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It is known that the Funk transform (the Funk-Radon transform) is invertible in the class of even (symmetric) continuous functions defined on the unit 2-sphere S^2. In this article, for the reconstruction of f from C(S^2) (can be non-even), an additional condition (to reconstruct an odd function) is found, and the injectivity of the so-called two data Funk transform is considered. An iterative inversion formula of the transform is presented. Such inversions have theoretical significance in convexity theory, integral geometry and spherical tomography. Also, the Funk-Radon transform is used in Diffusion-weighted magnetic resonance imaging., Comment: 18 pages, 2 figures

We generalize some of the well-known results of Karlin and James to Banach spaces with besselian Schauder frames (then in particular with unconditional Schauder frames). It is well-known that each Banach space with an unconditional Schauder basis has the Pe\l czy\'{n}ski's property (u). Also, that all of the classical Banach spaces ($C(\omega^{\omega})$, $C([0,1])$, $L_{1}([0,1])$, the James's space $\mathcal{J}$, and for each $p\geq q>1$: $K(l_{p},l_{q})$, $l_{p}\otimes_{\pi}l_{q^{*}}$, and $l_{p^{*}}\otimes_{\varepsilon}l_{q}$) have no unconditional Schauder bases. In this paper, we extend these results to Banach spaces with besselian Schauder frames (then in particular with unconditional Schauder frames). Finally, for each Banach space $E$ with a finite dimensional decomposition, we give an explicit method to construct a Schauder frame for $E$. Therefore, the Szarek's famous example becomes an example of a Banach space with a Schauder frame which fails to have a Schauder basis.

This paper explores a novel approach to modeling the positional dynamics of stars using discrete dynamical systems. We define star evolution through discrete-time update rules based on right ascension, declination, and distance, incorporating chaotic behavior via nonlinear functions and external perturbations. By applying Ricci flow and Riemannian metrics, we provide new insights into the positional dynamics of stars. Theoretical computations of Perelman entropy are used to assess system complexity, with high-precision Runge-Kutta methods ensuring accurate solutions for our chaotic model. We quantify chaos using Lyapunov exponents and perform bifurcation analysis to study how parameter variations affect the dynamics. Comparing our model to the Lorenz attractor reveals both similarities and unique characteristics in stellar dynamics. Our results show that entropy increases exponentially, indicating that predicting star positions with precision becomes increasingly challenging over time. This study advances the understanding of chaos in celestial systems and contributes to dynamical systems theory by integrating chaos theory with astronomical modeling., Comment: 30 pages,8 figures

Continual learning (CL) refers to the ability to continually learn over time by accommodating new knowledge while retaining previously learned experience. While this concept is inherent in human learning, current machine learning methods are highly prone to overwrite previously learned patterns and thus forget past experience. Instead, model parameters should be updated selectively and carefully, avoiding unnecessary forgetting while optimally leveraging previously learned patterns to accelerate future learning. Since hand-crafting effective update mechanisms is difficult, we propose meta-learning a transformer-based optimizer to enhance CL. This meta-learned optimizer uses attention to learn the complex relationships between model parameters across a stream of tasks, and is designed to generate effective weight updates for the current task while preventing catastrophic forgetting on previously encountered tasks. Evaluations on benchmark datasets like SplitMNIST, RotatedMNIST, and SplitCIFAR-100 affirm the efficacy of the proposed approach in terms of both forward and backward transfer, even on small sets of labeled data, highlighting the advantages of integrating a meta-learned optimizer within the continual learning framework., Comment: Published at the 3rd Conference on Lifelong Learning Agents (CoLLAs), 2024

