Search Results (24)

Edible Bird’s Nest (EBN) is a highly prized food product, making it a frequent target for economic adulteration. Consequently, robust quality assurance is paramount to protect consumers and ensure market integrity. A significant barrier to effective quality control, however, is an incomplete understanding of the natural chemical variability within authentic EBN. This variability, influenced by factors such as geographical origin, bird species, and post-harvest processing, can confound analytical measurements and complicate the definition of a standard reference. This study provides an existence proof in a defined cohort, characterizing microscale chemical heterogeneity in authentic A. fuciphagus EBN. We employed a multi-modal Fourier Transform Infrared (FTIR) spectroscopy approach, integrating transmission, macro-attenuated total reflectance (ATR), and high-resolution micro-ATR chemical imaging. A diverse set of validated, authentic EBN samples was analyzed using unsupervised Principal Component Analysis (PCA) to explore the data structure. Our results reveal significant and previously unquantified spectral heterogeneity, particularly in protein and glycoprotein-related regions. In our cohort, the chemical signatures of authentic EBN do not collapse to a single, uniform profile but span a broad, multi-dimensional continuum. This inherent variability presents a critical challenge for conventional quality control methods that rely on simplistic, single-spectrum standards, which may lead to the misclassification of genuine products. By establishing a robust chemical baseline for the authentic class, this work provides the foundational data essential for developing next-generation authentication models capable of reliably distinguishing this natural variance from deliberate adulteration. Full article

The Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates. Building upon our earlier work, where we developed both theoretical results—including novel proofs of the martingale property, connections between the Kennedy and HJM frameworks, and parameter estimation theory—and practical calibration methods, using maximum likelihood, Radon–Nikodym derivatives, and numerical optimization (stochastic gradient descent) on simulated and real par swap rate data, this study extends the analysis in several directions. We derive detailed formulas for the volatilities implied by the Kennedy model and investigate their asymptotic properties. A comprehensive sensitivity analysis is conducted to evaluate the impact of key parameters on derivative prices. We implement an industry-standard Monte Carlo method, tailored to the conditional distribution of the Kennedy field, to efficiently generate scenarios consistent with observed initial forward curves. Furthermore, we present closed-form pricing formulas for various interest rate derivatives, including zero-coupon bonds, caplets, floorlets, swaplets, and the par swap rate. A key advantage of these results is that the formulas are expressed explicitly in terms of the initial forward curve and the original parameters of the Kennedy model, which ensures both analytical tractability and consistency with market-observed data. These closed-form expressions can be directly utilized in calibration procedures, substantially accelerating multidimensional nonlinear optimization algorithms. Moreover, given an observed initial forward curve, the model provides significantly more accurate pricing formulas, enhancing both theoretical precision and practical applicability. Finally, we calibrate the Kennedy model to market-observed caplet prices. The findings provide valuable insights into the practical applicability and robustness of the Kennedy model in real-world financial markets. Full article

Background/Objectives: Animal and fungal sterols and stanols exhibit remarkable structural diversity, driven by variations in the number and position of C=C bonds within the steroidal tetracyclic core and side chain, along with diverse branching patterns of the latter. Similarly to phytosterols, these metabolites produce highly complex tandem mass spectra, whose interpretation has so far been limited. To address this gap, the fragmentation behavior of selected animal/fungal sterols and stanols was studied in this paper. Methods: Higher-Collisional-energy Dissociation–High-resolution tandem mass spectrometry (HCD-HRMS/MS) of protonated/dehydrated species generated via atmospheric pressure chemical ionization (APCI) was performed on structurally diverse compounds, including lathosterol, desmosterol, zymosterol, lanosterol, ergosterol, chalinasterol, and the stanols coprostanol and cholestanol. Results: Structurally diagnostic product ions originating from the side chains were unveiled, shedding light on the intramolecular migration of positive charge from the initial ionization site at C3 to alternative stable sites across the molecular structure, which is a typical mechanism also noted in cholesterol and phytosterols. In addition, characteristic fragmentation patterns related to the steroidal backbone were found and discussed for Δ⁷, Δ^5,7 and Δ⁸-sterols, and a novel elucidation of the fragmentation behavior of 4,4-dimethyl-Δ⁸-sterols, based on lanosterol as a model compound, was achieved. The relative intensities of diagnostic product ions allowed a correlation with specific structural motifs, and “cholesterol-like” and “stigmasterol-like” fragmentations pathways were recognized. These findings were integrated with prior data on cholesterol and plant sterol fragmentation acquired under identical analytical conditions. Moreover, as a proof of its relevance for novel sterol identification, MS/MS-related information was successfully applied to the identification of a positional isomer (Δ⁷) of zymosterol in baker’s yeast extract, along with typical fungal major sterols. Conclusions: The comprehensive archive of sterol/stanol fragmentations obtained by APCI-HCD-MS/MS might prove very useful for the future characterization of novel sterol/stanol species in complex matrices. Full article

