Local Probability Research Articles

Gaussian level-set percolation on complex networks.

We present a solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. It is achieved using a cavity or message passing approach, which allows one to obtain the essential ingredient required for the solution, viz. a self-consistent determination of locally varying percolation probabilities. The cavity solution can be evaluated both for single large instances of locally treelike graphs, and in the thermodynamic limit of random graphs of finite mean degree in the configuration model class. The critical level h_{c} of the percolation transition is obtained through the condition that the largest eigenvalue of a weighted version B of a nonbacktracking matrix satisfies λ_{max}(B)|_{h_{c}}=1. We present level-dependent distributions of local percolation probabilities for Erdős-Rényi networks and and for networks with degree distributions described by power laws. We find that there is a strong correlation between marginal single-node variances of a massless multivariate Gaussian and local percolation probabilities at a given level h, which is nearly perfect at negative values h, but weakens as h↗0 for the system with power-law degree distribution, and generally also for negative values of h, if the multivariate Gaussian acquires a nonzero mass. The theoretical analysis simplifies in the case of random regular graphs with uniform edge weights of the weighted graph Laplacian of the system and uniform mass parameter of the Gaussian field. An asymptotic analysis reveals that for edge weights K=K(c)≡1 the critical percolation threshold h_{c} decreases to 0, as the degree c of the random regular graph diverges. For K=(c)=1/c, however, the critical percolation threshold h_{c} is shown to diverge as c→∞.

Pituitary neuroendocrine tumors treated with stereotactic radiosurgery.

Pituitary neuroendocrine tumors (pitNETs) are benign tumors that may recur after surgical resection or persist following medical management. The objective of this study was to evaluate outcomes and toxicities of patients with pitNETs treated with stereotactic radiosurgery (SRS) at a single institution. We completed a retrospective, single-institution study of patients with pitNETs treated with frame-based, single-fraction, cobalt-60 SRS between September 2005 and June 2023. The primary endpoint was local tumor control. Secondary endpoints included endocrine control (for functional tumors), overall survival, and toxicities. A total of 88 lesions in 83 patients were treated with SRS. Most lesions (70%) were non-functional tumors. Of the 26 functioning tumors, 6 patients achieved endocrine remission with SRS alone (23%), and the remainder achieved remission with combined medical management. With a median patient follow-up of 4.7 years, no local tumor recurrences were observed with an estimated local control probability of 100%. Two- and five-year overall survival estimates were 97% (95% confidence interval [CI] 89-99) and 95% (95% CI 84-98), respectively. Causes of death were unrelated to PitNET or SRS. Twelve patients (14%) developed hypopituitarism after SRS. Despite the 34 lesions that were ≤ 3mm from optic structures, no patients developed any optic neuropathy or visual decline post SRS. SRS is a highly effective modality for recurrent or residual pitNETs. This study observed a local control of 100% with no cases of optic toxicities after a median follow-up of 4.7 years. These observed findings suggest that dose de-escalation may be possible for future treatment of pitNETs.

A spatially explicit assessment of factors shaping attitudes toward African elephant conservation.

Conservation plans that explicitly account for the social landscape where people and wildlife co-occur can yield more effective and equitable conservation practices and outcomes. Yet, social data remain underutilized, often because social data are treated as aspatial or are analyzed with approaches that do not quantify uncertainty or address bias in self-reported data. We conducted a survey (questionnaires) of 177 households in a multiuse landscape in the Kenya-Tanzania borderlands. In a mixed-methods approach, we used Bayesian hierarchical models to quantify and map local attitudes toward African elephant (Loxodonta africana) conservation while accounting for response bias and then combined inference from attitude models with thematic analysis of open-ended responses and cointerpretation of results with local communities to gain deeper understanding of what explains attitudes of people living with wildlife. Model estimates showed that believing elephants have sociocultural value increased the probability of respondents holding positive attitudes toward elephant conservation in general (mean increase=0.31 [95% credible interval, CrI, 0.02-0.67]), but experiencing negative impacts from any wildlife species lowered the probability of respondents holding a positive attitude toward local elephant conservation (mean decrease=-0.20 [95% CrI -0.42 to 0.03]). Qualitative data revealed that safety and well-being concerns related to the perceived threats that elephants pose to human lives and livelihoods, and limited incentives to support conservation on community and private lands lowered positive local attitude probabilities and contributed to negative perceptions of human-elephant coexistence. Our spatially explicit modeling approach revealed fine-scale variation in drivers of conservation attitudes that can inform targeted conservation planning. Our results suggest that approaches focused on sustaining existing sociocultural values and relationships with wildlife, investing in well-being, and implementing species-agnostic approaches to wildlife impact mitigation could improve conservation outcomes in shared landscapes.

