arXiv subjects

Arturo Tozzi

Publications and source records attributed to Arturo Tozzi.

At least 19 recordsLinked to original sources

arXiv2026

Topological reconstruction of Rubin multiple imputation via coarse proximity, Seifert van Kampen gluing and Hurewicz invariants

Rubin multiple imputation (MI) generates plausible data completions to account for uncertainty and statistical variability but provides little insight into their global organization. We introduce a topological reconstruction approach that complements MI by examining the ensemble of completed datasets. Individual imputations are represented as points in a reconstruction space whose coordinates summarize statistical properties. Concepts from coarse geometry and algebraic topology are then used to characterize relationships among alternative imputations across multiple scales. Coarse proximity (CP) defines large-scale neighborhoods, generating graphs in which nodes represent completed datasets and edges connect sufficiently similar imputations. Seifert van Kampen gluing provides a conceptual interpretation of how local reconstructions assemble into globally coherent structures, whereas Hurewicz-type invariants quantify persistent connectivity patterns. Synthetic multivariate biomedical datasets representing adult cardiometabolic cohorts were generated with controlled missingness levels. Multiple stochastic imputations were projected into the reconstruction space and analyzed through CP graphs, connected components, cycle descriptors and scale-dependent topological measures. MI generated structured spaces with distinct connectivity patterns rather than homogeneous clouds of solutions. Topological descriptors remained stable despite local numerical variability, whereas increasing missingness produced transitions in reconstruction-space connectivity together with progressive deterioration of reconstruction accuracy. Our approach could be applied to biological and social networks, systems medicine, ecological modeling and other domains in which large-scale structural organization contributes to reliable inference.

stat.AP↗

arXiv2026

From simple interactions to complex biology: a hypergraph percolation perspective

The emergence of biological complexity can be viewed as a transition from fragmented local interactions to extensive integrated organization, raising the question of how large-scale connectivity emerges from simple interacting elements. We investigated whether this transition can be understood as a consequence of hypergraph percolation driven by higher-order interactions. We performed computational simulations where elementary units constituted nodes and collective interactions formed hyperedges of variable size. Increasing hyperedge density enabled the characterization of connected-component growth, fragmentation, interaction overlap, participation and structural redundancy. Critical transition regions were identified as sparse local assemblies rapidly reorganized into extensive connected structures. These transitions were characterized by abrupt expansion of the largest connected component, progressive consolidation of previously disconnected clusters and increasing overlap among higher-order interactions. Connectivity growth was accompanied by the accumulation of alternative pathways and nested interaction patterns, pointing towards large-scale reorganization over a narrow range of interaction densities. Our findings suggest that, alongside the progressive evolution of molecular complexity, the origin of life and the emergence of biological organization may have involved rapid organizational transitions driven by higher-order connectivity and interaction architecture.

q-bio.OT↗

arXiv2026

Spatial confinement and boundary constraints governing biological chirality: a simulation study

Biological systems exhibit marked molecular asymmetry, with proteins based predominantly on L-amino acids and nucleic acids and carbohydrates largely composed of D-sugars. Explanations for homochirality include asymmetric photochemistry, autocatalytic amplification, stochastic symmetry breaking and mineral-surface stereoselectivity, but these mechanisms only partially address the influence of finite geometry and collective spatial interactions on stereochemical stabilization. Inspired by recent developments in condensed-matter physics, we investigated whether coherent chirality could emerge from the interplay among nonlinear stereochemical amplification, stochastic fluctuations and boundary-dependent spatial constraints. We developed a reaction-diffusion simulation in which local stereochemical populations evolved within finite two-dimensional domains under spatial coupling and weak geometrical bias fields. Our model combined bistable autocatalytic dynamics, nearest-neighbor interactions and suppression of locally inconsistent stereochemical configurations in order to quantify temporal evolution of enantiomeric excess, same-handed neighbor agreement and radial stereochemical organization under varying interaction strengths and fluctuation amplitudes. Our results showed progressive formation of chiral domains, segregation of opposite-handed regions and geometry-dependent modulation of local stereochemical organization. Spatial coupling increased local coherence and modified persistence of mixed stereochemical states, while finite boundaries influenced radial organization and anisotropic stabilization of molecular populations. Potential applications include geometrically controlled asymmetric synthesis, confined stereoselective catalytic systems, adaptive chiral materials and characterization of heterogeneous stereochemical distributions in microstructured reaction environments.

