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We study the distribution of colloidal particles confined in drying spherical droplets using both dynamic density functional theory (DDFT) and particle-based simulations. In particular, we focus on the advection-dominated regime typical of aqueous droplets drying at room temperature and systematically investigate the role of hydrodynamic interactions during this nonequilibrium process. In general, drying produces transient particle concentration gradients within the droplet in this regime, with a considerable accumulation of particles at the droplet's liquid-vapor interface. We find that these gradients become significantly larger with pairwise hydrodynamic interactions between colloidal particles instead of a free-draining hydrodynamic approximation; however, the solvent's boundary conditions at the droplet's interface (unbounded, slip, or no-slip) do not have a significant effect on the particle distribution. DDFT calculations leveraging radial symmetry of the drying droplet are in excellent agreement with particle-based simulations for free-draining hydrodynamics, but DDFT unexpectedly fails for pairwise hydrodynamic interactions after the particle concentration increases during drying, manifesting as an ejection of particles from the droplet. We hypothesize that this unphysical behavior originates from an inaccurate approximation of the two-body density correlations based on the bulk pair correlation function, which we support by measuring the confined equilibrium two-body density correlations using particle-based simulations. We identify some potential strategies for addressing this issue in DDFT., Comment: 16 pages, 7 figures

We investigate the problem of determining the zeros of quaternionic polynomials using matrix method. In a recent paper, Dar et al. \cite{RD} proved that the zeros of a quaternionic polynomial and the left eigenvalues of the corresponding companion matrix are identical. Building on this, we employ various newly developed matrix techniques to establish several results concerning the location of the zeros of regular polynomials of a quaternionic variable with quaternionic coefficients. These findings significantly enhance the understanding of quaternionic polynomials and their eigenvalues, offering a broader perspective on their mathematical properties., Comment: Right (and left) Quaternionic eigenvalues, Quaternionic polynomials, Companion matrix

Graph Neural Networks (GNNs) are powerful at solving graph classification tasks, yet applied problems often contain noisy labels. In this work, we study GNN robustness to label noise, demonstrate GNN failure modes when models struggle to generalise on low-order graphs, low label coverage, or when a model is over-parameterized. We establish both empirical and theoretical links between GNN robustness and the reduction of the total Dirichlet Energy of learned node representations, which encapsulates the hypothesized GNN smoothness inductive bias. Finally, we introduce two training strategies to enhance GNN robustness: (1) by incorporating a novel inductive bias in the weight matrices through the removal of negative eigenvalues, connected to Dirichlet Energy minimization; (2) by extending to GNNs a loss penalty that promotes learned smoothness. Importantly, neither approach negatively impacts performance in noise-free settings, supporting our hypothesis that the source of GNNs robustness is their smoothness inductive bias.

This paper explores the operational principles and monomiality principle that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining consistent with established findings. The primary focus of this study is the introduction of degenerate multidimensional Hermite-based Appell polynomials (DMHAP), denoted as ${}_{\mathbb{H}}\mathbb{A}^{[r]}_n(l_1, l_2, l_3, \dots, l_r; \vartheta)$. These DMHAP form essential families of orthogonal polynomials, demonstrating strong connections with classical Hermite and Appell polynomials. Additionally, we derive symmetric identities and examine the fundamental properties of these polynomials. Finally, we establish an operational framework to investigate and develop these polynomials further., Comment: 15 pages, 1 table

If $P(z)=\sum_{j=0}^{n}a_jz^j$ is a polynomial of degree $n$ having no zero in $|z|<1,$ then it was recently proved that for every $p\in[0,+\infty]$ and $s=0,1,\ldots,n-1,$ \begin{align*} \left\|a_nz+\frac{a_s}{\binom{n}{s}}\right\|_{p}\leq \frac{\left\|z+\delta_{0s}\right\|_p}{\left\|1+z\right\|_p}\left\|P\right\|_{p}, \end{align*} where $\delta_{0s}$ is the Kronecker delta. In this paper, we consider the class of polynomials having no zero in $|z|<\rho,$ $\rho\geq 1$ and obtain some generalizations of above inequality., Comment: Polynomials; Visser's inequality; Inequalities in the complex domain

In this paper, we consider a modified version of Smirnov operator and obtain some Bernstein-type inequalities preserved by this operator. In particular, we prove some compact generalizations of the well-known inequalities of Bernstein, Erd\"{o}s and Lax, Ankeny and Rivlin and others.

