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We present new expressions for the $k$-generalized Fibonacci numbers, say $F_k(n)$. They satisfy the recurrence $F_k(n) = F_k(n-1) +\dots+F_k(n-k)$. Explicit expressions for the roots of the auxiliary (or characteristic) polynomial are presented, using Fuss-Catalan numbers. Properties of the roots are enumerated. We quantify the accuracy of asymptotic approximations for $F_k(n)$ for $n\gg1$. Our results subsume and extend some results published by previous authors. We also comment on the use of multinomial sums for the $k$-generalized Fibonacci numbers and related sequences. We also employ the generating function to express $F_k(n)$ as a concise (non-nested) sum of binomial coefficients for arbitrary $k$. Finally, we present a basis (or `fundamental solutions') to solve the above recurrence for arbitrary initial conditions., Comment: 18 pages, 2 figures, v2 cited additional references

In 2013, Tapolcai demonstrated that a network with two completely independent spanning trees (CISTs) is sufficient for implementing protection routing. In a graph \( G \) with \( k \geq 2 \) spanning trees, denoted as \( T = \{T_1, T_2, \ldots, T_k\} \), these trees are termed completely independent spanning trees (CISTs) if the paths connecting any two vertices \( x \) and \( y \) across different trees do not overlap in vertices or edges, other than \( x \) and \( y \) themselves. Specifically, when \( k = 2 \), the trees form a dual-CIST, and when \( k = 3 \), they constitute a tri-CIST. The problem of determining whether a dual-CIST exists in a graph is NP-complete, as noted by Hasunuma (2002). In data networks, dual-CISTs facilitate fault-tolerant routing, while tri-CISTs enhance both reliability and secure message distribution. Recent advancements have focused on constructing CISTs within hypercube variant networks. Pai and Chang proposed a technique to generate two CISTs in hypercubes variant networks and called for the development of algorithms to extend this to more CISTs. Methods for constructing three CISTs have been established for various hypercube variants, including crossed cubes, Mobius cubes, and shuffle cubes. In 2017, Darties et al. asked if the 6-dimensional hypercube \( Q_6 \) can have three completely independent spanning trees, a question that remains unanswered. In this paper, we show how to construct three completely independent spanning trees in \( Q_n \) for \( n \geq 7 \). Two of these trees have diameters of at most \(2n+1\) and \(2n+3\), respectively, and the third tree has a diameter of at most \(2n+4\).

Intracorporeal needle-based therapeutic ultrasound (NBTU) is a minimally invasive option for intervening in malignant brain tumors, commonly used in thermal ablation procedures. This technique is suitable for both primary and metastatic cancers, utilizing a high-frequency alternating electric field (up to 10 MHz) to excite a piezoelectric transducer. The resulting rapid deformation of the transducer produces an acoustic wave that propagates through tissue, leading to localized high-temperature heating at the target tumor site and inducing rapid cell death. To optimize the design of NBTU transducers for thermal dose delivery during treatment, numerical modeling of the acoustic pressure field generated by the deforming piezoelectric transducer is frequently employed. The bioheat transfer process generated by the input pressure field is used to track the thermal propagation of the applicator over time. Magnetic resonance thermal imaging (MRTI) can be used to experimentally validate these models. Validation results using MRTI demonstrated the feasibility of this model, showing a consistent thermal propagation pattern. However, a thermal damage isodose map is more advantageous for evaluating therapeutic efficacy. To achieve a more accurate simulation based on the actual brain tissue environment, a new finite element method (FEM) simulation with enhanced damage evaluation capabilities was conducted. The results showed that the highest temperature and ablated volume differed between experimental and simulation results by 2.1884{\deg}C (3.71%) and 0.0631 cm$^3$ (5.74%), respectively. The lowest Pearson correlation coefficient (PCC) for peak temperature was 0.7117, and the lowest Dice coefficient for the ablated area was 0.7021, indicating a good agreement in accuracy between simulation and experiment., Comment: 9 pages, 9 figures, 7 tables

The most recent advances in medical imaging that have transformed diagnosis, especially in the case of interpreting X-ray images, are actively involved in the healthcare sector. The advent of digital image processing technology and the implementation of deep learning models such as Convolutional Neural Networks (CNNs) have made the analysis of X-rays much more accurate and efficient. In this article, some essential techniques such as edge detection, region-growing technique, and thresholding approach, and the deep learning models such as variants of YOLOv8-which is the best object detection and segmentation framework-are reviewed. We further investigate that the traditional image processing techniques like segmentation are very much simple and provides the alternative to the advanced methods as well. Our review gives useful knowledge on the practical usage of the innovative and traditional approaches of manual X-ray interpretation. The discovered information will help professionals and researchers to gain more profound knowledge in digital interpretation techniques in medical imaging., Comment: 29 pages, 20 figures