q-bio.OT↗

arXiv2026

An exponential logarithmic measure of drug receptor binding and saturation

Ligand receptor interactions are commonly assessed through equilibrium occupancy and pharmacodynamic measures that describe binding and saturation by means of bounded response curves. Thermodynamic approaches relate binding affinity to logarithmic concentration scaling, while probabilistic descriptions of occupancy arise from exponential relations. We introduce an exponential logarithmic descriptor (ELD) that integrates ligand availability and thermodynamic binding propensity within a single quantity. The logarithmic component corresponds to a thermodynamic term derived from concentration dependent free energy relations, whereas the exponential component is represented through an inverse normalized concentration term corresponding to the reciprocal of the exponential occupancy factor emerging from Boltzmann type binding formulations. We explored ELD behavior through numerical simulations spanning sub affinity, transition and saturating concentration regimes under multiple affinity conditions and time dependent exposure profiles. Compared with conventional occupancy curves, ELD retained a broader dynamic range and revealed asymmetric sensitivity across concentration scales, particularly at low exposure and near saturation, where bounded occupancy measures progressively compress variability. The resulting behavior reflects the coexistence of amplification and constraint processes within ligand receptor dynamics. ELD may provide quantitative representation for biological systems in which exponential and logarithmic processes coexist across different scales. Potential applications include characterization of dose response transitions, identification of subtherapeutic and saturating exposure states, comparison of compounds with different affinities, normalization across heterogeneous datasets and continuous tracking of pharmacodynamic regimes during time dependent exposure.

q-bio.OT↗

arXiv2026

Internally triggered retrospective learning in neural networks

Learning in artificial neural networks usually relies on continuous, externally driven weight updates, in which parameters are modified at every step in response to incoming data, error signals or reward feedback. In this setting, routine and informative inputs contribute similarly to parameter adjustment. We introduce a learning approach in which parameter updates are governed by internally generated events arising from the network own representational dynamics. During ongoing activity, synaptic interactions are accumulated as latent traces encoding recent coactivation patterns, without immediately modifying the underlying parameters. In parallel, an internal predictive process estimates the evolving latent state, while a scalar measure of discrepancy between predicted and observed states is continuously computed. When discrepancy exceeds an adaptive threshold derived from recent error statistics, a learning event is triggered, inducing a retrospective update selectively integrating past activity into the current configuration. We performed simulations using a minimal neural network exposed to structured sequential inputs with transient perturbations. We found that learning occurs through sparse, temporally localized events associated with increases in prediction error, leading to stepwise changes in synaptic efficacy and discrete transitions in latent state organization. By selectively reorganizing parameters in response to internally detected discrepancies, our episodic updating may reduce unnecessary parameter drift while preserving informative patterns. Potential applications include systems requiring selective adaptation to rare or informative inputs such as physiological, industrial or environmental monitoring, edge computing under limited energy budgets, autonomous systems operating in dynamic conditions and sequential computational data processing.

q-bio.NC↗

arXiv2026

Tumor containment as an anti-percolation process

Percolation theory from statistical physics has been applied to several aspects of tumor progression. Tumor growth on percolation clusters has been used to model spatial expansion, vascular percolation to describe nutrient supply and transport related percolation to investigate drug and gene delivery. At the molecular level, mutational percolation has been employed to account for the emergence of malignant phenotypes, while inverse percolation to represent treatment-induced structural disruption. We examined whether tumor containment can be interpreted as an anti percolation problem, in which spatial expansion depends on the formation of a connected malignant domain. We implemented a spatial simulation with biologically scaled parameters to represent tissue heterogeneity, local growth, cell movement and clearance. We measured both total malignant area and connectivity metrics, including the largest connected component and the probability of forming a spanning cluster. Our results indicate that tumor size and spatial connectivity are partially independent, with configurations of similar size showing different connectivity patterns. A transition from fragmented to connected structures emerged within a limited parameter range, consistent with a threshold like behavior. Incorporating spatial connectivity into quantitative analysis, our approach provides a complementary way to characterize tumor organization. Potential applications include integration of structural descriptors into computational models of tumor growth, design of experimental systems to probe spatial organization and interpretation of therapeutic approaches via connectivity-based metrics.

