Temporal visual processing deficits are well-documented in psychosis spectrum disorders and linked to core symptoms including hallucinations and cognitive disorganization. However, studying these mechanisms in isolation may overlook the influence of co-occurring autistic traits, which are increasingly recognized within psychosis populations. We hypothesized that psychosis-proneness and autistic traits would interactively affect temporal crowding. We investigated temporal crowding using an orientation-estimation task in neurotypical participants across two experiments (N1 = 81, N2 = 93). Participants viewed sequences of three randomly oriented stimuli at varying stimulus onset asynchronies (SOA: 200-400ms) and reported the middle item's orientation. Mixture models examined performance in terms of encoding precision, guessing rates, and substitution errors. The Community Assessment of Psychic Experiences (CAPE) and Autism-Spectrum Quotient (AQ) measured trait expression. Response surface analysis (RSA) mapped trait interactions. RSA revealed that balanced expressions of both traits (particularly when both were elevated) were associated with significantly reduced temporal order errors. These findings align with the diametric model, which suggests compensatory interactions between psychosis-proneness and autistic traits. Our findings extend this model to mid-to-high level perceptual mechanisms, suggesting that opposing cognitive tendencies can create mutual compensation at the perceptual level, with implications for understanding symptom heterogeneity across both conditions.

Bed rest accelerates bone loss and may exacerbate skeletal fragility. This study examined the effects of 14days of head-down tilt bed rest (HDBR) with or without exercise, and subsequent recovery, on bone turnover, density and structure in older adults. Twenty-two healthy older adults (55-65 years) completed the HDBR protocol. Participants were randomized to a control group that received passive physiotherapy (CON, n=11) or a group that performed daily exercise (EX, n=11). Serum biomarkers of bone formation (procollagen type 1 N-terminal propeptide (P1NP) and bone-specific alkaline phosphatase (BSAP)), resorption (N-terminal cross-linked telopeptide of type I collagen (NTX) and C-terminal cross-linked telopeptide of type I collagen (CTX)), and osteocalcin were measured at baseline (BDC4), day-9 (HDT9), and immediately (R1), 4weeks (4W), and 4months (4M) post-HDBR. Bone mineral density (BMD) was assessed via dual-energy X-ray absorptiometry (DXA) at BDC4, R1, 4W and 4M. Femoral bone structure was measured via peripheral quantitative computed tomography (pQCT) at BDC4 and R1. CTX and NTX increased at R1 vs. BDC4 (time: P<0.001), while P1NP and BSAP increased at 4W and 4M (time: P<0.001). No DXA-derived BMD changes occurred. pQCT revealed reduced femoral trabecular volumetric BMD at 4% (EX: 342.3±7.8 to 337.9±8.0mg/cm3; CON: 329.3±8.1 to 326.4±8.4mg/cm3; time: P=0.05) and cortical volumetric BMD at 25% (EX: 1089.5±6.7 to 1087.5±7.1mg/cm3; CON: 1102.7±6.7 to 1095.7±7.1mg/cm3; time: P=0.05). However, changes were within the precision error of pQCT measurements. Fourteen days of HDBR, with or without exercise, increased biomarkers of bone resorption but did not alter BMD or bone structure.