Understanding overfitting in random forest for probability estimation: a visualization and simulation study

BackgroundRandom forests have become popular for clinical risk prediction modeling. In a case study on predicting ovarian malignancy, we observed training AUCs close to 1. Although this suggests overfitting, performance was competitive on test data. We aimed to understand the behavior of random forests for probability estimation by (1) visualizing data space in three real-world case studies and (2) a simulation study.MethodsFor the case studies, multinomial risk estimates were visualized using heatmaps in a 2-dimensional subspace. The simulation study included 48 logistic data-generating mechanisms (DGM), varying the predictor distribution, the number of predictors, the correlation between predictors, the true AUC, and the strength of true predictors. For each DGM, 1000 training datasets of size 200 or 4000 with binary outcomes were simulated, and random forest models were trained with minimum node size 2 or 20 using the ranger R package, resulting in 192 scenarios in total. Model performance was evaluated on large test datasets (N = 100,000).ResultsThe visualizations suggested that the model learned “spikes of probability” around events in the training set. A cluster of events created a bigger peak or plateau (signal), isolated events local peaks (noise). In the simulation study, median training AUCs were between 0.97 and 1 unless there were 4 binary predictors or 16 binary predictors with a minimum node size of 20. The median discrimination loss, i.e., the difference between the median test AUC and the true AUC, was 0.025 (range 0.00 to 0.13). Median training AUCs had Spearman correlations of around 0.70 with discrimination loss. Median test AUCs were higher with higher events per variable, higher minimum node size, and binary predictors. Median training calibration slopes were always above 1 and were not correlated with median test slopes across scenarios (Spearman correlation − 0.11). Median test slopes were higher with higher true AUC, higher minimum node size, and higher sample size.ConclusionsRandom forests learn local probability peaks that often yield near perfect training AUCs without strongly affecting AUCs on test data. When the aim is probability estimation, the simulation results go against the common recommendation to use fully grown trees in random forest models.

Skin-directed radiotherapy for primary cutaneous T-cell lymphomas.

To evaluate the efficacy and toxicities of skin-directed radiotherapy (RT) in primary cutaneous T-cell lymphoma (CTCL). We retrospectively analyzed 57 CTCL lesions treated with skin-directed RT between January 2000 and December 2022. Lesions were categorized into three distinct groups: early-stage disease treated with local RT, advanced-stage disease treated with local RT, and advanced-stage disease treated with total skin electron beam therapy (TSEBT). Treatment outcomes, including response rates, recurrence patterns, and local progression probability, were assessed for each group. Mycosis fungoides (MF) constituted 90.9% of the advanced-stage pathologies, while CD4+ primary cutaneous small/medium T-cell lymphoproliferative disorder was common in the early stage lesions (55%). Median RT doses were 30.6 Gy, 27 Gy, and 32 Gy for the local RT with early stage, the local RT with advanced stage, and TSEBT with advanced stage, respectively. The complete response rates were high across the groups: 95.5%, 70.8%, and 90.9%, respectively. Seven local recurrences (29.2%) occurred in the local RT group with advanced stage, while seven patients (63.6%) in the TSEBT group experienced local failure. All recurrences were observed in lesions and patients with MF. Acute toxicities were mainly grade 1 or 2, with no grade 3 or higher events. No significant association between RT dose and local progression rates in MF lesions was found. Skin-directed RT in CTCL is effective for local control and well-tolerated with less toxicity.