This study compares Term Frequency-Inverse Document Frequency (TF-IDF) features with Sentence Transformers for detecting writers' stances--favorable, opposing, or neutral--towards three significant topics: COVID-19 vaccine, digital transformation, and women empowerment. Through empirical evaluation, we demonstrate that Sentence Transformers outperform TF-IDF features across various experimental setups. Our team, dzStance, participated in a stance detection competition, achieving the 13th position (74.91%) among 15 teams in Women Empowerment, 10th (73.43%) in COVID Vaccine, and 12th (66.97%) in Digital Transformation. Overall, our team's performance ranked 13th (71.77%) among all participants. Notably, our approach achieved promising F1-scores, highlighting its effectiveness in identifying writers' stances on diverse topics. These results underscore the potential of Sentence Transformers to enhance stance detection models for addressing critical societal issues., Comment: Accepted for publication in the conference proceedings of ArabicNLP 2024

Psychological evidence reveals the influence of personality traits on decision-making. For instance, agreeableness is generally associated with positive outcomes in negotiations, whereas neuroticism is often linked to less favorable outcomes. This paper introduces a simulation framework centered on Large Language Model (LLM) agents endowed with synthesized personality traits. The agents negotiate within bargaining domains and possess customizable personalities and objectives. The experimental results show that the behavioral tendencies of LLM-based simulations could reproduce behavioral patterns observed in human negotiations. The contribution is twofold. First, we propose a simulation methodology that investigates the alignment between the linguistic and economic capabilities of LLM agents. Secondly, we offer empirical insights into the strategic impact of Big-Five personality traits on the outcomes of bilateral negotiations. We also provide a case study based on synthesized bargaining dialogues to reveal intriguing behaviors, including deceitful and compromising behaviors., Comment: Findings of EMNLP 2024

The reactivity and mechanistic intricacies of azatrienes in Diels-Alder reactions have been relatively unexplored despite their intriguing potential applications. In this study, we employ Molecular Electron Density Theory to theoretically investigate the hetero-Diels-Alder reaction involving azatrienes with ethyl vinyl ether and allenyl methyl ether. Analysis of Conceptual Density Functional Theory, energetic profiles, and the topological characteristics is conducted to elucidate the reactions. The revealed mechanism manifests as a polar one-step two-stages process under kinetic control. We establish a clear relationship of between the periselectivity, regioselectivity, and stereoselectivity on one hand and the characteristics of the reactions mechanism on the other hand. The influence of weak interactions on reaction activation barriers and bonding evolution are discussed in detail. We demonstrate that substituents enhancing the reverse electron density flux facilitate the feasibility of the reactions. The results lay ground for a meticulous control of the reaction of azatriene in similar synthetic scenarios., Comment: accepted in Journal of Molecular Graphics and Modelling

Current blockchain-based reputation solutions for crowdsourcing fail to tackle the challenge of ensuring both efficiency and privacy without compromising the scalability of the blockchain. Developing an effective, transparent, and privacy-preserving reputation model necessitates on-chain implementation using smart contracts. However, managing task evaluation and reputation updates alongside crowdsourcing transactions on-chain substantially strains system scalability and performance. This paper introduces RollupTheCrowd, a novel blockchain-powered crowdsourcing framework that leverages zkRollups to enhance system scalability while protecting user privacy. Our framework includes an effective and privacy-preserving reputation model that gauges workers' trustworthiness by assessing their crowdsourcing interactions. To alleviate the load on our blockchain, we employ an off-chain storage scheme, optimizing RollupTheCrowd's performance. Utilizing smart contracts and zero-knowledge proofs, our Rollup layer achieves a significant 20x reduction in gas consumption. To prove the feasibility of the proposed framework, we developed a proof-of-concept implementation using cutting-edge tools. The experimental results presented in this paper demonstrate the effectiveness and scalability of RollupTheCrowd, validating its potential for real-world application scenarios., Comment: 9 pages, 8 figures, 2 tables, Paper accepted at IEEE 48th Annual Computers, Software, and Applications Conference (COMPSAC) IEEE, Osaka, Japan (2024)

We aim to present families of generators with minimal cardinality -- we call such families bases -- of the free abelian group Was$(\mathbb{K}) / \mathbf{Z}(\mathbb{K})$ whenever $\mathbb{K}$ is a real cyclotomic field $\mathbb{Q}(\zeta_n)^{+}$ or $\mathbb{K}$ is a totally deployed abelian number field. Here, Was$(\mathbb{K})$ refers to the group of Washington's circular units of $\mathbb{K}$ and $\mathbf{Z}(\mathbb{K})$ refers to the group of roots of unity lying in $\mathbb{K}$.