A new approach has been developed to establish the public value (utility) set for the generic health measure used in quality-adjusted life year estimates. In contrast to conventional approaches, it establishes the complete utility set for an individual and aggregates a sample of these to achieve the public set. The novel way of establishing the complete utility set for an individual has the potential to transform the nature and extent of a patient's participation in the clinical decision-making process. We have modified the online elicitation of personal utility functions approach to overcome its impracticalities in a clinical consultation. The main modification is the replacement of choice-based items by scale-based ones, on the grounds that the former's time and cognitive demands, while tolerable in the research context, make it infeasible in practice. The personal utility set for healthcare (PUSH) approach, like the online elicitation of personal utility functions one, may be used with any multidimension, multilevel instrument, including condition-specific ones, but the empirical application here is with the health-related quality of life instrument EQ-5D-5L. PUSH for EQ-5D-5L is a decision support tool in the form of a spreadsheet workbook. The clinician assists nondirectively in the elicitation of the patient's utility set for EQ-5D-5L. Subsequently, the clinician, drawing on the best available evidence and information, enters the EQ-5D-5L states they judge, on the balance of probabilities, the patient will be in (at an agreed future time point), for specific interventions, plus no intervention. The relevant country's public set utility for each displayed health state is simultaneously revealed. (Those for 13 countries are in the current template.) It is envisaged that the clinician holds the PUSH template on their computer and opens a new copy for use with each patient. They agree with the patient on what, if anything, is to be saved as part of their electronic medical record. The deliberation following engagement with PUSH and personalized evaluation of the contemplated interventions will typically involve sensitivity testing and possible revision of the patient and clinician inputs. One key responsibility of the clinician is to dispel any "aura of exactness" or pseudo-precision that may be created by the use of precise percentages (or values to 2 decimal places). PUSH participation is to be seen as a component of deliberative co-productive decision-making to which both parties contribute significantly but in role-appropriate ways. The outputs are intended to provide a useful, analysis-framed input into the subsequent discussion and co-produced decision. As a major clinical innovation that transforms both patient participation and clinician contribution, it is advanced here for the discussion and critique that will enable a conceptually sound trial protocol to be developed (including clinician tutoring).

Gene expression data in bioinformatics studies often contain multivariate or high-dimensional variables. One key research problem is to uncover the network structure among gene expression variables, which can help identify pathway-level disruptions associated with diseases and support the development of targeted therapies. With the increasing availability of auxiliary variables (known as covariates), it is desirable to incorporate them to enhance network detection of the main variables (known as responses). The main challenge lies in accurately selecting informative covariates and recovering the network structure among responses, especially when using linear or nonlinear models to characterize the relationships between multivariate responses and covariates. Another challenge is the presence of measurement error in gene expression data, which may result from limitations in measurement precision or human recording errors. To address these challenges and provide a reliable, publicly accessible analytical tool, we develop an R package named PAGE. This package includes three core functions that support measurement error correction, variable selection, and network estimation under both linear and nonlinear modeling frameworks. The application of PAGE is demonstrated using a yeast cell cycle dataset. Based on the analysis and demonstration, we find that the R package PAGE is valid for dealing with the complex network structure. In addition, throughout the simulation studies, we find that the correction of measurement error is crucial, and the R package PAGE is useful to handle error-prone data.

Objective: To construct an edge-enhanced triple-branch neural network (T-Net) for automated three-dimensional(3D) segmentation of the mandibular condyle from cone-beam computed tomography (CBCT) images, aiming to improve segmentation accuracy. Methods: CBCT images of 354 patients with malocclusion (708 condyles) who attended the Department of Orthodontics, Xiangya Stomatological Hospital, Central South University, from January 2022 to January 2024 were retrospectively collected. The dataset was divided into training (424 condyles), validation (142 condyles), and test (142 condyles) sets in a ratio of 6∶2∶2. The T-Net model was built on a single-encoder and dual-decoder architecture. It introduced an edge decoder supervised by edge information as labels. Through skip connections and feature interaction between the segmentation decoder and the edge decoder, the model's capability to extract contour feature information was effectively enhanced. Manual annotation of all images using 3D Slicer software served as the gold standard. The T-Net model parameters were optimized using the validation set, and its performance was evaluated on the test set and compared with four mainstream models (3D U-Net, Attention U-Net, Swin UNETR, and V-Net). Qualitative and quantitative evaluations were performed using visual segmentation results and metrics such as Dice coefficient, intersection over union (IoU), accuracy, precision, F1-score, sensitivity, and mean absolute error (MAE). Results: The T-Net model achieved precise and complete segmentation of the condyle. Its Dice coefficient (0.976±0.011), IoU (0.953±0.021), accuracy (0.999±0.001), precision (0.979±0.010), sensitivity (0.974±0.019) and F1-score (0.976±0.011) were superior to those of the other four models. Compared with the gold standard, the T-Net model yielded the smallest MAE values for condylar morphological parameters (volume: 550 mm³, surface area: 81 mm², length: 0.473 mm, width: 0.781 mm, height: 1.876 mm). Conclusions: The T-Net model demonstrates excellent performance in the condyle segmentation task, with its metrics significantly outperforming the other four models. The model can accurately extract condylar morphological features from CBCT images to achieve precise segmentation and three-dimensional reconstruction.