q-bio.OT↗

arXiv2026

Energy gradients as potential drivers of pre-cellular chemical organization

The onset of life is often framed around membrane bound compartments and encoded metabolism, leaving unresolved how spatial organization arose before stable boundaries. In this context, environmental gradients are usually treated as boundary conditions rather than variables structuring chemical dynamics. We ask whether spatial localization and functional coupling can emerge under realistic environmental gradients in the absence of membranes, proposing that spatial variations in energy availability act as organizing variables that bias transport and reaction. We introduce a reaction diffusion model in which interacting chemical species evolve within an externally imposed activity landscape defined by coupled gradients in pH, redox potential and temperature, integrating diffusion, gradient driven drift and position dependent reaction kinetics. We performed simulations across a range of gradient strengths representative of hydrothermal vent like conditions. Our results suggest that sufficiently strong gradients induce spontaneous accumulation of reactants, spatial alignment of reaction maxima and the emergence of stable, confined chemical states. Localization arises above a threshold at which gradient driven transport overcomes diffusive and degradative losses. We conclude that spatially structured energy landscapes can support organized chemical dynamics without predefined compartments, providing a mechanism for coupling and persistence in continuous media. Potential applications include experimental platforms for studying prebiotic chemistry, microfluidic systems with controlled gradients and the design of chemically responsive materials.

q-bio.OT↗

arXiv2026

Baseline glycemia exhibits non-random, history-dependent variation across repeated meals

Glycemic regulation is often described as maintaining glucose levels near a stable baseline. However, continuous glucose monitoring after meals displays intra-individual variability even under controlled conditions, suggesting intrinsic system dynamics beyond sensor noise, measurement error or short-term variability around a fixed set point. Therefore, we estimated pre-meal glucose baselines, tracking their changes across repeated identical meal challenges within individuals. The baseline was defined as the median glucose level in a pre-meal window, while successive displacements were computed between consecutive repetitions. Using a publicly available dataset of normoglycemic subjects, we observed systematic changes in baseline levels across repeated exposures. These displacements exceeded short-term fluctuations within the same pre-meal interval and were robust to alternative baseline definitions. Moreover, the magnitude of each baseline shifted is positively related to the size of the preceding postprandial response. This association persisted under permutation testing, indicating that it cannot be explained by random temporal ordering. Overall, these findings suggest that glycemic dynamics cannot be fully described as independent fluctuations around a fixed baseline. Instead, baseline levels evolve across repeated perturbations through history-dependent adjustments, such that each perturbation influences subsequent system states. Potential applications include refined interpretation of continuous glucose monitoring data and development of models that incorporate temporal dependence in glucose dynamics.

q-bio.OT↗

arXiv2026

Toward buoyancy-driven flow at Campi Flegrei: coupled phase change and asymmetric geometry

Bradyseism at Campi Flegrei is usually interpreted in terms of hydrothermal pressurization and magmatic degassing. Fluid flow, often treated as a passive response to pressure accumulation, is commonly modeled using simplified geometries and homogeneous permeability fields. We introduce a model in which phase transition, structural heterogeneity and geometric asymmetry jointly influence fluid flow and pressure distribution within a heterogeneous subsurface environment. We hypothesize that coupling among phase change, density gradients and flows may follow a mechanism similar to the self-propulsion observed in asymmetric floating bodies like melting ice blocks, where phase change generates buoyancy-driven currents along their inclined surfaces and net motion in the opposite direction. We simulate pressure evolution in a shallow gas-rich reservoir subject to time-dependent forcing and hydraulic relaxation, coupled to buoyancy-enhanced Darcy flow along prescribed preferential pathways. Our numerical simulations, grounded in reported deformation rates and seismicity depths at Campi Flegrei, reproduce temporal variations in uplift and the persistence of spatially localized flow. Within this framework, asymmetric geometry may promote channelized upward transport, while phase change may enhance buoyancy and contribute to pressure redistribution. Our model predicts nonlinear uplift acceleration, shallow localized seismicity and velocity scaling with pressure and buoyancy. Integration with existing multiphase models would enable the examination of how buoyancy-driven flows influence pressure evolution and deformation during volcanic unrest.