This article examines the promising prospects and potential hurdles associated with the development of MentorAI, a conceptual AI-driven mentorship platform for professional growth yet to be actualized. The article explores the essential characteristics and technological underpinnings required for the successful creation and efficacy of the MentorAI platform in providing tailored mentorship experiences. The article highlights the transformative potential of MentorAI on various dimensions of professional growth, such as boosting career progression, nurturing skill development, and supporting a balanced work-life environment for professionals. MentorAI, through its AI-based approach, aspires to offer real-time guidance, resources, and assistance customized to each individual's specific needs and goals. Furthermore, the article examines the core technologies crucial to MentorAI's operation, including artificial intelligence, machine learning, and natural language comprehension. These technologies will empower the platform to process user inputs, deliver context-sensitive responses, and dynamically adjust to user preferences and objectives. The deployment of MentorAI presents potential challenges and ethical concerns, as with any groundbreaking technology. The article outlines critical issues like data protection, security, algorithmic bias, and moral quandaries concerning substituting human mentors with AI systems. Addressing these challenges proactively and deliberately is vital to ensure a positive impact on users.

Public Cloud Computing has become a fundamental part of modern IT infrastructure as its adoption has transformed the way businesses operate. However, cloud security concerns introduce new risks and challenges related to data protection, sharing, and access control. A synergistic integration of blockchain with the cloud holds immense potential. Blockchain's distributed ledger ensures transparency, immutability, and efficiency as it reduces the reliance on centralized authorities. Motivated by this, our framework proposes a secure data ecosystem in the cloud with the key aspects being Data Rights, Data Sharing, and Data Validation. Also, this approach aims to increase its interoperability and scalability by eliminating the need for data migration. This will ensure that existing public cloud-based systems can easily deploy blockchain enhancing trustworthiness and non-repudiation of cloud data.

This research paper proposes a novel methodology for image-to-image style transfer on objects utilizing a single deep convolutional neural network. The proposed approach leverages the You Only Look Once version 8 (YOLOv8) segmentation model and the backbone neural network of YOLOv8 for style transfer. The primary objective is to enhance the visual appeal of objects in images by seamlessly transferring artistic styles while preserving the original object characteristics. The proposed approach's novelty lies in combining segmentation and style transfer in a single deep convolutional neural network. This approach omits the need for multiple stages or models, thus resulting in simpler training and deployment of the model for practical applications. The results of this approach are shown on two content images by applying different style images. The paper also demonstrates the ability to apply style transfer on multiple objects in the same image., Comment: In Proceedings of the Fourth International Conference on Innovations in Computational Intelligence and Computer Vision

The global scientific landscape emerges from a complex interplay of collaboration and competition, where nations vie for dominance while simultaneously fostering the diffusion of knowledge on a global scale. This raises crucial questions: What underlying patterns govern international scientific recognition and influence? How does this structure impact knowledge dissemination? Traditional models view the global scientific ecosystem through a core-periphery lens, with Western nations dominating knowledge production. Here, we investigate the dynamics of international scientific recognition through the lens of national preferences, introducing a novel signed measure to characterize national citation preferences and enabling a network analysis of international scientific recognition. We find that scientific recognition is related to cultural and political factors in addition to economic strength and scientific quality. Our analysis challenges the conventional core-periphery narrative, uncovering instead several communities of international knowledge production that are rapidly fragmenting the scientific recognition ecosystem. Moreover, we provide compelling evidence that this network significantly constrains the diffusion of ideas across international borders. The resulting network framework for global scientific recognition sheds light on the barriers and opportunities for collaboration, innovation, and the equitable recognition of scientific advancements, with significant consequences for policymakers seeking to foster inclusive and impactful international scientific endeavors., Comment: 30 pages (main text), 3 figures (main text), 1 table (main text), 20 SI pages

The negative binomial distribution NB$(k,r)$ of Type I is the probability distribution for a sequence of independent Bernoulli trials (with success parameter $p\in(0,1)$) with $r$ nonoverlapping success runs of length $\ge k$. We present a new, more concise, expression for its probability mass function. We show it can also be succinctly written using hypergeometric functions. We also present new expressions (combinatorial sums) for its moments and factorial moments, as opposed to only the mean and variance (which are already known). Next, we present an alternative non-combinatorial viewpoint, which yields expressions for the factorial moments not only for nonoverlapping success runs, but also for runs with an overlap of $\ell$, where $\ell\in[0,k-1]$. The case $\ell=k-1$ is the negative binomial distribution NB$(k,r)$ of Type III. The results also yield the solution for the negative binomial distribution NB$(k,r)$ with a minimum gap between the success runs (explained in the text). Addendum 1/23/2024: The probability mass function and factorial moments are derived from the probability generating function. Addendum 1/26/2024: Alternative expressions are presented for the negative binomial distribution NB$(k,r)$ of Type II., Comment: 25 pages