Abstract-The rapid expansion of the global gig economy has fundamentally changed the structure of personal finance management. Unlike salaried professionals who operate within predictable monthly income cycles, freelancers and independent contractors face highly volatile cashflow patterns characterized by delayed client payments, irregular project pipelines, seasonal fluctuations, and unstable liquidity reserves. Traditional Personal Financial Management (PFM) systems primarily focus on historical transaction tracking and static budgeting, making them ineffective for proactive financial survival planning in modern freelance ecosystems. This project introduces Prophet AI v1.1, an AI-driven financial intelligence platform engineered specifically to simulate, forecast, and analyze unstable freelance cashflow environments using distributed cloud infrastructure, cryptographic verification, and real-time neural intelligence. The proposed system functions as a Financial Flight Simulator that allows freelancers to model financial risk before it becomes catastrophic in real life. The platform combines machine learning-based forecasting, stochastic risk simulation, cryptographic integrity validation, asynchronous AI orchestration, and multilingual neural voice synthesis within a single integrated ecosystem. The system architecture follows a distributed deployment model consisting of a Next.js 14 frontend hosted on Vercel, a FastAPI Intelligence Gateway hosted on Render, and a Supabase PostgreSQL secure transaction vault. This decoupled architecture ensures scalability, modularity, low frontend latency, and reliable handling of long-running AI inference tasks. The financial forecasting engine utilizes a hybrid intelligence pipeline combining statistical forecasting principles and ensemble-based analytical logic. The platform generates 30-day rolling liquidity forecasts, safe spending corridors, and stress-based runway simulations that help users evaluate financial survival scenarios under varying burn conditions. Unlike conventional financial dashboards, Prophet AI introduces dynamic What-If simulation controls, allowing users to manipulate variables such as liquidity lag, expense escalation, and delayed client payments in real time. To establish institutional-grade trust and forensic-grade auditability, the system implements an Integrity Shield powered by the SHA-256 cryptographic hashing algorithm. Every transaction entered into the system generates a unique digital fingerprint using transaction attributes including amount, date, category, and user identification. This verification mechanism ensures that tampered or manipulated financial records cannot enter the intelligence pipeline, thereby maintaining a Verified Ledger architecture. The project additionally documents real-world deployment challenges involving decimal precision mismatches between JavaScript and Python environments and explains the implementation of strategic normalization bypass mechanisms for stable production deployment. The intelligence layer of Prophet AI is powered using Llama 3.3-70B via Groq infrastructure, enabling high-speed financial reasoning and structured JSON-based strategy generation. The platform utilizes a carefully engineered Ruthless Financial Strategist system prompt designed to deliver direct, survival-oriented financial recommendations rather than emotionally comforting advice. This design philosophy reflects the real-world operational needs of freelancers who require accurate liquidity warnings and actionable strategic insights during financial instability. The generated intelligence is converted into multilingual audio briefings using the edge-tts neural voice synthesis engine, supporting both English and Hindi voice outputs. To avoid cloud timeout failures and synchronous processing bottlenecks, the platform implements an asynchronous polling architecture using UUID-based job orchestration. The frontend submits a /briefing request and continuously polls a /briefing-status/{job_id} endpoint until the AI-generated strategy and MP3 briefing become available. This architecture enables the system to safely execute computationally expensive large language model inference and neural voice generation workflows even on limited-resource cloud infrastructure. The completed system demonstrates the practical integration of distributed AI infrastructure, cryptographic verification, asynchronous backend engineering, financial forecasting, and multimodal intelligence synthesis within a real-world production environment. Prophet AI v1.1 represents a transition from passive financial recordkeeping to proactive survival-oriented financial intelligence. The project establishes a scalable blueprint for next-generation AI-powered fintech systems capable of delivering real-time strategic decision support for the rapidly growing global freelance economy.Keywords-Freelance finance; cashflow forecasting; stochastic simulation

