Frontiers in Applied Mathematics and Statistics

Patients suffering from sepsis need to be treated with an effective antibiotic therapy within the first hour after sepsis onset to decrease their risk of death. Microbiological data that provide information about the suitability of antibiotic therapies, however, is usually available only after 72 hours. Consequently, the treating physicians need to judge a therapy's effectiveness based on the patients' measured health records and their general health condition. This medical assessment is complex and requires years of experience. In our study, we investigate how statistical modeling can contribute to assessing the effectiveness of antibiotic therapies. To that purpose, we describe the effectiveness of antibiotic therapies by modeling sepsis patients' health conditions using a three-state continuous-time hidden Markov model (ctHMM). In literature, procalcitonin (PCT) and lactate have proven to be helpful for deriving the health condition in this context. The state probabilities obtained by the ctHMM are subsequently used to quantify the effectiveness of antibiotic therapies. To this end, we apply two different approaches, namely (i) averaging of the state probabilities and (ii) a logistic regression model. For (i), we calculate the average of the state probabilities for the state indicating a sepsis-free condition over an antibiotic administration period of 48 hours. For (ii), we use the information about antibiotic susceptibility testings as dependent variable in the logistic regression model; as independent variables, we calculate the difference between state probabilities at the start of antibiotic administration and 48 hours later. With this work, we are able to better understand the relationship between laboratory values, in particular PCT and lactate, and the patients' health condition. We further provide approaches for quantifying the effectiveness. Therefore, our work contributes to developing a clinical decision support system which helps physicians assess the effectiveness of antibiotic therapies in patients with sepsis. Supported by such a system, a physician is able to quickly adjust an ineffective therapy which avoids antibiotic resistances and increases a patient's chance to survive a sepsis.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

BackgroundDengue has been a major health threat globally in recent years. In particular, dengue incidences continue to increase annually and the epidemic area has expanded primarily due to global warming. Therefore, effective case detection and surveillance strategies are crucial to tackle this global health challenge. In clinical practice, the rapid test kit detecting dengue non-structural protein 1 antigen and commonly referred as NS1, is widely employed for early diagnosis. However, real-world studies revealed that the sensitivity of the NS1 test kit ranged from approximately 61% to 95%. Since early diagnosis is really critical for disease surveillance in the early stage of a dengue epidemic, scientists have been working hard to develop novel diagnosis methods that can provide higher sensitivity levels. Methodology/Principal FindingsIn response to this challenge, in this study, we have developed a novel diagnosis procedure that integrates machine learning technologies with the NS1 test kit. Our experimental results revealed that we would be able to raise the sensitivity of the dengue diagnosis procedure to higher than 99% by incorporating machine learning based prediction models to screen the suspected patients with a negative NS1 result. Furthermore, the relative risks between the suspected patients who were predicted to be positive and those who were predicted to be negative exceeded 4.8. Conclusions/SignificanceThese results illustrate that the proposed approach provides an effective and efficient diagnosis procedure to address the global health challenge caused by spread of dengue. Author SummaryThis study has aimed to enhance surveillance of the dengue disease by integrating machine learning technologies with the rapid test kit commonly employed in early diagnosis. In clinical practice, the NS1 rapid test kit is widely employed for early diagnosis. However, real-world studies revealed that a certain percentage of the patients with a negative NS1 test result, ranging from 5% to 39%, were actually infected by dengue. Since early diagnosis is critical for disease control in the early stage of a dengue epidemic, scientists have been working hard to tackle this challenge. Based on this observation, this study was launched to investigate the effects of incorporating machine learning based prediction models to further screen those patients with a negative NS1 test result. The experimental results revealed that the proposed approach was able to identify over 99% of the patients who were infected by the dengue disease. Furthermore, the risk of the suspected patients who were predicted to be positive was 4.8 times higher than the risk of those who were predicted to be negative. The experimental results illustrate that the proposed approach provides an effective and efficient diagnosis procedure to enhance surveillance of the dengue disease.

We develop a mathematical model of Rift Valley Fever integrating mosquito vectors, ruminants, and humans, based on an SEIR-type structure with vertical transmission in vectors. Local data from the Sudanian and especially the Sahelian zones are used to capture the impact of climatic variations on mosquito population dynamics. The mathematical analysis establishes the models positivity, determines the basic reproduction number R0, and demonstrates the local and global stability of the disease-free equilibrium. Sensitivity analysis (PRCC) highlights the most influential parameters, while the stochastic approach using a continuous-time Markov chain confirms the major role of seasonal rainfall. Numerical simulations reveal a peak in animal and human infections around the 9th month, correlating with periods of heavy rainfall. This model provides a relevant tool for surveillance and prevention within a "One Health" approach in Chad.