Background: Class imbalance and limited interpretability remain major barriers to the clinical adoption of machine learning in diabetes prediction. These challenges often result in poor sensitivity to high-risk cases and reduced trust in AI-based decision support. This study addresses these limitations by integrating SMOTE-based resampling with SHAP-driven explainability, aiming to enhance both predictive performance and clinical transparency for real-world deployment. Objective: To develop and validate an interpretable machine learning framework that addresses class imbalance through advanced resampling techniques while providing clinically meaningful explanations for enhanced decision support. This study serves as a methodologically rigorous proof-of-concept, prioritizing analytical integrity over scale. While based on a computationally feasible subset of 1500 records, future work will extend to the full 100,000-patient dataset to evaluate scalability and external validity. We used the publicly available, de-identified Diabetes Prediction Dataset hosted on Kaggle, which is synthetic/derivative and not a clinically curated cohort. Accordingly, this study is framed as a methodological proof-of-concept rather than a clinically generalizable evaluation. Methods: We implemented a robust seven-stage pipeline integrating the Synthetic Minority Oversampling Technique (SMOTE) with SHapley Additive exPlanations (SHAP) to enhance model interpretability and address class imbalance. Five machine learning algorithms—Random Forest, Gradient Boosting, Support Vector Machine (SVM), Logistic Regression, and XGBoost—were comparatively evaluated on a stratified random sample of 1500 patient records drawn from the publicly available Diabetes Prediction Dataset (n = 100,000) hosted on Kaggle. To ensure methodological rigor and prevent data leakage, all preprocessing steps—including SMOTE application—were performed within the training folds of a 5-fold stratified cross-validation framework, preserving the original class distribution in each fold. Model performance was assessed using accuracy, area under the receiver operating characteristic curve (AUC), sensitivity, specificity, F1-score, and precision. Statistical significance was determined using McNemar’s test, with p-values adjusted via the Bonferroni correction to control for multiple comparisons. Results: The Random Forest-SMOTE model achieved superior performance with 96.91% accuracy (95% CI: 95.4–98.2%), AUC of 0.998, sensitivity of 99.5%, and specificity of 97.3%, significantly outperforming recent benchmarks (p < 0.001). SHAP analysis identified glucose (SHAP value: 2.34) and BMI (SHAP value: 1.87) as primary predictors, demonstrating strong clinical concordance. Feature interaction analysis revealed synergistic effects between glucose and BMI, providing actionable insights for personalized intervention strategies. Conclusions: Despite promising results, further validation of the proposed framework is required prior to any clinical deployment. At this stage, the study should be regarded as a methodological proof-of-concept rather than a clinically generalizable evaluation. Our framework successfully bridges algorithmic performance and clinical applicability. It achieved high cross-validated performance on a publicly available Kaggle dataset, with Random Forest reaching 96.9% accuracy and 0.998 AUC. These results are dataset-specific and should not be interpreted as clinical performance. External, prospective validation in real-world cohorts is required prior to any consideration of clinical deployment, particularly for personalized risk assessment in healthcare systems. Full article

This paper establishes two novel recurrence relations for Stirling numbers of the second kind—an L recurrence and a vertical recurrence—discovered through a probabilistic analysis of Poisson higher-order origin moments. While the link between these moments and Stirling numbers is known, our derivation via a specific expectation identity provides a clear and efficient pathway to their computation, circumventing the need for infinite series. The primary theoretical contribution is the proof of these previously undocumented combinatorial recurrences, which are of independent mathematical interest. Furthermore, we demonstrate the severe practical inadequacy of high-order sample moments as estimators, highlighting the necessity of our analytical approach to obtaining reliable estimates in applied fields. Full article