physics.geo-ph↗

arXiv2026

Truth and distortion in complex networks: a global consistency approach

Understanding how reliable information emerges in interconnected populations is a challenge in social science, network theory and data analysis. Many existing approaches model treat truth as an external reference or a property of individual statements, rather than a global consistency feature of the network itself. We introduce a network-based approach in which truth arises from global relational coherence in a multiplex system of interacting individuals. Nodes are individuals with internal states, while edges capture different types of interactions, including declared relations, observed behavior, influence asymmetries and information exchange. We evaluate how well node states align with cooperative or antagonistic interactions, incorporating coercion, variability and mismatches between what individuals say and what they do. Simulations on synthetic networks of one thousand nodes show that the minimum global inconsistency does not coincide with majority opinion or simple averaging. Nodes contributing most to inconsistency create conflicting constraints across interaction layers, defining a measurable distortion field. For example, in online social media during an election, a small number of accounts spreading inconsistent or manipulative information across groups can disrupt overall coherence, even when most users appear to agree. These results suggest possible applications in assessing relational coherence, identifying irreducible inconsistencies and analyzing constraints on collective states. Therefore, truth can be seen as the state of maximal relational coherence, rather than simple agreement or correctness of individual statements.

physics.soc-ph↗

arXiv2026

Electrokinetic sensing in cartilage: a porous-material perspective on joint mechanics

Mechanical loading in articular cartilage drives interstitial fluid flow through the porous collagen proteoglycan matrix, generating electrokinetic signals. We investigate whether the structural organization of cartilage histology can be translated into a computational representation capable of predicting its electrokinetic behavior. Histological pictures were analyzed to build a pore-network graph representing potential pathways for interstitial fluid transport. Pressure driven flow was simulated using hydraulic conductance relations, while electrical potentials were estimated through electrokinetic coupling between pressure gradients and ion displacement. Simulations comparing networks derived from healthy and degenerative cartilage showed that pathological structures exhibited fragmented connectivity and lower predicted signal amplitudes, whereas physiological architecture generated more coherent transport trajectories and stronger electrical responses. Our simulations yield testable predictions, depth-dependent electrical signals across cartilage layers with directional anisotropy relative to collagen orientation. Potential applications include improved experimental assessment of cartilage transport biomechanics and integration of microstructural imaging with computational models of charged porous biomaterials.

q-bio.OT↗

arXiv2026

A geometric scaling between collective organizations and interaction-space dimension

The number of stable macroscopic organizations in complex systems is often much smaller than the large number of microscopic degrees of freedom would suggest. Yet theoretical approaches rarely address whether general limits constrain the diversity of admissible macroscopic organizations. We develop a geometric framework in which interactions among system components define a coarse-grained interaction space endowed with a metric structure. When this space has finite intrinsic dimensionality, geometric packing constraints impose bounds on the number of mutually distinguishable collective organizations. We derive a dimension-dependent scaling law showing that the number of stable macroscopic regimes grows polynomially with exponent equal to the intrinsic dimensionality of the interaction space. This implies that increasing microscopic complexity alone does not necessarily expand the range of macroscopic organizations. Instead, diversification requires an increase in the dimensionality of effective interactions. To illustrate our approach, we analyze an interacting system in which collective regimes correspond to regions of a low-dimensional parameter space describing effective interactions. In this setting, geometric packing constrains the number of robust organizations that the system can support. Overall, we argue that dimensionality of interaction space may act as a control parameter governing a variety of collective organization across physical and biological systems.