Accurate and accessible screening tools for periodontitis are essential for early detection and disease prevention. This study evaluated a non-invasive diagnostic approach integrating sociodemographic data, self-reported oral health (SROH) questionnaires, and salivary biomarkers, using both conventional statistical and machine learning (ML) predictive models. Seventy-seven adults completed a validated SROH questionnaire and provided saliva samples for quantification of six biomarkers: interleukins (IL-1β, IL-6), tumour necrosis factor (TNF-α), matrix metalloproteinases (MMP-8, MMP-9), and metallothionein (MT). Participants were clinically classified as having (i) periodontal health, (ii) gingivitis, or (iii) periodontitis. Predictive models were developed using Logistic Regression (LR), Random Forest (RF), and Naive Bayes (NB) across three feature sets: (i) SROH, salivary biomarkers and sociodemographic, (ii) SROH and salivary biomarkers, (iii) SROH and sociodemographic and (v) SROH alone. Model performance was assessed using 10-fold cross-validation and standard evaluation metrics. The RF model trained on SROH, and salivary biomarkers achieved the highest accuracy with area under the receiver operating characteristic curve (AUC = 0.856), with superior precision (70.13%), sensitivity (0.701) and lower error rates (RMSE = 0.371) compared with NB (AUC = 0.795) and LR (AUC = 0.724) models in detecting periodontitis. This non-invasive, SROH and biomarker-integrated approach shows potential as a first-line screening and referral tool in primary care and population-based settings where comprehensive periodontal examination is not routinely available. Further validation in larger, more diverse populations is warranted to support clinical translation.

BackgroundSelecting appropriate sample sizes in magnetic resonance imaging studies is a complex process that requires to balance statistical rigor with the practical challenges of measuring a large patient population. In this Institutional Review Board approved study, we evaluate the dominant error types (“finite N” errors versus precision errors) for apparent diffusion coefficient (ADC)-based lesion characterization in diffusion-weighted magnetic resonance imaging (DWI) of the female breast in a local dataset and compare our results with current literature.MethodsFirst, in a literature review including 24 published breast DWI studies, the standard error of the area under the receiver operating characteristic curve as a measure of sample size-related errors (finite N errors) was estimated for the reported ADC values and compared to the values, derived from expert readings of a university hospital’s cohort of 171 patients with suspicious breast lesions. Second, precision errors were assessed based on published analyses of the coefficient of variation of ADC values, measured in breast DWI exams.ResultsFinite N errors were dominant in the in-house study and most of the 24 reviewed studies. The median sample size at which finite N errors and precision errors were equal was determined to be n = 932.DiscussionThis analysis of dominant error types shows that the required sample sizes for the considered use case are not unreasonably large and that reducing sample sizes may not be justified based on the merits of the conducted analysis. Nonetheless, incorporating dominant error type assessments into future studies may provide valuable insights for optimizing study design and improving methodological rigor.

Restarting Two-Term Nonlinear Conjugate Gradient Methods Based on a Finite Precision Arithmetic Analysis

We study the expected number of rolls required for the cumulative sum of a fair six-sided die to first enter a prescribed target set H ⊂ Z ≥ 0 . A one-variable dynamic-programming formulation is introduced that removes dependence on the roll count. Within this framework, the infinite process is truncated at a large cutoff N and corrected by an analytically derived overshoot term that accounts for the rare event of exceeding N before entering H . Explicit bounds on this residual yield a strict two-sided estimate of the truncation error. The method is numerically efficient, requiring constant memory and linear time in the cutoff. For the perfect-square target set H = { n 2 : n ∈ N } , all quantities are evaluated explicitly, yielding E [ T ] = 7.07976423755110510389555305690818489468 … , provably correct to 1017 decimal places. This constitutes the most precise result known to date and establishes a general framework for high-accuracy computation of discrete hitting times.