Organisations are increasingly adopting the Chain of Custody (CoC) standards in the mining industry to enhance the traceability of minerals. It ensures that the minerals they have received are from credible sources and accompanied by verifiable information. However, unlikeother industries such as timber, where the effectiveness and benefits of CoC standards are mainly explored, this study subtly shifts the focus towards identifying strategic opportunities and innovation areas within the CoC standards that could extend beyond traceability. Four CoC standards were selected, and their provisions examined. It was found that implementing these requirements could not only enhance transparency but also support broader sustainability goals across the entire value chain. The study also identifies several challenges that could act as barriers to the CoC system, and these are seen as opportunities for innovative approaches to enhance the effectiveness of the standards. These are labelled as transformative innovation areas, and while they do include blockchains and analytical proof of origin technologies, this study also seeks to advocate for solutions that are more pragmatic and scalable. By identifying opportunities and areas of innovation, the findings will help improve the practical implementation of the standards and suggest areas for future evaluations of effectiveness that could consider aspects beyond traceability, such as sustainability and transparency. Full article

Background: Many patients harbor minimal residual disease (MRD)—small clusters of residual tumor cells that survive therapy and evade conventional detection but drive recurrence. Although advances in molecular and computational methods have improved circulating tumor DNA (ctDNA)-based MRD detection, these approaches face challenges: ctDNA shedding fluctuates widely across tumor types, disease stages, and histological features. Additionally, low levels of driver mutations originating from healthy tissues can create background noise, complicating the accurate identification of bona fide tumor-specific signals. These limitations underscore the need for refined technologies to further enhance MRD detection beyond DNA sequences in solid malignancies. Methods: Profiling circulating cell-free mRNA (cfmRNA), which is hyperactive in tumor and non-tumor microenvironments, could address these limitations to inform postoperative surveillance and treatment strategies. This study reported the development of OncoMRD BREAST, a customized, gene signature-informed cfmRNA assay for residual disease monitoring in breast cancer. OncoMRD BREAST introduces several advanced technologies that distinguish it from the existing ctDNA-MRD tests. It builds on the patient-derived gene signature for capturing tumor activities while introducing significant upgrades to its liquid biopsy transcriptomic profiling, digital scoring systems, and tracking capabilities. Results: The OncoMRD BREAST test processes inputs from multiple cutting-edge biomarkers—tumor and non-tumor microenvironment—to provide enhanced awareness of tumor activities in real time. By fusing data from these diverse intra- and inter-cellular networks, OncoMRD BREAST significantly improves the sensitivity and reliability of MRD detection and prognosis analysis, even under challenging and complex conditions. In a proof-of-concept real-world pilot trial, OncoMRD BREAST’s rapid quantification of potential tumor activity helped reduce the risk of incorrect treatment strategies, while advanced predictive analytics contributed to the overall benefits and improved outcomes of patients. Conclusions: By tailoring the assay to individual tumor profiles, we aimed to enhance early identification of residual disease and optimize therapeutic decision-making. OncoMRD BREAST is the world’s first and only gene signature-powered test for monitoring residual disease in solid tumors. Full article

The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters. By working in Duffing approximation, we apply the Melnikov method to the original Ziegler system, showing that the first non-vanishing Melnikov integral appears in the second order. An explicit expression for the Melnikov integral is derived in the presence of a time-periodic external force and for a suitable choice of the parameters, as well as in the presence of a dissipative term acting on the lower rod of the pendulum. These results allow us to define fundamental relationships between the Melnikov integral and a proper control parameter that distinguishes between regular and chaotic orbits for the original dynamical system. Finally, in the appendix, we present proof of a conjecture concerning the non-validity of Devaney’s chaoticity definition for a discrete map associated with the system. Full article