Deceptive patterns (DPs) in digital interfaces manipulate users into making unintended decisions, exploiting cognitive biases and psychological vulnerabilities. These patterns have become ubiquitous across various digital platforms. While efforts to mitigate DPs have emerged from legal and technical perspectives, a significant gap in usable solutions that empower users to identify and make informed decisions about DPs in real-time remains. In this work, we introduce AutoBot, an automated, deceptive pattern detector that analyzes websites' visual appearances using machine learning techniques to identify and notify users of DPs in real-time. AutoBot employs a two-staged pipeline that processes website screenshots, identifying interactable elements and extracting textual features without relying on HTML structure. By leveraging a custom language model, AutoBot understands the context surrounding these elements to determine the presence of deceptive patterns. We implement AutoBot as a lightweight Chrome browser extension that performs all analyses locally, minimizing latency and preserving user privacy. Through extensive evaluation, we demonstrate AutoBot's effectiveness in enhancing users' ability to navigate digital environments safely while providing a valuable tool for regulators to assess and enforce compliance with DP regulations.

We derive a thermoelectric inequality in thermoelectric conversion between the material figure of merit (ZT) and the module effective ZT using the Constant Seebeck-coefficient Approximation combining with the Wiedemann-Franz law. In a P-N leg-pair module, the effective ZT lies between the individual ZT values of the P- and N-legs. In a single-leg module, however, the effective ZT is less than approximately one-third of the leg's ZT. This reduction results from the need for an external wire to complete the circuit, introducing additional thermal and electrical losses. Multi-dimensional numerical analysis shows that, although structural optimization can mitigate these losses, the system efficiency remains limited to below half of the ideal single-leg material efficiency. Our findings explain the single-leg efficiency overestimation and highlight the importance of optimizing the P-N leg-pair module structure. They also underscore the need for thermoelectric leg-compatibility, particularly with respect to Seebeck coefficients., Comment: (main) 17 pages, 1 table, 3 figures, 15 references (all including Supporting Materials) 24 pages, 2 supporting tables, 2 supporting figures

We present near-simultaneous X-ray and optical polarization measurements in the high synchrotron peaked (HSP) blazar Mrk 421. The X-ray polarimetric observations were carried out using {\it Imaging X-ray Polarimetry Explorer} ({\it IXPE}) on 06 December 2023. During {\it IXPE} observations, we also carried out optical polarimetric observations using 104cm Sampurnanand telescope at Nainital and multi-band optical imaging observations using 2m Himalayan Chandra Telescope at Hanle. From model-independent analysis of {\it IXPE} data, we detected X-ray polarization with degree of polarization ($\Pi_X$) of 8.5$\pm$0.5\% and an electric vector position angle ($\Psi_X$) of 10.6$\pm$1.7 degrees in the 2$-$8 keV band. From optical polarimetry on 06 December 2023, in B, V, and R bands, we found values of $\Pi_B$ = 4.27$\pm$0.32\%, $\Pi_V$= 3.57$\pm$0.31\%, and $\Pi_R$= 3.13$\pm$0.25\%. The value of $\Pi_B$ is greater than that observed at longer optical wavelengths, with the degree of polarization suggesting an energy-dependent trend, gradually decreasing from higher to lower energies. This is consistent with that seen in other HSP blazars and favour a stratified emission region encompassing a shock front. The emission happening in the vicinity of the shock front will be more polarized due to the ordered magnetic field resulting from shock compression. The X-ray emission, involving high-energy electrons, originates closer to the shock front than the optical emission. The difference in the spatial extension could plausibly account for the observed variation in polarization between X-ray and optical wavelengths. This hypothesis is further supported by the broadband spectral energy distribution modeling of the X-ray and optical data., Comment: 9 pages, 3 figures. Accepted for publication in ApJ