In this paper, we define a q-adic factorial and we demonstrate some properties of a generalized p-adic gamma function. Also, some numerical examples have been given

This review article discusses the roles of federated learning (FL) and transfer learning (TL) in cancer detection based on image analysis. These two strategies powered by machine learning have drawn a lot of attention due to their potential to increase the precision and effectiveness of cancer diagnosis in light of the growing importance of machine learning techniques in cancer detection. FL enables the training of machine learning models on data distributed across multiple sites without the need for centralized data sharing, while TL allows for the transfer of knowledge from one task to another. A comprehensive assessment of the two methods, including their strengths, and weaknesses is presented. Moving on, their applications in cancer detection are discussed, including potential directions for the future. Finally, this article offers a thorough description of the functions of TL and FL in image-based cancer detection. The authors also make insightful suggestions for additional study in this rapidly developing area.

In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the theorem of Lame. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.

Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using the spherical Radon transform over spheres centered on a plane, the injectivity of the so-called two data spherical Radon transform is considered. An inversion formula of the transform that uses the local data of the spherical integrals to reconstruct the unknown function is presented. Such inversions are the mathematical base of modern modalities of imaging, such as Thermo and photoacoustic tomography and radar imaging, and have theoretical significance in many areas of mathematics, Comment: 20 pages, 2 figures

In this paper, we explore novel chaotic dynamics derived from the Riemann and von Mangoldt function formula regarding the distribution of nontrivial zeros of the Riemann zeta function. By computing Lyapunov exponents, we demonstrate that the derived dynamics exhibit chaotic behavior when the gaps between zeros are within a certain bound, specifically up to 2.4. Beyond this threshold, the dynamics do not display chaotic behavior. Furthermore, we derive a chaotic operator for the Riemann zeta function within the critical strip, utilizing the correction term from the Riemann-von Mangoldt formula. We establish the chaotic nature and Hermiticity of this operator, and discuss its diagonalization properties. Moreover, our study reveals a remarkable compatibility between our derived chaotic operator and the quantum hydrogen model, as evidenced by the analysis of its eigenvalues resembling the energy levels of hydrogen. Numerical evidence, including Lyapunov exponents, bifurcation analysis, and entropy computation, underscores the unpredictability of the system. Additionally, we establish a connection between our chaotic operator and the prime number theorem regarding the density of primes. Furthermore, our investigation suggests that this chaotic operator strongly supports the validity of the Riemann hypothesis, as proposed by Hilbert and Polya. These findings shed light on the intricate relationship between chaotic dynamics, number theory, and quantum mechanics, offering new perspectives on the behavior of the Riemann zeta function and its zeros. Finally, we demonstrate the Hermiticity and diagonalization properties of our operator using the spectral theorem, further elucidating its mathematical properties and unboundedness., Comment: 21 pages, 3 figures

In this paper, we present an innovative derivation of chaotic dynamics rooted in the Montgomery conjecture, specifically addressing the pair correlation of Riemann zeta function zeros. Our exploration unveils a recursive relation inspired by the conjecture, manifesting chaotic behavior. Remarkably, we interpret this derived chaotic dynamics as a unique representation of an electrical system, providing a novel perspective within the domain of electrical engineering. Beyond this groundbreaking derivation, our study delves into the potential applications of chaos theory, bifurcation analysis, and entropy within the framework of this electrical system. We scrutinize the implications of chaos for signal processing, conduct stability analysis through bifurcation studies, and investigate the role of entropy in quantifying the randomness or predictability of electrical signals. Additionally, we explore energy distribution aspects within the electrical system, shedding light on how chaotic dynamics influence energy dissipation and allocation. In the course of our research, a new finding emerged, contributing to our understanding of the derived chaotic dynamics. This discovery enhances the applicability of our framework within electrical engineering, paving the way for innovative applications and deeper explorations in the realm of system dynamics. Moreover, we draw comparisons with the dynamics presented in our recent paper published in the European Physical Journal, specifically addressing Yitang Zhang's contributions. This comparative analysis further underscores the unique characteristics and potential applications of the derived chaotic dynamics. This study not only elucidates the intricate connection between chaotic dynamics and number theory but also offers a transformative perspective that extends the boundaries of conventional electrical system analysis, Comment: 25 pages ,13 figures