Complexity measures of electric screening effect in interstellar medium

Using the screening potential, we explore probability density properties in interstellar mediums (ISM) in information theory. With the eigenfunctions obtained for the screening potential using the Schrodinger equation, we studied the probability distribution for Shannon entropy, Fisher information, and their complexity measures for the values of n and l. From our numerical result, for Shannon entropy, we observed a more localized probability distribution in position and a decreasing localization in the momentum space as the values of n and l increases. For Fisher information, localization increases in the position space and, consequently, delocalization in their momentum spaces. The uncertainty relations of Shannon entropy and Fisher information were computed and satisfied the relations. For interstellar mediums, our findings align with Heinsberg’s uncertainty principle. Complexity measure was also studied for the interstellar mediums and our findings showed increasing disorder in the position space for increasing values of n and l. Furthermore, we extended the Debye-Hückel length to other regimes particularly, Magnetosphere (D=102) and Intergalactic Mediums (D=105)

Hierarchies from landscape probability gradients and critical boundaries

If the gradient of a probability distribution on a landscape of vacua aligns with the variation of some fundamental parameter, the parameter may be likely to take some non-generic value. Such non-generic values can be associated to critical boundaries, where qualitative changes of the landscape properties happen, or an anthropic bound is located. Assuming the standard volume-weighted and the local probability measures, we discuss ordered landscapes which can produce several types of the aligned probability gradients. The resulting values of the gradients are defined by the “closeness” of a given vacuum to the highest- or the lowest-energy vacuum. Using these ingredients we construct a landscape scanning independently the Higgs mass and the cosmological constant (CC). The probability gradient pushes the Higgs mass to its observed value, where a structural change of the landscape takes place, while the CC is chosen anthropically.

Stone's theorem for distributional regression in Wasserstein distance

We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distributions with local probability weights satisfying the conditions of Stone's theorem provide universally consistent estimates of the conditional distributions, where the error is measured by the Wasserstein distance of order p ≥ 1 . Furthermore, for p = 1, we determine the minimax rates of convergence on specific classes of distributions. We finally provide some applications of these results, including the estimation of conditional tail expectation or probability weighted moments.

Updating local and global probabilities during maze navigation.

We examined the human ability to encode and utilize local and global uncertainty information during a navigational task. Participants were tasked with navigating a virtual maze in which wall locations were obscured. Local cues and a global direction provided guidance. The validities of the global and local cues were separately and jointly varied across the two experiments. The results demonstrated that participants effectively utilized both global and local cues for navigation with a stronger reliance on local cues and a heightened precision in estimating their reliability. Our findings suggest that the representation of uncertainty for proximate events can be dissociated from that of distal events. Furthermore, humans effectively integrate both forms of information when making decisions during navigation tasks. This research advances our understanding of uncertainty processing and its implications for decision making in complex environments. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Learning neural implicit surfaces with local probability standard variance

AbstractReconstructing geometric shapes from sparse multiview has always been a challenging task. With the development of neural implicit surfaces, geometry‐based volume rendering surface reconstruction methods have been proven to be able to reconstruct high‐quality surfaces. However, existing geometry‐based reconstruction methods completely associate volume density with signed distance function or unsigned distance function, resulting in the same volume density peak that can only be reconstructed near the object surface. When there are transparent surfaces in the scene, existing methods prioritize the reconstruction of opaque surfaces, neglecting the reconstruction of transparent surfaces, which is disadvantageous when reconstructing real scenes. To solve this problem, we introduce local probability standard variance, which calculates volume density together with signed distance function. In this way, it can reconstruct the volume density that matches the transparency characteristics of the object surface. The method can reconstruct the surface of transparent objects, and experiments on two transparent surface datasets show that the method performs better.

Robustness of Structural Health Monitoring Systems for Offshore Energy Structures based on Damage Characteristics

Offshore energy structures such as fixed/floating wind turbines, tidal turbines and wave energy converters are exposed to loads coming from different sources. Recent advances in SHM offer many unique opportunities to assess the structural integrity of offshore energy infrastructure. The process of SHM generally involves the use of a system of sensors mounted on a structure; the processing of signals received from the sensors to attain damage sensitive features; and the detection of damage in the structure. Over the past decades, most of the research in SHM has been focused on improving and developing new sensor technology, signal processing, and damage detection algorithms. However, there are very few studies assessing the performance of SHM systems with respect to damage detection, localization, and quantification. Moreover, most of the performance analysis models for SHM systems rely only on 'probability of detection (POD)', that is an assessment index used in NDT to evaluate the probability of detecting a damage as a function of its size. For SHM systems, the replicability of POD is influenced by the environment, measurement noise, and the deterioration of sensors and instruments. Therefore, the distribution of POD is often determined by performing an extensive number of test sets with existing damage of varying magnitude. This paper aims to reduce the volume of experimental data required, as well as the uncertainties associated with POD prediction by using a model-assisted probability of detection (MAPOD) approach. We develop a Bayesian network (BN) method to evaluate the performance of SHM systems in terms of damage detection, localization, and assessment. In addition to POD, the probability of accurate localization (POAL) and probability of accurate assessment (POAA) are also incorporated into the analysis. The BN and limit state functions are applied to a fixed offshore energy structure equipped with a vibration based SHM system.

