence of the proposed biological system through subsystems correlations. For specific values of the kappa parameter we can expect deterministic laws associated with a single biological polymer in the short term before the polymer explores over time all the possible ways it can exist.

Abstract: Highly pathogenic avian influenza (HPAI) has expanded its host range with recent detections in dairy cattle, raising critical concerns regarding within-herd persistence and cross-species spillover. This study develops a stochastic SEI_sI_aR − B compartmental model to analyse HPAI transmission, explicitly accounting for environmental pathogen reservoirs and noise intensities through Wiener processes. The positivity and boundedness of solutions are established, and the disease-free and endemic equilibria are analytically derived. The basic reproduction number is determined using the next-generation matrix method. Numerical simulations confirm that the model dynamics are consistent with theoretical analysis and illustrate how stochastic fluctuations significantly influence disease persistence. Furthermore, sensitivity analysis using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC) identifies the transmission rate from asymptomatic infectious cattle (β_a) as the primary driver of transmission. The model effectively captures the dynamics of environmental variability affecting HPAI spread, suggesting that effective control strategies must prioritise the early detection and isolation of asymptomatic carriers alongside environmental management.

Abstract: Accurate identification of promoters is essential for deciphering gene regulation but remains challenging due to the complexity and variability of transcriptional initiation signals. Existing deep learning models often fail to simultaneously capture long-range dependencies and precise local motifs in DNA sequences. To address this, we propose DNABERT2-CAMP, a hybrid deep learning framework that integrates global sequence context with localized feature extraction for enhanced promoter recognition in Escherichia coli. The model leverages a pre-trained DNABERT-2 Transformer to encode evolutionary conserved patterns across extended contexts, while a novel CAMP (CNN-Attention-Mean Pooling) module detects fine-grained promoter motifs through convolutional filtering, multi-head attention, and mean pooling. By fusing global embeddings with high-resolution local features, our approach achieves robust discrimination between promoter and non-promoter sequences. Under 5-fold cross-validation, DNABERT2-CAMP attained an accuracy of 93.10% and a ROC AUC of 97.28%. It also demonstrated strong generalization on independent external data, achieving 89.83% accuracy and 92.79% ROC AUC. These results underscore the advantage of combining global contextual modeling with targeted local motif analysis for accurate and interpretable promoter identification, offering a powerful tool for synthetic biology and genomic research.

Abstract: In this work, we pose and aim to answer the following questions, among others: Which quantitative characteristics, being satisfied, led to the phase transition from "primordial soup" to living organisms? How to measure the negentropy of a certain organic matter that underpinned the appearance of a certain species? To what extent do the biosequences of living organisms differ from random sequences? How do we quantitatively distinguish primitive from higher-level organisms? How can we compare the complexity of two living things? Is there an adequate mathematical structure that naturally and appropriately represents each organism biosequence and all of them as a whole? What are the properties of that structure? How does that structure evolve, and what are the theoretical limits of any further evolution? Is it likely that these bounds will be reached, and what are the "limits of life?" How to estimate the effect on the mechanism of evolution of natural selection vs. the one of chance and mutations? To this end, we introduce relevant mathematical structures and use them for modeling purposes. Finally, we also speculate on possible scenarios of the origin of life, evolution, and related issues.