This study presents a highly efficient and accurate approximate method based on a convergence acceleration parameter to approximate a nonlinear multidimensional aggregation population balance equation. Optimal tuning of the acceleration parameter significantly enhances solution quality over extended temporal domains and overcomes key limitations of existing approaches. Deeper mathematical insight is provided through a discussion of the existence of the proposed approach within the framework of a nonlinear aggregation model. Convergence analysis and error estimates are established using the fixed point theorem and the contractive mapping principle, thereby proving the existence of solutions to the aggregation model. The accuracy and efficiency of the proposed approach are demonstrated by computing approximate solutions for the number density function and its moments for physically relevant kernels. For analytically tractable kernels, results are validated against exact solutions. For complex size-dependent kernels, including polymerization, Ruckenstein-Pulvermacher, and shear kernels, the obtained results are compared with the existing finite volume scheme, homotopy analysis method, and optimal decomposition method. The results show that the proposed approach achieves higher accuracy in capturing number density functions and their integral moments while requiring significantly fewer series terms than existing methods.
Selectively gated state-space models (SSMs), notably Mamba, are increasingly used for financial time series, yet how they internally represent market regimes (bull, bear, sideways) remains opaque. This paper applies Mechanistic Interpretability (MI) to a six-layer Mamba trained on approximately twenty-one years of daily data for a point-in-time set of S&P 500 constituents plus macroeconomic and Fama-French factors, decomposing per-layer hidden states with Top-K Sparse Autoencoders (SAEs). Our central contribution is methodological and cautionary. A prior, uncontrolled configuration recovered market regimes from SAE features at F1 = 1.00. Under a controlled protocol that (i) removes the three input features that overlap the HMM label definition, (ii) disables the auxiliary regime-classification head, (iii) uses a point-in-time constituent universe, and (iv) evaluates against labels disjoint from the inputs, the same regime label is recovered at only F1 = 0.398, indistinguishable from a logistic baseline on raw inputs (0.435) and from an SAE trained on a randomly initialized, untrained Mamba (0.364). A 2 & times; 2 attribution grid shows the near-perfect result is an interaction of auxiliary supervision and label-defining inputs: neither factor alone exceeds F1 similar to 0.40. Effect sizes with block-bootstrap inference show the residual selective-gate (Delta t) regime effect is statistically detectable but economically negligible and uniform across layers rather than layer-specialized; the apparent polysemanticity gradient disappears under continuous, theory-grounded measures. We contribute a reproducible leakage-control protocol for interpretability evaluation of financial SSMs, a quantified demonstration that previously reported regime structure is a label-contamination artifact, and a modest economically grounded feature subset that genuinely survives the controls.
Random numbers are central to cryptography and various other tasks. The intrinsic probabilistic nature of quantum mechanics has allowed us to construct a large number of quantum random number generators (QRNGs) that are distinct from the traditional true number generators. This article provides a review of the existing QRNGs with a focus on their various possible features (e.g., device independence, semi-device independence) that are not achievable in the classical world. It also discusses the origin, applicability, and other facets of randomness. Specifically, the origin of randomness is explored from the perspective of a set of hierarchical axioms for quantum mechanics, implying that succeeding axioms can be regarded as a superstructure constructed on top of a structure built by the preceding axioms. The axioms considered are: (Q1) incompatibility and uncertainty; (Q2) contextuality; (Q3) entanglement; (Q4) nonlocality and (Q5) indistinguishability of identical particles. Relevant toy generalized probability theories (GPTs) are introduced, and it is shown that the origin of random numbers in different types of QRNGs known today are associated with different layers of nonclassical theories and all of them do not require all the features of quantum mechanics. Further, classification of the available QRNGs has been done and the technological challenges associated with each class are critically analyzed. Commercially available QRNGs are also compared.
Viral infections remain a significant threat to global health, causing widespread morbidity and mortality. The continuous emergence of new viral strains and the limitations of current antiviral therapies highlight the urgent need for effective and safe treatment options. Herbal remedies, long used in traditional medicine, offer promising avenues for antiviral drug discovery. In this study, we explore the antiviral potential of phytoconstituents from Glycyrrhiza glabra (Yasthimadhu), a well-known medicinal herb with established therapeutic properties. Using in silico molecular docking techniques, we investigated the interaction of key bioactive compounds Glycyrrhizin, Shinflavanone, Hispaglabridin A, Glycyrrhetic acid, Glabiridin, and Shinpterocarpin with the SARS-CoV-2 main protease (3CLpro; PDB ID: 6LU7), a critical viral enzyme responsible for as predicted binding of SARS-CoV-2. Our findings reveal that these phytochemicals predicted binding and complex stability consistent with potential SARS-CoV-2 3CLpro inhibition, which warrants experimental validation. This study underscores the promise of Glycyrrhiza glabra phytoconstituents as potential SARS-CoV-2 3CLpro inhibitors, paving the way for further experimental validation and drug development.
Globally, colon cancer ranks third among the leading causes of death from cancer. Colon cancer can be prevented by detecting and removing precancerous lesions, such as polyps, at an early stage. In polyp segmentation, artificial intelligence, particularly deep learning, plays an important role. This study aims to propose two models based on the DeepLabv3 + model with attention, as well as the attention-based Bidirectional Long Short Term Memory model. Attention mechanisms learn to focus on features that are most relevant for the segmentation of polyps. In addition, the attention-based Bidirectional Long Short Term Memory mechanism also learns to identify long-range dependencies within an image. Three publicly available datasets were used to evaluate the proposed models: CVC-ColonDB, CVC-Clinic DB, and Kvasir-SEG. This study found that attention and attention-based Bidirectional Long Short-Term Memory DeepLabv3 + models effectively improved DeepLabv3 + performance and provided a comparative analysis of state of the art models. In healthcare practice, these proposed models may improve the accuracy and effectiveness of polyp segmentation.