The EU’s regulatory framework for genetically modified organisms (GMOs) was developed for “classical” transgenic GMOs, yet advancements in so-called “new genomic techniques (NGTs)” have led to implementation challenges regarding detection and identification. As traceability can complement detection and identification strategies, improvements to the existing traceability strategy for GMOs are investigated in this study. Our results are based on a comprehensive analysis of existing traceability systems for globally traded agricultural products, with a focus on soy. Alternative traceability strategies in other sectors were also analysed. One focus was on traceability strategies for products with characteristics for which there are no analytical verification methods. Examples include imports of “conflict minerals” into the EU. The so-called EU Conflict Minerals Regulation requires importers of certain raw materials to carry out due diligence in the supply chain. Due diligence regulations, such as the EU’s Conflict Minerals Regulation, can legally oblige companies to take responsibility for certain risks in their supply chains. They can also require the importer to prove the regional origin of imported goods. The insights from those alternative traceability systems are transferred to products that might contain GMOs. When applied to the issue of GMOs, we propose reversing the burden of proof: All companies importing agricultural commodities must endeavour to identify risks of unauthorised GMOs (including NGTs) in their supply chain and, where appropriate, take measures to minimise the risk to raw material imports. The publication concludes that traceability is a means to an end and serves as a prerequisite for due diligence in order to minimise the risk of GMO contamination in supply chains. The exemplary transfer of due diligence to a company in the food industry illustrates the potential benefits of mandatory due diligence, particularly for stakeholders actively managing non-GMO supply chains. Full article

The paper concerns a nonlinear second-order parabolic evolution equation, one of the well-known objects of mathematical physics, which describes the processes of high-temperature thermal conductivity, nonlinear diffusion, filtration of liquid in a porous medium and some other processes in continuum mechanics. A particular case of it is the well-known porous medium equation. Unlike previous studies, we consider the case of several spatial variables. We construct and study solutions that describe disturbances propagating over a zero background with a finite speed, usually called ‘diffusion-wave-type solutions’. Such effects are atypical for parabolic equations and appear since the equation degenerates on manifolds where the desired function vanishes. The paper pays special attention to exact solutions of the required type, which can be expressed as either explicit or implicit formulas, as well as a reduction of the partial differential equation to an ordinary differential equation that cannot be integrated in quadratures. In this connection, Cauchy problems for second-order ordinary differential equations arise, inheriting the singularities of the original formulation. We prove the existence of continuously differentiable solutions for them. A new example, an analog of the classic example by S.V. Kovalevskaya for the considered case, is constructed. We also proved a new existence and uniqueness theorem of heat-wave-type solutions in the class of piece-wise analytic functions, generalizing previous ones. During the proof, we transit to the hodograph plane, which allows us to overcome the analytical difficulties. Full article

In this article, we study ovals of constant width in a plane, comparing them to particular circles. We use the vertices on the oval, after counting them, as a reference to measure the length of the curve between opposite points. A new proof of Barbier’s theorem is introduced. A distance function from the origin to the points of the oval is introduced, and it is shown that extreme values of the distance function occur at the vertices and opposite points. Comparisons are made between ovals and particular circles. We prove that the differences in the distances from the origin between the particular circles and the ovals are small and within a certain range. We also prove that all types of ovals described in this paper are analytically and geometrically enclosed between two defined circles centered at the origin. Full article

At microwave frequencies, radar cross-section (RCS) measurements are usually performed by placing the target in the far-field region of the antenna. The wavefront of the radiating field from the antenna can be approximated as planar, ensuring that the incident field and the power interact with the target independently of the antenna. However, for electrically large targets, the required distance becomes significant, posing challenges for implementation. Scaled-model RCS measurements offer an alternative solution. RCS measurements at terahertz and optical frequencies typically require a collimated beam as the source, where the intercepted power and RCS become dependent on the excitation. To address this dependency, researchers have proposed modifying the RCS definition to account for the intercepted power and to analytically formulate the scattering problem. However, such modifications require prior knowledge of the target’s geometry and material properties, which are often not readily available in practice. This also limits the study to only canonical targets. In this paper, we propose an alternative approach for modelling the intercepted power. The Gaussian beam is decomposed into a number of plane waves travelling to different directions using the theory of plane wave spectrum. The scattering problem is solved using the full-wave method of moment. Through theoretical proofs and numerical examples involving spheres and a non-canonical target, with a scaled-model aircraft, we demonstrate that the original RCS definition can serve as a good approximation for scaled measurements, provided that the beam waist is approximately four times the target’s dimensions. These findings provide valuable guidelines for radar engineers when performing scaled measurements using collimated beams. The results, which match those obtained from full-model measurements, enable us to predict the RCS of full-scale targets. This capability facilitates various target-related applications, such as target characterization, classification, detection, and even recognition. Full article