physics.soc-ph↗

arXiv2026

Topological analysis of bladder filling

Bladder function is typically assessed through pressure volume relations, compliance indices and flow measurements, whereas structural evaluation relies largely on qualitative imaging findings. These approaches do not formally quantify how bladder geometry changes during filling. To distinguish structural reorganization from pure mechanical stiffness, we developed a simulation based topological analysis of bladder filling grounded in mechanical parameters derived from the literature. Progressive filling was modeled under quasi static conditions, generating multi volume geometries from which spatial descriptors were computed. Drawing on the Freudenthal suspension theorem, filling was interpreted as a dimensional expansion process and structural stability was evaluated by testing whether geometric invariants remain preserved across increasing volumes. Simulated smooth expansion and controlled structural perturbations were compared under identical loading conditions. Pressure trajectories and wall stress estimates were similar across configurations when compliance was matched, whereas geometric descriptors showed divergent volume indexed stability profiles in the presence of remodeling. Computable instability measures identified progressive spatial heterogeneity despite preserved global pressure behavior. By providing a quantitative measure of geometric continuity across successive filling states, our approach indicates that structural remodeling may become detectable before conventional functional impairment appears. Progressive surface irregularity can arise even when compliance, detrusor pressure and flow parameters remain within reference limits. Serial imaging over time may support identification of individuals at greater risk of diverticula formation, decompensation or structural complications despite stable pressure measurements.

q-bio.OT↗

arXiv2026

Geometric and topological constraints on oral seal formation during infant breastfeeding

Breastfeeding efficiency relies on coordinated tongue motion, sustained tissue contact and maintenance of an effective intraoral seal. Current assessments of seal formation mainly use local kinematic descriptors or pressure recordings, which do not capture the global structural continuity of the sealing region. We introduce a systolic geometry based approach in which each sagittal ultrasound frame is modeled as a two dimensional deformable domain bounded by tongue, palate and nipple contours. Global seal continuity is formalized through the shortest closed curve that cannot be contracted to a point because of the overall geometry of the domain. The nipple defines a central region that must be circumferentially enclosed by a contact band to maintain suction. Within this band, closed curves encircling the nipple exactly once can be identified; the shortest of these curves defines a normalized systolic index representing the tightest admissible sealing loop. Simulations of symmetric thinning, localized discontinuities and cyclic perturbations reveal feasibility boundaries separating seal preserving from seal breaking configurations. Notably, admissible encircling curves may transiently disappear even when overall geometric motion remains smooth. By capturing global circumferential continuity that cannot be inferred from local metrics alone, our approach generates testable hypotheses linking the existence and temporal stability of admissible encircling curves to milk transfer efficiency and vacuum stability. Applied to segmented ultrasound data and integrated with pressure measurements, our systolic approach could provide a quantitative framework for objective assessment of seal integrity and longitudinal monitoring of latch stability.

physics.med-ph↗

arXiv2026

Towards a topological view of blood pressure regulation

Blood pressure regulation is commonly addressed in terms of local mechanisms such as vascular resistance, compliance and neurohumoral control. However, the human vasculature encompasses multiple quasi-closed flow loops under both physiological and pathological conditions. To test whether these loops could influence pressure dynamics beyond local control, we address the role of vascular topology in blood pressure regulation. Using one dimensional flow simulation models, we compared pressure dynamics in open vascular segments and closed vascular loops. We found that in open segments pressure fades away and remains spatially localized, whereas in closed loops pressure can keep circulating around the loop even if resistance in one spot is modified. Since parallel pathways within loops are dynamically coupled rather than independent, pressure changes in one place can affect the entire closed loop, allowing system level pressure patterns to emerge. Also, we assessed the temporal evolution of pressure fluctuations within closed vascular loops in normotensive and hypertensive parameter regimes, before and after loop breaking intervention. This topological approach helps clarifying why drugs or local interventions may fail to lower blood pressure in looped vascular architectures, providing a theoretical interpretation of some forms of resistant hypertension. Because disrupting a loop restores pressure relaxation, it may also help explain the disproportionate pressure changes observed after topology altering events like thrombosis, vascular surgery or embolization of arteriovenous malformations and shunts. Therefore, vascular topology can influence cardiovascular physiology by coupling local pressure flow relations to global constraints on blood pressure regulation, with physiological, pathological and clinical implications.