In computer-aided diagnosis tools employed for skin cancer treatment and early diagnosis, skin lesion segmentation is important. However, achieving precise segmentation is challenging due to inherent variations in appearance, contrast, texture, and blurry lesion boundaries. This research presents a robust approach utilizing a dilated convolutional residual network, which incorporates an attention-based spatial feature enhancement block (ASFEB) and employs a guided decoder strategy. In each dilated convolutional residual block, dilated convolution is employed to broaden the receptive field with varying dilation rates. To improve the spatial feature information of the encoder, we employed an attention-based spatial feature enhancement block in the skip connections. The ASFEB in our proposed method combines feature maps obtained from average and maximum-pooling operations. These combined features are then weighted using the active outcome of global average pooling and convolution operations. Additionally, we have incorporated a guided decoder strategy, where each decoder block is optimized using an individual loss function to enhance the feature learning process in the proposed AD-Net. The proposed AD-Net presents a significant benefit by necessitating fewer model parameters compared to its peer methods. This reduction in parameters directly impacts the number of labeled data required for training, facilitating faster convergence during the training process. The effectiveness of the proposed AD-Net was evaluated using four public benchmark datasets. We conducted a Wilcoxon signed-rank test to verify the efficiency of the AD-Net. The outcomes suggest that our method surpasses other cutting-edge methods in performance, even without the implementation of data augmentation strategies.

We report the experimental observation of fully developed Kolmogorov turbulence originating from self-excited vortex flows in a three-dimensional (3D) dust cloud. The characteristic -5/3 scaling of three-dimensional Kolmogorov turbulence is universally observed in both the spatial and temporal power spectra. Additionally, the 2/3 scaling in the second-order structure function further confirms the presence of Kolmogorov turbulence. We also identified a slight deviation in the tails of the probability distribution functions for velocity gradients. The dust cloud formed in the diffused region away from the electrode and above the glass device surface in the glow discharge experiments. The dust rotation was observed in multiple experimental campaigns under different discharge conditions at different spatial locations and background plasma environments., Comment: 13 pages, 14 figures

Federated Learning (FL) is the most widely adopted collaborative learning approach for training decentralized Machine Learning (ML) models by exchanging learning between clients without sharing the data and compromising privacy. However, since great data similarity or homogeneity is taken for granted in all FL tasks, FL is still not specifically designed for the industrial setting. Rarely this is the case in industrial data because there are differences in machine type, firmware version, operational conditions, environmental factors, and hence, data distribution. Albeit its popularity, it has been observed that FL performance degrades if the clients have heterogeneous data distributions. Therefore, we propose a Lightweight Industrial Cohorted FL (LICFL) algorithm that uses model parameters for cohorting without any additional on-edge (clientlevel) computations and communications than standard FL and mitigates the shortcomings from data heterogeneity in industrial applications. Our approach enhances client-level model performance by allowing them to collaborate with similar clients and train more specialized or personalized models. Also, we propose an adaptive aggregation algorithm that extends the LICFL to Adaptive LICFL (ALICFL) for further improving the global model performance and speeding up the convergence. Through numerical experiments on real-time data, we demonstrate the efficacy of the proposed algorithms and compare the performance with existing approaches.

Large Language Models (LLMs) demonstrate remarkable capabilities in replicating human tasks and boosting productivity. However, their direct application for data extraction presents limitations due to a prioritisation of fluency over factual accuracy and a restricted ability to manipulate specific information. Therefore to overcome these limitations, this research leverages the knowledge representation power of pre-trained LLMs and the targeted information access enabled by RAG models, this research investigates a general-purpose accurate data scraping recipe for RAG models designed for language generation. To capture knowledge in a more modular and interpretable way, we use pre trained language models with a latent knowledge retriever, which allows the model to retrieve and attend over documents from a large corpus. We utilised RAG model architecture and did an in-depth analysis of their capabilities under three tasks: (i) Semantic Classification of HTML elements, (ii) Chunking HTML text for effective understanding, and (iii) comparing results from different LLMs and ranking algorithms. While previous work has developed dedicated architectures and training procedures for HTML understanding and extraction, we show that LLMs pre-trained on standard natural language with an addition of effective chunking, searching and ranking algorithms, can prove to be efficient data scraping tool to extract complex data from unstructured text. Future research directions include addressing the challenges of provenance tracking and dynamic knowledge updates within the proposed RAG-based data extraction framework. By overcoming these limitations, this approach holds the potential to revolutionise data extraction from vast repositories of textual information.