Reliability Assessment of Damage Localization Techniques for Guided Wave-based Structural Health Monitoring Systems in Composite Stiffened Structures

In Guided Wave-based Structural Health Monitoring (GWSHM) systems, the reliability assessment is of utmost importance. The primary focus is the smallest damage that can be detected with 90 percent probability and 95 percent confidence. However, the probability of correct damage localization is equally crucial as the probability of detection. In this view, defining the smallest damage that can be localized accurately in a statistically meaningful way is quite challenging. Several localization techniques have been developed in the literature to localize damage resorting to a GW sensor network, like SAFT and RAPID. This article investigates the reliability of such SHM systems with these localization techniques using an experimental data set from the Open Guided Waves (OGW) platform and compares it with predictions obtained via a simulation model using the EFIT method. A carbon fibre-reinforced plate-like structure reinforced by an omega stringer and a GWSHM system employing twelve piezoceramic transducers bonded over the surface to excite and receive guided waves are used. Pseudo damage of thirteen different sizes are attached to three different locations using a damping tacky tape. Moreover, the EFIT modelling tool is used to simulate the experiment with an extensive number of damage scenarios at the defined three damage locations with a high degree of consistency with the experimental data, facilitating a more robust analysis. The Outcome concerning the influence and correlation between damage size on localization accuracy, considering various localization techniques, were explored and discussed. In addition, the reliability assessment allowed to establish the performance of the localization approaches in a rigorous way.

Quantifying the Reliability Performance of a Guided Wave-Based SHM System Using Piezoelectric Wafer Actuator Sensors

The adoption of structural health monitoring systems can bring important benefits to the aerospace industry. However, the current implementation of SHM technologies in today's aerospace industry remains limited. One of the primary obstacles hindering the adoption of SHM technologies is the challenge associated with assessing the reliability of SHM systems. In aerospace applications, SHM hardware is exposed to harsh environments, including high or low temperatures, vibrations, moisture, and radiation. Consequently, the long-term performance of SHM systems is adversely affected. This study delves into various issues related to the evaluation of SHM system reliability and performance quantification, placing special emphasis on guided wave-based SHM using Piezoelectric Wafer Actuator Sensors. We present experimental and numerical modeling examples designed to illustrate the detrimental effects of aging at the unitary sensor and sensor network levels. Conclusions are drawn regarding the current challenges in quantifying system reliability, emphasizing relevant performance metrics such as the probability of detection, localization, and false call rates.

Imbalanced optimal feedback motor control system in spinocerebellar ataxia type 3.

Human motor planning and control depend highly on optimal feedback control systems, such as the neocortex-cerebellum circuit. Here, diffusion tensor imaging was used to verify the disruption of the neocortex-cerebellum circuit in spinocerebellar ataxia type 3 (SCA3), and the circuit's disruption correlation with SCA3 motor dysfunction was investigated. This study included 45 patients with familial SCA3, aged 17-67 years, and 49 age- and sex-matched healthy controls, aged 21-64 years. Tract-based spatial statistics and probabilistic tractography was conducted using magnetic resonance images of the patients and controls. The correlation between the local probability of probabilistic tractography traced from the cerebellum and clinical symptoms measured using specified symptom scales was also calculated. The cerebellum-originated probabilistic tractography analysis showed that structural connectivity, mainly in the subcortical cerebellar-thalamo-cortical tract, was significantly reduced and the cortico-ponto-cerebellar tract was significantly stronger in the SCA3 group than in the control group. The enhanced tract was extended to the right lateral parietal region and the right primary motor cortex. The enhanced neocortex-cerebellum connections were highly associated with disease progression, including duration and symptomatic deterioration. Tractography probabilities from the cerebellar to parietal and sensorimotor areas were significantly negatively correlated with motor abilities in patients with SCA3. To our knowledge, this study is the first to reveal that disrupting the neocortex-cerebellum loop can cause SCA3-induced motor dysfunctions. The specific interaction between the cerebellar-thalamo-cortical and cortico-ponto-cerebellar pathways in patients with SCA3 and its relationship with ataxia symptoms provides a new direction for future research.