This brief work discusses potential superspreading events that may occur during the World Cup in Mexico. The study is particularly focused on the city of Guadalajara due to a large recent outbreak in January and February and insufficient vaccine coverage prior to 2026. Keywords: Superspreading; measles outbreak; branching process; individual reproduction number; World Cup

Hemodynamic forces play a key role in early cardiac morphogenesis, yet many computational studies assume Newtonian blood behavior. Here, we evaluate the impact of nonNewtonian shearthinning rheology on flow patterns, pressure distributions, and wall shear stress (WSS) during cardiac looping using idealized threedimensional models of the embryonic heart tube. Five geometries representing progressive looping stages, from a linear tube to an Sshaped configuration with ventricular ballooning, were analyzed under pulsatile flow using both Newtonian and powerlaw viscosity models. Across all stages, Reynolds numbers (Re {approx} 1-7) and Womersley numbers (Wo {approx} 0.3) indicated laminar, quasisteady flow consistent with embryonic conditions. Incorporating shearthinning rheology produced substantial deviations from Newtonian predictions, with peak systolic WSS differing by up to [~]40% and pressure drops by up to [~]20%. These effects were most pronounced in regions of increased curvature and geometric complexity. These findings demonstrate that nonNewtonian rheology significantly influences predicted hemodynamic environments during cardiac looping and should be incorporated into computational models aimed at understanding mechanobiological regulation of early heart development.

In this paper, we propose a new model to estimate the impact of an intervention on human hosts of a vector-borne infection, such as dengue, which occurs in yearly outbreaks of different magnitudes. The model applies to these outbreaks and, in fact, is independent of their intensity, that is, it does not require the steady-state assumption. The model takes as input the officially reported age-dependent number of cases of a vector-borne infection. It is deterministic and does not account for stochasticity. Our objective is to estimate the impact of the intervention (the efficacy), and we rely on the observed fact that the age distribution of the proportion of cases of the infections transmitted by the same vector is independent of both the intensity of transmission and the geographic area studied, at least for Brazilian regions. This finding is highlighted in the main text and forms the basis of our calculations. A hypothetical intervention is simulated using a dengue vaccine, which allows the determination of the optimal strategy for a vaccination campaign.

The aim of this paper is to model homeless accommodation settings to investigate how vaccination mitigates the outbreaks, highlighting the importance of vaccination in vulnerable settings. We estimate the daily per capita contact rate with wider community, the internal transmission rate, and the achieved vaccine coverage. We present stochastic simulation of the final size of disease outbreaks given choices of internal and external transmission. We conclude that vaccine that has effect in reducing transmission will mitigate the outbreak in homeless hostels but it will have better results when the household population has large vaccination coverage, which may lead to more cost from the health economic perspective.

Abstract Purpose This study introduces a novel approach to address unmeasured confounding in terminal event studies using the prior event rate ratio (PERR) method. The proposed approach PERR_{proxy} used a proxy event to replace the original terminal event in the pre-exposure period, enabling the application of PERR in terminal event settings. Additionally, we also applied difference in difference (DID) regression, which is conceptually analogous to PERR to estimate the standard errors and confidence intervals of PERR_{proxy}. Methods We conducted numeric simulations to evaluate the validity of PERR_{proxy} approach and assessed its performance under varying levels of unmeasured confounding effects, baseline hazard ratios, and the correlation between the proxy and terminal events. To demonstrate its practical applicability, we also performed an empirical analysis to investigate the impact of severe hospitalized COVID-19 on circulatory system disease mortality using the PERR_{proxy}. Results In simulation studies, PERR_{proxy} effectively reduced the unmeasured confounding effects compared to the conventional methods. The performance of PERR_{proxy} was influenced by the strength of unmeasured confounding, baseline hazard ratios, and the correlation between the proxy and terminal outcomes. In addition, difference in difference (DID) regression had much faster computational speed for estimating standard errors and confidence intervals compared to bootstrap. In the empirical analysis, PERR_{proxy} identified that severe hospitalized COVID-19 as a significant risk factor for the circulatory system disease mortality and reduced the unmeasured confounding effects. Conclusions The PERR_{proxy} approach extends the applicability of the original PERR method to terminal event studies, offering a promising solution for addressing unmeasured confounding. Additionally, the DID regression framework provides a computationally efficient alternative for parameter estimation in PERR-based studies. However, careful consideration is still required in PERR_{proxy} for proxy events selection and other underlying assumptions of the PERR method to ensure valid results. Keywords: prior event rate ratio, unmeasured confounding, proxy event, terminal event study, observational study, electronic health records