The determination of airflow rate in a fluidized bed drying system is a critical requirement in fluidized bed drying operations, as it directly governs the fluidization regime and the efficiency of heat and mass transfer, particularly for high-quality agricultural products. This study developed and evaluated an experimental airflow measurement system using a cluster of three ISA 1932 standard nozzles integrated into a rectangular plenum chamber. The system’s performance was investigated across a fan operating frequency range of 20 Hz to 60 Hz. Airflow rates calculated from differential pressure $(\Delta p)$ at eight different static pressure tapping positions were cross-validated against reference values derived from duct centerline velocity measurements. Experimental results demonstrate a strong linear correlation between fan frequency and airflow velocity, consistent with centrifugal blower characteristics. The relative error between the two measurement methods fluctuated between 5.94 % and 24.31 %. Notably, the highest precision (error &lt; 10 %) was consistently achieved at higher operating frequencies (55 – 60 Hz) and specifically at tapping positions 4 and 5, located toward the lower boundaries of the plenum chamber. This study identified an optimal pressure tapping configuration, demonstrating that while the multi-nozzle arrangement is a viable method for extending measurement ranges, accuracy is highly sensitive to the spatial location of the taps. To achieve optimal measurement accuracy, the static pressure taps were strategically positioned at the lower edges of the plenum chamber, where flow redistribution was most stable and less affected by localized turbulence. These findings provide a technical foundation for optimizing drying kinetics and enhancing energy efficiency in post-harvest processing.

Speech remains a primary mode of human communication; however, automated speech recognition (ASR) systems face challenges from accent variability, temporal fluctuations, noise, and data privacy concerns. This paper proposes an enhanced ASR architecture incorporating an Adaptive Phoneme State Learning (APSL) algorithm with a Backpropagation Neural Network (BPNN) and Hidden Markov Model (HMM). APSL dynamically adjusts HMM state probabilities using phoneme confidence scores derived from the BPNN, thereby improving phoneme transition modeling and alignment. The multi-stage ASR pipeline includes noise reduction, speech-pause detection, and feature extraction via framing and windowing. APSL’s adaptive mechanism reduces ambiguities in phoneme transitions, resulting in a more accurate speech-to-text conversion. A comparative evaluation framework assesses the baseline HMM, standalone BPNN, and integrated APSL-BPNN-HMM model. Experiments were conducted using a custom-built dataset of 2000 audio files alongside five benchmark corpora: BNC, ANC, COCA, Buckeye, and Emu. Key evaluation metrics—recall, precision, F-score, and Word Error Rate (WER)—demonstrate that the APSL-enhanced model significantly outperforms baseline systems, achieving 95.7% recall, 92.95% precision, 94.53% F-score, and 96% overall accuracy. Notably, APSL-BPNN-HMM consistently yielded the lowest WER across all datasets, validating its effectiveness. This work highlights the benefits of adaptive learning in probabilistic frameworks for achieving robust and accurate speech recognition.

We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like ⟨tr X^{2}⟩ in the confining phase of the theory in the infinite N limit. Exploiting the symmetries of these models and applying nonlinear relaxation, we impose constraints that include traces of words of length up to 14. Our results yield rigorous bounds on the large-N ground-state dynamics, along with estimates of selected low-order observables to eight significant digits.

To address the uneven spatial distribution and significant variations in observation data quality among multi-GNSS experiment (MGEX) stations, this paper proposes an adaptive station selection method (comprehensive adaptive site selection, CAS) for uncalibrated phase delay (UPD) estimation that incorporates observation data quality, thereby overcoming the limitations of traditional methods that neglect station geometry and data quality. A position dilution of precision (PDOP) and UPD error propagation model is developed. Using marginal benefit theory, the optimal number of stations is determined. A multi-indicator evaluation system based on Dempster-Shafer (D-S) evidence theory is established to assess data quality, enabling a dynamic grid algorithm that balances spatial geometry and data quality. The experiments are conducted using BeiDou‑3 navigation satellite system (BDS‑3) data. Experimental results demonstrate that the proposed method selects 80 optimal stations, accounting for only 30% of the global stations. The estimated Narrow-Lane (NL) UPD products achieve an accuracy better than 0.05 cycles, with a discrepancy of less than 0.002 cycles compared to the full-station solution, indicating comparable precision. Furthermore, the computational time is reduced by 54.1%.