physics.med-ph↗

arXiv2026

Fubini Study geometry of representation drift in high dimensional data

High dimensional representation drift is commonly quantified using Euclidean or cosine distances, which presuppose fixed coordinates when comparing representations across time, training or preprocessing stages. While effective in many settings, these measures entangle intrinsic changes in the data with variations induced by arbitrary parametrizations. We introduce a projective geometric view of representation drift grounded in the Fubini Study metric, which identifies representations that differ only by gauge transformations such as global rescalings or sign flips. Applying this framework to empirical high dimensional datasets, we explicitly construct representation trajectories and track their evolution through cumulative geometric drift. Comparing Euclidean, cosine and Fubini Study distances along these trajectories reveals that conventional metrics systematically overestimate change whenever representations carry genuine projective ambiguity. By contrast, the Fubini Study metric isolates intrinsic evolution by remaining invariant under gauge-induced fluctuations. We further show that the difference between cosine and Fubini Study drift defines a computable, monotone quantity that directly captures representation churn attributable to gauge freedom. This separation provides a diagnostic for distinguishing meaningful structural evolution from parametrization artifacts, without introducing model-specific assumptions. Overall, we establish a geometric criterion for assessing representation stability in high-dimensional systems and clarify the limits of angular distances. Embedding representation dynamics in projective space connects data analysis with established geometric programs and yields observables that are directly testable in empirical workflows.

cs.LG↗

arXiv2026

Hyperdisorder in tumor growth

Tumor growth is constrained by spatial, mechanical, and metabolic factors whose alignment progressively breaks down across cellular, mesoscopic, and tissue scales as tumors expand. We hypothesize that this misalignment drives tumors toward a distinct architectural regime, termed hyperdisorder. Hyperdisorder is not defined by increased heterogeneity alone, but by the coexistence of elevated disorder across scales and spatial nonstationarity within the same tumor. Unlike ordinary randomness, where independent fluctuations diminish under spatial averaging, disorder here persists, reorganizes, or even amplifies with increasing observation scale, preventing convergence toward a stable architectural description. Using hematoxylin and eosin stained whole-slide images of gastric cancer from The Cancer Genome Atlas, we quantify tumor architecture using tile-based metrics that capture complementary aspects of organization, including texture entropy, microstructural fragmentation, orientation isotropy, and multiscale entropy variation. These measures are combined into a standardized hyperdisorder index, enabling unsupervised comparison across spatial regions. We find that architectural disruption is unevenly distributed and partially decoupled across scales within individual slides, consistent with growth-driven multiscale incoherence rather than uniform stochastic variability. Testable consequences include anomalous scaling of heterogeneity with sampling size, failure of coarse graining to converge, and systematic differences between tumor cores and invasive fronts. In diagnostic and clinical contexts, this framework clarifies when measurements from limited tissue samples are representative of the whole tumor and when they are dominated by scale- and location-dependent effects.

q-bio.OT↗

arXiv2026

Towards mathematical spaces for biological processes

Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical laws, stability and invariants become expressible and testable. In contrast, biology lacks an agreed-upon notion of space capturing context dependence, partial observability, degeneracy and irreversible dynamics. To address this gap, we introduce a unified mathematical space tailored to biological processes where states are represented in locally convex spaces indexed by context, where context includes both environment and history. Within our setting, proximity is defined through families of seminorms rather than a single global metric, allowing biological relevance to vary across conditions. Admissible sets encode biological constraints, observation maps formalize partial observability and many-to-one relations between state and dynamics capture irreversibility without requiring convergence to fixed points. Stabilization is characterized by neighborhood inclusion and degeneracy arises naturally through quotient structures induced by observation. We develop explicit constructions, operators and bounds within this space, yielding quantitative predictions dictated by its structure. A worked example based on EGFR-mutant non-small-cell lung cancer shows how single-cell data can be mapped into our framework, how numerical thresholds can be calibrated from the literature and how testable predictions can be formulated concerning rare tolerant states, context-dependent proximity and early stabilization. Overall, by providing biology with a space playing a role analogous to those used in physics, we aim to support structurally grounded and quantitative analyses of biological systems across contexts.

q-bio.OT↗