The impact of weather on the health of Americans and the American health system is substantial. Using available health and economic data, we developed a data-driven scenario that describes a compounded heat emergency in an archetypal community in the United States. We then characterize the potential human and economic costs of such a heat emergency to demonstrate the widespread impact on health outcomes, health systems, and society.

Diagnosed diabetes disproportionately burdens socioeconomically disadvantaged populations in the United States, particularly Hispanic communities in the Texas-Mexico border region. Few studies have quantified whether geographic border-region status is independently associated with county-level diagnosed diabetes prevalence after accounting for lifestyle and food-environment factors. This cross-sectional ecological study examined 253 Texas counties using CDC PLACES 2025 health estimates and USDA Food Environment Atlas food-access data, including the 2015 county-level low-food-access measure. Border-region counties were defined using the official La Paz Agreement 32-county definition, which includes counties within 100 km of the US-Mexico boundary. Multiple linear regression with HC3 robust standard errors was used to estimate associations between border-region status, low food access, physical inactivity, and diagnosed diabetes prevalence. Variance inflation factor analysis assessed multicollinearity, and Global Moran's I tested spatial autocorrelation in diagnosed diabetes prevalence and OLS residuals. Border-region counties had 33% higher unadjusted mean diagnosed diabetes prevalence than non-border counties (16.1% vs. 12.1%). After adjustment, border-region status remained significantly associated with a 0.625 percentage-point higher diagnosed diabetes prevalence ({beta} = 0.625, 95% CI [0.357, 0.893], p < 0.001). Physical inactivity was the strongest independent predictor ({beta} = 0.404, 95% CI [0.391, 0.417], p < 0.001). The model explained 96.0% of county-level variance (R{superscript 2} = 0.960, N = 253), reflecting ecological associations among modeled county-level health indicators. Global Moran's I confirmed strong spatial clustering of diagnosed diabetes prevalence (I = 0.5734, p = 0.001), with reduced but significant residual spatial autocorrelation after OLS adjustment (I = 0.1696, p = 0.001). These findings suggest that border-region status is associated with elevated diagnosed diabetes prevalence beyond physical inactivity and low food access, supporting targeted public health investment in the Texas-Mexico border region

Artificial intelligence (AI) tools have been rapidly adopted by medical researchers, yet whether early career researchers in low and middle income countries possess the awareness and habits needed to use these tools safely remains poorly documented. This study characterized AI adoption patterns, hallucination awareness, and verification and disclosure practices among early career medical researchers in Pakistan. A cross sectional anonymous online survey was conducted among medical students, house officers, residents, physicians, and faculty involved in research or academic work across Pakistan (May 2026). Descriptive statistics and chi square tests were applied to 373 eligible responses. AI use was near universal (99.7%), with 60.3% using AI tools daily. The most commonly reported tool in this sample was Claude (40.5%), followed by ChatGPT (29.2%) and Perplexity (26.0%), though this ranking likely reflects sampling characteristics. Despite high adoption, 59.2% typically did not verify AI outputs before use, and 40.2% had never heard that AI can generate fabricated scientific references. In behavioral vignettes, 36.5% assumed convincing AI generated references were authentic, and 54.2% would continue using remaining AI content after discovering one fabricated reference. Formal research training was strongly associated with consistent disclosure (51.7% vs. 17.1%; chi square=48.43, p less than 0.001). Role, daily use frequency, and research training were not significantly associated with verification behavior. Early career medical researchers in Pakistan demonstrate high AI adoption alongside incomplete hallucination awareness and infrequent verification, a pattern that may carry implications for research integrity. Formal training was the only factor significantly associated with consistent disclosure. Integration of AI literacy into medical curricula and institutional governance frameworks merits consideration.