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain new criteria equivalent to the Riemann hypothesis. Later, the same theorem was applied to calculate certain infinite sums and study the properties of zeroes of a few analytical functions. In this study, we apply this approach to elliptic functions of Jacobi and Weierstrass. Numerous sums over inverse powers of zeroes and poles are calculated, including some results for the Jacobi elliptic functions sn(z, k) and others understood as functions of the index k. The consideration of the case of the derivative of the Weierstrass rho-function, ${\wp }_z(z{,}_{}\tau )$, leads to quite easy and transparent proof of numerous equalities between the sums over inverse powers of the lattice points $m+n\tau$ and “demi-lattice” points $m+1/2+n\tau$, $m+(n+1/2)\tau$, $m+1/2+(n+1/2)\tau$. We also prove theorems showing that, in most cases, fundamental parallelograms contain exactly one simple zero for the first derivative ${\theta }_1\prime (z|\tau )$ of the elliptic theta-function and the Weierstrass $\zeta$-function, and that far from the origin of coordinates such zeroes of the $\zeta$-function tend to the positions of the simple poles of this function. Full article

The article considers a non-stationary three-dimensional spatial mathematical model of biological kinetics and geochemical processes with nonlinear coefficients and source functions. Often, the step of analytical study in models of this kind is skipped. The purpose of this work is to fill this gap, which will allow for the application of numerical modeling methods to a model of biogeochemical cycles and a computational experiment that adequately reflects reality. For this model, an initial-boundary value problem is posed and its linearization is carried out; for all the desired functions, their final spatial distributions for the previous time step are used. As a result, a chain of initial-boundary value problems is obtained, connected by initial–final data at each step of the time grid. To obtain inequalities that guarantee the convergence of solutions of a chain of linearized problems to the solution of the original nonlinear problems, the energy method, Gauss’s theorem, Green’s formula, and Poincaré’s inequality are used. The scientific novelty of this work lies in the proof of the convergence of solutions of a chain of linearized problems to the solution of the original nonlinear problems in the norm of the Hilbert space L₂ as the time step τ tends to zero at the rate O(τ). Full article

The rapid development of three-dimensional (3D) acquisition technology based on 3D sensors provides a large volume of data, which are often represented in the form of point clouds. Point cloud representation can preserve the original geometric information along with associated attributes in a 3D space. Therefore, it has been widely adopted in many scene-understanding-related applications such as virtual reality (VR) and autonomous driving. However, the massive amount of point cloud data aggregated from distributed 3D sensors also poses challenges for secure data collection, management, storage, and sharing. Thanks to the characteristics of decentralization and security, Blockchain has great potential to improve point cloud services and enhance security and privacy preservation. Inspired by the rationales behind the software-defined network (SDN) technology, this paper envisions SAUSA, a Blockchain-based authentication network that is capable of recording, tracking, and auditing the access, usage, and storage of 3D point cloud datasets in their life-cycle in a decentralized manner. SAUSA adopts an SDN-inspired point cloud service architecture, which allows for efficient data processing and delivery to satisfy diverse quality-of-service (QoS) requirements. A Blockchain-based authentication framework is proposed to ensure security and privacy preservation in point cloud data acquisition, storage, and analytics. Leveraging smart contracts for digitizing access control policies and point cloud data on the Blockchain, data owners have full control of their 3D sensors and point clouds. In addition, anyone can verify the authenticity and integrity of point clouds in use without relying on a third party. Moreover, SAUSA integrates a decentralized storage platform to store encrypted point clouds while recording references of raw data on the distributed ledger. Such a hybrid on-chain and off-chain storage strategy not only improves robustness and availability, but also ensures privacy preservation for sensitive information in point cloud applications. A proof-of-concept prototype is implemented and tested on a physical network. The experimental evaluation validates the feasibility and effectiveness of the proposed SAUSA solution. Full article