By using a refined K-means algorithm that includes optimized initial centroid selection and lessened distance computations, this research clusters students based on their campus behavior patterns utilizing a sample of 324 students who are enrolled at the XX Vocational College. Associations between these behavior patterns and academic results are then computed through an improved version of the Apriori algorithm. To optimize SVM parameters, a fruit fly optimization algorithm (FOA) is presented to allow early detection of students at academic risk. Main observations indicate that most students spend between 600 and 900 yuan per month, with the average being 789.37 yuan. Internet fees on the campus are mostly 37.64 yuan per month (43.52 percent), but it has been seen that the cost ranges between 9 and 48 yuan. Frequency of bathing is 9-17 per month in 48.77 percent of the sample and the lowest book borrowing group is 73.15 percent of the students who borrow an average of only 6.67 books each. Daily living habits and academic engagement were found as the main determinants of academic performance among the behavioral dimensions evaluated, with spending patterns having relatively low predictive power. It is worth noting that irregular routines seem to result in increased expenditure, implying that lifestyle discipline affects financial behavior too. The suggested model shows high fitting precision and low prediction error, providing a consistent model to be used by vocational college administrators to establish a constant loop of monitoring, early warning, specific intervention, and systematic improvement when it comes to student development.

The growing interest in 3D-DXA reconstructions for possible uses in fracture risk prediction or patient follow-up, e.g., in conjunction with finite element analyses, asks for precision data to increase the interpretability of results making use of the 3D-DXA technique. Using two datasets and a total of 2427 DXA scans of the proximal femur we evaluated the short- and long-term precision of standard DXA measurements. All the available scans were reconstructed using 3D-Shaper software and processed through a nonlinear finite element pipeline for femoral strength estimation. Short- and long-term precision were computed for thirty 3D-DXA-based parameters as well as femoral strength in fall and stance configurations. Precision errors were related to change rates of the respective parameters by calculating the trend assessment interval (TAI). Simultaneously, spatially resolved precision errors were computed for cortical parameters and error progression from DXA to 3D-DXA and FEA was considered. Precision errors were amplified through the different processing steps. Long-term precision errors were 1.6%, 2.0% and 7.5% for total hip aBMD, total hip integral vBMD and strength in fall, respectively. Errors between processing steps were only weakly correlated. Higher change rates for vBMD and strength compensated the larger precision errors, resulting in similar TAIs for total hip aBMD (5.5 years), total hip integral vBMD (4.6) and strength (5.8), respectively. Relative local precision errors of cortical parameters were largest in the superior and anterior neck region and above the lesser trochanter. 3D-DXA and thereon based FEA may offer interesting insights into the densitometric and mechanical quality of the proximal femur. The here reported results should offer a help for the interpretation of sequential measurements where these are required.

Abstract: Myopia and pathological myopia (PM) have been recognized as one of the leading causes of visual impairment globally. Optical coherence tomography (OCT) provides high-resolution imaging of retinal and choroidal structural changes and plays an increasing role in the diagnosis and prognostication of PM and myopia-related complications. Recent advances in OCT technology have produced a potential platform for artificial intelligence (AI), particularly deep learning (DL), to enhance diagnostic accuracy and prognostic capabilities. First, AI-assisted detection of myopia based on OCT-derived biomarkers such as retinal curvature, optic nerve morphology, and inner retinal thinning have the potential to detect high myopia. However, precise refractive error estimation or differentiation of lower-grade myopia remains modest. Future integration of OCT angiography may refine the prediction of myopia progression. Second, AI may improve automated segmentation and quantification of the choroid, with DL algorithms consistently delineating choroidal boundaries and quantifying region-specific choroidal thicknesses. Recent algorithms have extended beyond basic segmentation to choroidal sublayer segmentation and calculating choroidal vascularity indices, enhancing structural characterization in myopic eyes. Third, AI methods have advanced the detection of PM-related OCT lesions, reliably identifying critical lesions including myopic traction maculopathy, myopic choroidal neovascularization, and dome-shaped macula. Recent models have also shown the ability to categorize disease severity according to validated clinical frameworks, such as the Atrophy–Traction–Neovascularization and myopic tractional maculopathy staging systems. Despite these advances, current AI methods face challenges including inconsistent OCT protocols, limited longitudinal data, inadequate external validation, and difficulties handling poor-quality scans. Addressing these limitations could facilitate clinical integration, enhancing early diagnosis, prognostication, and possibly, personalized myopia management in the future.