Federated learning has emerged as a promising approach for training machine learning models on decentralized data sources while preserving data privacy. However, challenges such as communication bottlenecks, heterogeneity of client devices, and non-i.i.d. data distribution pose significant obstacles to achieving optimal model performance. We propose a novel framework that combines federated learning with meta-learning techniques to enhance both efficiency and generalization capabilities. Our approach introduces a federated modulator that learns contextual information from data batches and uses this knowledge to generate modulation parameters. These parameters dynamically adjust the activations of a base model, which operates using a MAML-based approach for model personalization. Experimental results across diverse datasets highlight the improvements in convergence speed and model performance compared to existing federated learning approaches. These findings highlight the potential of incorporating contextual information and meta-learning techniques into federated learning, paving the way for advancements in distributed machine learning paradigms.

The problem of recovering a moment-determinate multivariate function $f$ via its moment sequence is studied. Under mild conditions on $f$, the point-wise and $L_1$-rates of convergence for the proposed constructions are established. The cases where $f$ is the indicator function of a set, and represents a discrete probability mass function are also investigated. Calculations of the approximants and simulation studies are conducted to graphically illustrate the behavior of the approximations in several simple examples. Analytical and simulated errors of proposed approximations are recorded in Tables 1-3.

In this article, we consider several models of random walks in one or several dimensions, additionally allowing, at any unit of time, a reset (or "catastrophe") of the walk with probability $q$. We establish the distribution of the final altitude. We prove algebraicity of the generating functions of walks of bounded height $h$ (showing in passing the equivalence between Lagrange interpolation and the kernel method). To get these generating functions, our approach offers an algorithm of cost $O(1)$, instead of cost $O(h^3)$ if a Markov chain approach would be used. The simplest nontrivial model corresponds to famous dynamics in population genetics: the Moran model. We prove that the height of these Moran walks asymptotically follows a discrete Gumbel distribution. For $q=1/2$, this generalizes a model of carry propagation over binary numbers considered e.g. by von Neumann and Knuth. For generic $q$, using a Mellin transform approach, we show that the asymptotic height exhibits fluctuations for which we get an explicit description (and, in passing, new bounds for the digamma function). We end by showing how to solve multidimensional generalizations of these walks (where any subset of particles is attributed a different probability of dying) and we give an application to the soliton wave model.

This paper discusses the role of Transfer Learning (TL) and transformers in cancer detection based on image analysis. With the enormous evolution of cancer patients, the identification of cancer cells in a patient's body has emerged as a trend in the field of Artificial Intelligence (AI). This process involves analyzing medical images, such as Computed Tomography (CT) scans and Magnetic Resonance Imaging (MRIs), to identify abnormal growths that may help in cancer detection. Many techniques and methods have been realized to improve the quality and performance of cancer classification and detection, such as TL, which allows the transfer of knowledge from one task to another with the same task or domain. TL englobes many methods, particularly those used in image analysis, such as transformers and Convolutional Neural Network (CNN) models trained on the ImageNet dataset. This paper analyzes and criticizes each method of TL based on image analysis and compares the results of each method, showing that transformers have achieved the best results with an accuracy of 97.41% for colon cancer detection and 94.71% for Histopathological Lung cancer. Future directions for cancer detection based on image analysis are also discussed., Comment: 6 pages, 4 figures, and 3 tables

We consider the stability of Schauder frames and besselian Schauder frames under perturbations. Our results are inspirit close to the results of Heil [18].