Stereotactic Body Radiotherapy for Centrally Located Inoperable Early-Stage NSCLC: EORTC 22113–08113 LungTech Phase II Trial Results

IntroductionThe international phase II single-arm LungTech trial 22113-08113 of the European Organization for Research and Treatment of Cancer assessed the safety and efficacy of stereotactic body radiotherapy (SBRT) in patients with centrally located early-stage NSCLC. MethodsPatients with inoperable non-metastatic central NSCLC (T1-T3 N0 M0, ≤7cm) were included. After prospective central imaging review and radiation therapy quality assurance for any eligible patient, SBRT (8 × 7.5 Gy) was delivered. The primary endpoint was freedom from local progression probability three years after the start of SBRT. ResultsThe trial was closed early due to poor accrual related to repeated safety-related pauses in recruitment. Between August 2015 and December 2017, 39 patients from six European countries were included and 31 were treated per protocol and analyzed. Patients were mainly male (58%) with a median age of 75 years. Baseline comorbidities were mainly respiratory (68%) and cardiac (48%). Median tumor size was 2.6 cm (range 1.2–5.5) and most cancers were T1 (51.6%) or T2a (38.7%) N0 M0 and of squamous cell origin (48.4%). Six patients (19.4%) had an ultracentral tumor location. The median follow-up was 3.6 years. The rates of 3-year freedom from local progression and overall survival were 81.5% (90% confidence interval [CI]: 62.7%–91.4%) and 61.1% (90% CI: 44.1%–74.4%), respectively. Cumulative incidence rates of local, regional, and distant progression at three years were 6.7% (90% CI: 1.6%–17.1%), 3.3% (90% CI: 0.4%–12.4%), and 29.8% (90% CI: 16.8%–44.1%), respectively. SBRT-related acute adverse events and late adverse events ≥ G3 were reported in 6.5% (n = 2, including one G5 pneumonitis in a patient with prior interstitial lung disease) and 19.4% (n = 6, including one lethal hemoptysis after a lung biopsy in a patient receiving anticoagulants), respectively. ConclusionsThe LungTech trial suggests that SBRT with 8 × 7.5Gy for central lung tumors in inoperable patients is associated with acceptable local control rates. However, late severe adverse events may occur after completion of treatment. This SBRT regimen is a viable treatment option after a thorough risk–benefit discussion with patients. To minimize potentially fatal toxicity, careful management of dose constraints, and post-SBRT interventions is crucial.

Kinetic equation for stochastic vector bundles

The kinetic equation is crucial for understanding the statistical properties of stochastic processes, yet current equations, such as the classical Fokker–Planck, are limited to local analysis. This paper derives a new kinetic equation for stochastic systems on vector bundles, addressing global scale randomness. The kinetic equation was derived by cumulant expansion of the ensemble-averaged local probability density function, which is a functional of state transition trajectories. The kinetic equation is the geodesic equation for the probability space. It captures global and historical influences, accounts for non-Markovianity, and can be reduced to the classical Fokker–Planck equation for Markovian processes. This paper also discusses relative issues concerning the kinetic equation, including non-Markovianity, Markov approximation, macroscopic conservation equations, gauge transformation, and truncation of the infinite-order kinetic equation, as well as limitations that require further attention.

A graphical comparison of screening designs using support recovery probabilities

A screening experiment attempts to identify a subset of important effects using a relatively small number of experimental runs. Given the limited run size and a large number of possible effects, penalized regression is a popular tool used to analyze screening designs. In particular, an automated implementation of the Gauss-Dantzig selector has been widely recommended to compare screening design construction methods. Here, we illustrate potential reproducibility issues that arise when comparing two-level screening designs via simulation, and recommend a graphical method, based on screening probabilities, which compares designs by evaluating them along the penalized regression solution path. This method can be implemented using simulation, or, in the case of lasso, by using exact local lasso sign recovery probabilities. Our approach circumvents the need to specify tuning parameters associated with regularization methods, leading to more reliable design comparisons. This article contains Supplementary Materials including code to implement the proposed methods.