Wave propagation modeling is fundamental to optics, facilitating diverse applications including lens design, computational imaging, and optical computing. However, existing approaches encounter a critical trade-off between computational accuracy and efficiency, primarily limited by numerical precision constraints. In this study, we establish the explicit numerical limits in wave propagation modeling and demonstrate that accurate simulations are achievable with reduced precision. Our analysis reveals that the limited significant decimal digits and dynamic range of floating-point arithmetic compromise phase and amplitude representation accuracy, thereby constraining the dimensions and space-bandwidth product of optical systems that can be reliably modeled. To address this challenge, we introduce a differentiable modeling scheme that maintains accurate phase representation through wrapping from double precision and appropriately prescales the amplitude to ensure the integral result remains within the representable dynamic range. We validate our approach by simulating point spread functions of optical systems, solving phase retrieval problems, and synthesizing holograms for light shaping. Our method achieves, on average, ∼20× acceleration in diffraction modeling while retaining accuracy comparable to double-precision implementations. Optical experiments further demonstrate our approach’s effectiveness. Specifically, our method successfully reconstructs complex amplitudes of laser beams from coded measurements and designs phase-only holograms for desired diffraction patterns. We envision that this technique will advance research in computational optics with enhanced computational efficiency.

Cellular water content governs the concentration of all biomolecules inside a cell, thereby influencing the physical and functional properties of the cell. However, measurements of water content in physiologically relevant cell culture models remain largely unavailable, particularly in three-dimensional (3D) models such as tumor spheroids and organoids. Here, we achieve such measurements using an industrial-grade capillary steel tube. The steel tube functions as a mechanical resonator that inertially senses the buoyant mass of particles. For microgram-scale particles ≥ 400 micrometers in diameter, we achieve <1% precision error in buoyant mass with a 5-minute acquisition interval. By sequentially measuring the buoyant mass of individual, patient-derived glioblastoma tumor spheroids derived from patients with glioblastoma in media of different densities and cell permeabilities, we determine the absolute and fractional (volume/volume) water content of the spheroids, along with their dry mass, volume, and density properties. We achieve ~0.5% precision error in fractional water content with a throughput of three spheroids per hour. This enables us to detect both interspheroid heterogeneity in fractional water content and acute responses to kinase inhibition. Overall, we establish a simple and accessible technique for quantifying water content in living 3D cell culture models, opening previously unexplored avenues for studying biophysical regulation in multicellular systems.

The discrete ordinates method has served as a cornerstone of numerical radiative transfer since A. Schuster introduced its foundation in 1905. G.C. Wick and S. Chandrasekhar significantly advanced the method in the mid-20th century to study planetary atmospheres. In 1963, B.G. Carlson formally applied the method to neutron transport, initiating its widespread use thereafter. Since then, the discrete ordinates method has grown from simple linear interpolation to sophisticated multidimensional algorithms applied to reactor analysis and weapons design. In this work, we consider a 1D, monoenergetic response matrix discrete ordinates method to solve the even-parity, second-order form analytically with hyperbolic matrix functions. Our focus then turns to incorporating a nascent delta function source (DFS) through faux interpolation of discrete angular fluxes. Finally, we benchmark the DFS approach against the conventional first collision source (FCS) to demonstrate agreement to eight or nine significant digits.