Diagnosed diabetes affects approximately 38.4 million Americans, but its burden is not evenly distributed across U.S. counties. Existing machine-learning studies have mainly focused on individual risk prediction using biometric, clinical, or survey variables. These approaches are less suited to explaining why diagnosed diabetes prevalence differs geographically across counties. We developed an explainable gradient-boosting framework for predicting county-level diagnosed diabetes prevalence across 2,957 U.S. counties using an ecological cross-sectional design. The analysis integrated food-environment, socioeconomic, occupational, demographic, health-behavior, and clinical indicators from five public data sources. Four regression models were compared: Elastic Net, Random Forest, XGBoost, and LightGBM. LightGBM was selected as the primary model based on validation-set RMSE and interpreted using SHAP TreeExplainer. The validation-selected LightGBM model achieved a held-out test RMSE of 0.423 percentage points, R{superscript 2} = 0.964, and MAPE = 2.76%. Although XGBoost achieved a lower test RMSE of 0.399 and R{superscript 2} = 0.968, it was retained as a secondary benchmark because primary-model selection was based only on validation performance. A sensitivity model using only structural and contextual predictors, and excluding CDC PLACES health-behavior and clinical covariates, retained substantial predictive performance (R{superscript 2} = 0.827). Poverty rate was the most frequent dominant positive structural SHAP contributor nationally (n = 772 counties, 26.1%), followed by food insecurity rate (n = 707, 23.9%), Supplemental Nutrition Assistance Program (SNAP) participation rate (n = 316, 10.7%), unemployment rate (n = 224, 7.6%), and median household income (n = 178, 6.0%). Residual Morans I decreased from 0.665 to 0.069 after model fitting. Explainable machine learning using public county-level data can characterize geographic variation in diagnosed diabetes prevalence. County-level SHAP maps may support local hypothesis generation, but should be interpreted as explanations of model predictions rather than causal effects.

Introduction: Physical activity during pregnancy can be tracked directly by accelerometer measurements and indirectly by validated questionnaires. Considering the advancement of the Internet of Things (IOT), managing and/or monitoring physical activities can be better explored to analyze individuals, as well as indirectly compare the intensity and domains of physical activities carried out by pregnant women. The project, called 'EVA'(Expert Virtual Assistant), suggests combining several fields of knowledge to obtain better information about physical activity during pregnancy, surpassing the claim made in previous research that studying and measuring the duration of daily physical activities in pregnant women is a challenge. Objective: In the present study, we present the results of the first stage of the EVA project, which aims to develop a Virtual Assistant (VA) in Portuguese, providing examples of health management features for monitoring Physical Activity measurements for pregnant women assisted in the Unified Health System (SUS) and the adaptation of the Pregnancy Physical Activity Questionnaire (PPAQ). Methods and Analysis: The methods used were developed in two stages: adapting the physical activity questionnaire and building the Virtual Assistent to monitor physical activities. Thirty pregnant women who used the Unified Health System (SUS) in the city of Ribeir&atildeo Preto, Brazil participated in the study. The pregnant women wore sensor wristbands (accelerometers) and answered the sociodemographic, lifestyle and physical activity questionnaires via an application developed for this study. Results: The questionnaire used was the PPAQ adapted for Brazilian pregnant women. The most important changes were in the occupational domain for the house cleaning and in sedentary behavior activities. In the pilot study, it was observed that pregnant women spend more energy at home and in light and moderate intensity activities. textbfConclusion:This study made important contributions to evaluating PA in pregnant women. The proposal and studies for the construction of the AV-EVA, the inclusion of a specific occupational domain for pregnant women with domestic occupations and the new cutoff points for PA intensity measurements obtained via accelerometers.