Modification of Local Site Preference for Achieving Tunable Color Emission from Blue to Near-White in Sr3(PO4)2:Dy3+ Phosphor

The color tunability of Sr3(PO4)2:1%Dy3+ phosphor from blue to near white is studied at various annealing conditions. Higher temperature annealing promotes agglomerated rhombohedral (α) phase formation. Experimental and theoretical analysis reveal dopant preference at the low-symmetry Sr(II) site, altering electric (4F9/2→6H13/2) and magnetic (4F9/2→6H15/2) dipole transitions, thereby affecting the yellow-to-blue (Y/B) ratio. The luminescence intensity variation and color tunability are explained based on the local site symmetry and occupation probability of the dopant in the host lattice. An increase in the luminescence intensity up to an annealing temperature of 1200 °C, followed by quenching is observed due to the oxygen vacancies. Commission Internationale d'Eclairage (CIE) color coordinates of (0.31, 0.38), Correlated Color Temperature (CCT) of 6341 K, and color purity of 22.57% confirm the potential of Sr3(PO4)2:1%Dy3+ phosphor annealed at (1200 °C, 6 hrs) for white light generation. A probable photoluminescence mechanism involving 4f→5d→4f transitions in Sr3(PO4)2:1%Dy3+ is proposed.

The effects of additional food and environmental stochasticity on the asymptotic properties of a nutrient–phytoplankton model

In this paper, we investigate the deterministic and stochastic features of an additional food provided nutrient–phytoplankton model, and discuss the effects of additional food and environmental stochasticity (noise) on its asymptotic properties. A detailed global dynamics analysis of the deterministic model is firstly provided, and then the critical conditions for persistence and extinction of phytoplankton is found. For the stochastic model, we establish some sufficient conditions for the exponential extinction of phytoplankton and the existence of stationary distribution. By solving the Fokker–Planck equation, the explicit expression of local probability density of the stochastic model is further derived. With the help of probability density, we obtain the mean, variance, skewness and kurtosis of the biomass of phytoplankton, and numerically find the additional food and stochasticity have complex effects on these statistical properties. Both theoretical and numerical findings indicate that the additional food source is favorable for the growth of phytoplankton, whereas the stochasticity is adverse to its growth. Moreover, the additional food source and stochasticity play important roles in the formation of phytoplankton bloom.

Histology-driven hypofractionated radiation therapy schemes for early-stage lung adenocarcinoma and squamous cell carcinoma

Background and PurposeHistology was found to be an important prognostic factor for local tumor control probability (TCP) after stereotactic body radiotherapy (SBRT) of early-stage non-small-cell lung cancer (NSCLC). A histology-driven SBRT approach has not been explored in routine clinical practice and histology-dependent fractionation schemes remain unknown. Here, we analyzed pooled histologic TCP data as a function of biologically effective dose (BED) to determine histology-driven fractionation schemes for SBRT and hypofractionated radiotherapy of two predominant early-stage NSCLC histologic subtypes adenocarcinoma (ADC) and squamous cell carcinoma (SCC). Material and MethodsThe least-χ2 method was used to fit the collected histologic TCP data of 8510 early-stage NSCLC patients to determine parameters for a well-developed radiobiological model per the Hypofractionated Treatment Effects in the Clinic (HyTEC) initiative. ResultsA fit to the histologic TCP data yielded independent radiobiological parameter sets for radiotherapy of early-stage lung ADC and SCC. TCP increases steeply with BED and reaches an asymptotic maximal plateau, allowing us to determine model-independent optimal fractionation schemes of least doses in 1–30 fractions to achieve maximal tumor control for early-stage lung ADC and SCC, e.g., 30, 44, 48, and 51 Gy for ADC, and 32, 48, 54, and 58 Gy for SCC in 1, 3, 4, and 5 fractions, respectively. ConclusionWe presented the first determination of histology-dependent radiobiological parameters and model-independent histology-driven optimal SBRT and hypofractionated radiation therapy schemes for early-stage lung ADC and SCC. SCC requires substantially higher radiation doses to maximize tumor control than ADC, plausibly attributed to tumor genetic diversity and microenvironment. The determined optimal SBRT schemes agree well with clinical practice for early-stage lung ADC. These proposed optimal fractionation schemes provide first insights for histology-based personalized radiotherapy of two predominant early-stage NSCLC subtypes ADC and SCC, which require further validation with large-scale histologic TCP data.