In this study, we delve into a novel dynamic system inspired by Montgomery's pair correlation conjecture in number theory. The dynamic system is intricately designed to emulate the behavior of the nontrivial zeros of the Riemann zeta function. Our exploration encompasses bifurcation analysis and Lyapunov exponents to scrutinize the system's behavior and stability, offering insights into both small and large initial conditions. Our efforts extend to unveiling the probability distribution characterizing the dynamics for varying initial conditions. The dynamic system unfolds intricate behaviors, displaying sensitivity to initial conditions and revealing complex bifurcation patterns. Small deviations in the initial conditions unveil significantly different trajectories, reminiscent of chaotic systems. Lyapunov exponents become our lens into understanding stability and chaos within the system. A comparative analysis between the dynamic system's approximate solutions and the actual nontrivial zeros of the Riemann zeta function enhances our comprehension of model accuracy and its potential implications for number theory. This research illuminates the versatility of dynamic systems as analogs for studying complex mathematical phenomena. It provides fresh perspectives on the pair correlation conjecture, establishing connections with nonlinear dynamics and chaos theory. Notably, we delve into the boundedness of solutions for both small and large initial conditions, unraveling the distinctive probability distribution governing the dynamics in each scenario. Furthermore, we introduce an in-depth analysis of the entropy of our dynamic system for both small and large initial conditions. The entropy study enhances our understanding of the predictability and stability of the system, shedding light on its behavior in different parameter regimes., Comment: 37pages,14figure,4tables

The surveillance of indoor air quality is paramount for ensuring environmental safety, a task made increasingly viable due to advancements in technology and the application of artificial intelligence and deep learning (DL) tools. This paper introduces an intelligent system dedicated to monitoring air quality and categorizing activities within indoor environments using a DL approach based on 1D Convolutional Neural Networks (1D-CNNs). Our system integrates six diverse sensors to gather measurement parameters, which subsequently train a 1D CNN model for activity recognition. This proposed model boasts a lightweight and edge-deployable design, rendering it ideal for real-time applications. We conducted our experiments utilizing an air quality dataset specifically designed for Activity of Daily Living (ADL) classification. The results illustrate the proposed model's efficacy, achieving a remarkable accuracy of 97.00%, a minimal loss value of 0.15%, and a swift prediction time of 41 milliseconds., Comment: 6 pages, 6 figures, and 4 tables

This research paper delves into the dynamics of a novel ecology model that describes the intricate interplay between radioactivity and cancer cases. Organized into three main sections, the study covers numerical analysis using advanced techniques, the analysis of discrete dynamical systems, and explores the potential applications of the model in the context of cancer research and ecological systems. By conducting a comprehensive bifurcation analysis, we unveil the model's sensitivity to external factors, interactive behaviors between radioactivity and cancer cases, and the emergence of multiple attractors. These findings open up new avenues for understanding cancer dynamics, ecological systems, and clinical scenarios, where even subtle variations in external factors can lead to significant variations in cancer incidence. The insights gained from this study have promising implications for both theoretical and applied research in cancer epidemiology and ecology, providing a deeper understanding of the complex dynamics underlying these systems. In our research, we present a new ecology model that reveals the intricate and often nonlinear relationship between radioactivity and cancer incidence, offering novel insights into cancer dynamics and environmental influences., Comment: 31 pages,16figures

This study delves into the realm of chaotic dynamics derived from Dirichlet L functions, drawing inspiration from Yitang Zhang's groundbreaking work on Landau Siegel zeros. The dynamic behavior reveals a profound chaos, corroborated by the calculated Lyapunov exponents and entropy, which attest to the system's inherent unpredictability. The examination of stability further uncovers the instability of fixed points. Most notably, these findings unveil a compelling connection between the studied dynamics and the intricate distribution of zeros, thereby offering indirect support for Zhang's groundbreaking theorem concerning Landau Siegel zeros., Comment: 15 pages,9 figures