Introduction: Climate change disproportionately affects disadvantaged communities, yet construction workforce education rarely addresses interconnected pathways linking energy efficiency, nature exposure, and public health. Green-blue infrastructure delivers co-optimized benefits: reducing building energy consumption 15-30% while decreasing heat-related mortality by approximately 3.9% per degree Celsius of urban cooling (Gasparrini et al., 2017) -- epidemiological benchmarks that inform the dose-response functions embedded in the Ecosystem Justice Translator (EJT). This protocol describes, to our knowledge, the first randomized controlled trial evaluating a curriculum intervention designed to develop planetary health competencies and environmental justice awareness among high school students pursuing construction careers. Methods and analysis: This two-arm, parallel-group randomized controlled trial targets enrollment of N=200 high school students (ages 14-18) from construction career pathway programs in the San Francisco Bay Area (over-recruitment target N=250; 25% buffer for attrition). Students are individually randomized 1:1 to intervention (Community-Centered Design curriculum integrating the Ecosystem Justice Translator) or control (traditional Virtual Design and Construction curriculum), stratified by school site using block randomization. The 6-month intervention features the Ecosystem Justice Translator (EJT) -- a computational system using large language models to translate community health equity concerns into quantifiable investment priorities. The EJT's 51-theme health equity taxonomy was derived from validated public health frameworks (Centers for Disease Control and Prevention [CDC] Social Vulnerability Index, Environmental Protection Agency [EPA] EJScreen, Healthy People 2030). Primary outcome is Health-Integrated Equity Consciousness Index (HI-ECI), measured at baseline, 3, 6 (primary endpoint), and 12 months. Analysis uses intention-to-treat linear mixed-effects models with random intercepts for participants. The minimum required sample (n=26 per arm; G*Power, two-tailed a=0.05, 80% power, Hedges' g=0.80) is exceeded by enrolled N=200, which provides >99% power at Hedges' g=0.80 and supports multi-site confirmatory factor analysis. Ethics and dissemination: This protocol has been approved by Stanford University Institutional Review Board (IRB eProtocol #84369, approved February 13, 2026). Parental consent from a parent or guardian and written assent from each student participant are required prior to enrollment. All instruments, curriculum materials, and EJT source code will be released open-source under CC BY-NC-SA 4.0, permitting free use for educational, research, and non-profit purposes, concurrent with primary publication. Commercial licensing may be pursued separately through Stanford University Office of Technology Licensing (OTL docket S25-565). Trial registration: ClinicalTrials.gov NCT07315919. Pre-results. Protocol version 4.0, June 2026.

Recent studies have shown that implementing explicit social cues, such as gaze, facial expressions, and gestures, in artificial agents can improve impressions of these agents. However, humans may also use implicit physiological cues, such as facial coloration and cardiac information, in social perception. The present study examined whether subtle skin color changes reflecting pulse signals enhance the perceived human likeness of artificial agents, and whether this effect depends on agent type, signal type, observers interoceptive sensibility, and their awareness of the skin color changes. Participants observed morphed face stimuli created from artificial agents and human faces and judged whether each stimulus appeared human-like or robot-like. In Experiment 1, skin color changes based on human-derived pulse wave signals enhanced perceived human likeness for a highly human-like agent, but not for a less human-like agent. In Experiment 2, perceived human likeness was enhanced not only by pulse-based skin color changes but also by sinusoidal skin color changes matched to the pulse wave signal in terms of mean amplitude and number of peaks. In addition, participants with higher scores on some subscales of the Multidimensional Assessment of Interoceptive Awareness (MAIA), a subjective measure of interoceptive sensibility, tended to notice the skin color changes. However, neither observers interoceptive sensibility nor their awareness of skin color changes directly explained the enhancement of perceived human likeness induced by skin color changes. These results suggest that subtle skin color changes reflecting pulse wave information may function as implicit dynamic cues signaling embodiment or biologicalness in artificial agents, thereby contributing to perceived human likeness.

Non-invasive wrist pulse monitoring has been integrated into various medical systems for cardiovascular assessment. However, different definitions of pulse transit time are used in the literature, and their statistical behavior when measured locally at the wrist using pressure sensors has not been systematically examined. Wearable wristbands designed to measure pulse transit time (PTT) have emerged as valuable tools for evaluating cardiac activity. While several algorithms have been developed to predict blood pressure using PTT, it is well recognized that PTT and its inverse parameter, pulse wave velocity (PWV), exhibit temporal variability. In this study, PTT was explicitly measured at the wrist's radial artery to investigate its statistical variation and relationship with different arterial pressures. The experiment exhibits two distinct methodologies for PTT computation using onset-based and peak based measurements. Data were recorded across five cuff pressure levels at 20, 40, 60, 80, and 100 mmHg using the pulse pressure sensor (PPS). PTTonset time shows lower coefficient of variation as compared to PTTpeak time within the 100 mmHg pressure range. The weak correlation coefficient is recorded between PTT values. However, dynamic time warping (DTW) analysis revealed a notable similarity in the time series of PTTonset and PTTpeak, regardless of the applied pressure level. For the multi participant dataset, the mean DTW distances ranged from 0.029 to 0.046 across the tested cuff pressures, illustrating consistent similarity between PTTonset and PTTpeak over time. The objective of this study is to examine the statistical behavior, stability, and temporal similarity of the two commonly used PTT definitions when measured at the radial artery using pressure sensors. Statistical analysis shows consistent differences between the two PTT definitions across participants. PTTonset shows lower variation than PTTpeak. However, PTTpeak requires simpler computation and produces fewer detection errors, while PTTonset provides lower statistical variation.

Time-resolved measurements are central to calibrating mechanistic dynamical models, but current inference frameworks typically assume that reported measurement times are exact. In practice, actual sampling times may deviate from reported times because of sample-handling delays, imper-fect synchronization, or reporting errors. Here, we present a Bayesian framework for parameter inference in ordinary differential equation models that explicitly accounts for uncertainty in measurement times. We formulate latent measurement times as random variables and derive a joint and marginalized posterior. To compute the marginal likelihood efficiently, we augment the original dynamical system with additional state variables that evaluate the required integrals during numerical simulation. This reduces the dimensionality of the estimation problems and allows for efficient and reliable Markov chain Monte Carlo sampling. Across synthetic examples and a published model of carotenoid cleavage in Arabidopsis thaliana, neglecting time uncertainty led to biased estimates and overconfident uncertainty quantification, whereas the proposed marginalized formulation recovered reliable parameter estimates while substantially improving sampling efficiency and scalability. These results identify measurement time uncertainty as an important source of variability in dynamic modeling and establish posterior marginalization as a practical strategy for robust mechanistic inference.

The research was carried out in Tartus (Syria), in a plastic greenhouse during the season 2024-2025. Two tomato hybrids "Levovil and Shannon" were grafted onto two tomato "Spirit and Maxifort" rootstocks. Four levels of salinity (0, 50, 100 and 150 mM NaCl) were applied on the hybrids and grafted plants. Salinty stress induced physiological and biochemical changes in plant. At salinity level of 150 mM, the absolute value of the osmotic pressure increased to -1.18 and -1.12 Mpa, in Levovil and Shannon hybrids, as compared to -0.80 and - 0.74 Mpa in the controls, respectively. While 150 mM salinity level led to an increase of the contents of dry matter, proline, sugars and chlorine, it caused a decrease of K: Na ratio in the two hybrids (1.99 and 1.8) as compared to the controls (5.29 and 4.68, respectively). The salinity stress at 150 mM, reduced the yield of the two hybrids (26.26 and 25.28 kg/m2) as compared to the controls (33.90 and 33.11 kg/m2, respectively). The tomato scions "Levovil and Shannon hybrids" grafted onto the "Spirit and Maxifort" rootstocks enhanced the osmotic adjustment phenomenon, especially when the two hybrids were grafted onto Spirit. While tomato grafting had a significant effect on the accumulation of some osmotic compounds such as proline and sugars, in addition to increasing K: Na ratio, it reduced the absolute value of the osmotic pressure of the plant and its sodium content. Therefore, the yield increased in grafted tomato plants compared with non-grafted plants under saline conditions. The results of PCA analysis showed that the first two principal components (PC1 and PC2) explained 89.08% of the total variation, wherease all the studied parameters were well represented. The dendrogram was obtained based on the same variables as PCA, and it led to classify "Spirit" rootstock as tolerant to salt stress, "Maxifort" rootstock as half tolerant, and the non-grafted hybrids "Levovil and Shannon" as sensitive to salt stress.

Length and time constants are foundational to the study of conduction in neurons and other biological cables but are exactly defined only for passive membranes. Here we define and derive exact length and time constants for propagating action potentials in unmyelinated axons. This derivation exploits specific instants during action potential conduction when the net transmembrane ionic current is zero, but axial current remains non-zero. At these instants, we define a curvature parameter,{kappa} , explore its determinants using computer modelling, demonstrate that it is the local real Laplace exponent of the action potential upstroke, and suggest practical approaches for its experimental measurement. From{kappa} , we define action potential length and time constants, {lambda}AP = 1/{surd}({kappa}racm) and {tau}AP = 1/{kappa}, and show that action potential propagation velocity is exactly {lambda}AP/{tau}AP.