We derive a simple expression for the $r^{th}$ factorial moment $\mu_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically, $\mu_{(r)} = r!f_k((r+1)k+r)/((qp^k)^{r+1})$., Comment: 5 pages

Autonomous underwater vehicles (AUV) have become the de facto vehicle for remote operations involving oceanography, inspection, and monitoring tasks. These vehicles operate in different and often challenging environments; hence, the design and development of the AUV involving hydrodynamics and control systems need to be designed in detail. This book chapter presents a study on the modelling and robust control of a research vehicle in the presence of uncertainties. The vehicle's dynamic behaviour is modelled using a 6-degree-of-freedom approach, considering the effect of ocean currents. The level flight requirements for different speeds are derived, and the resulting model is decomposed into horizontal and vertical subsystems for linear analysis. The simulation results presented focus on the efficacy of linear controllers within three key subsystems: depth, yaw, and speed. Moreover, level-flight outcomes are demonstrated for a speed of 4 knots. The nonlinear control strategies employed in this study encompass conventional and sliding-mode control (SMC) methodologies. To ensure accurate tracking performance, the controller design considers the vehicle's dynamics with various uncertainties such as ocean currents, parameter uncertainty, CG (Center of Gravity) deviation and buoyancy variation. Both conventional and nonlinear SMC controllers' outcomes are showcased with a lawn-mowing manoeuvre scenario. A systematic comparison is drawn between the robustness of SMC against disturbances and parameter fluctuations in contrast to conventional controllers. Importantly, these results underscore the trade-off that accompanies SMC's robustness, as it necessitates a higher level of complexity in terms of controller design, intricate implementation intricacies, and the management of chattering phenomena., Comment: Accepted for publication in Assistive Robotics, CRC Press, Taylor & Francis, USA. This is the preprint version of the book chapter

The factorial moments of the standard Poisson distribution are well known and are simple, but the raw moments are considered to be more complicated (Touchard polynomials). The present note presents a recurrence relation and an explicit combinatorial sum for the raw moments of the Poisson distribution of order $k$. Unlike the standard Poisson distribution (the case $k=1$), for $k>1$ the structure of the raw and factorial moments have many similarities and the raw moments are not more complicated (formally, at least) than the factorial moments. We remark briefly on the central moments (i.e.~moments centered on the mean) of the Poisson distribution of order $k$., Comment: 6 pages

Questions posed by information-seeking users often contain implicit false or potentially harmful assumptions. In a high-risk domain such as maternal and infant health, a question-answering system must recognize these pragmatic constraints and go beyond simply answering user questions, examining them in context to respond helpfully. To achieve this, we study assumptions and implications, or pragmatic inferences, made when mothers ask questions about pregnancy and infant care by collecting a dataset of 2,727 inferences from 500 questions across three diverse sources. We study how health experts naturally address these inferences when writing answers, and illustrate that informing existing QA pipelines with pragmatic inferences produces responses that are more complete, mitigating the propagation of harmful beliefs., Comment: Accepted to NAACL 2024

The rise of social media platforms has led to an increase in cyber-aggressive behavior, encompassing a broad spectrum of hostile behavior, including cyberbullying, online harassment, and the dissemination of offensive and hate speech. These behaviors have been associated with significant societal consequences, ranging from online anonymity to real-world outcomes such as depression, suicidal tendencies, and, in some instances, offline violence. Recognizing the societal risks associated with unchecked aggressive content, this paper delves into the field of Aggression Content Detection and Behavioral Analysis of Aggressive Users, aiming to bridge the gap between disparate studies. In this paper, we analyzed the diversity of definitions and proposed a unified cyber-aggression definition. We examine the comprehensive process of Aggression Content Detection, spanning from dataset creation, feature selection and extraction, and detection algorithm development. Further, we review studies on Behavioral Analysis of Aggression that explore the influencing factors, consequences, and patterns associated with cyber-aggressive behavior. This systematic literature review is a cross-examination of content detection and behavioral analysis in the realm of cyber-aggression. The integrated investigation reveals the effectiveness of incorporating sociological insights into computational techniques for preventing cyber-aggressive behavior. Finally, the paper concludes by identifying research gaps and encouraging further progress in the unified domain of socio-computational aggressive behavior analysis., Comment: 40 pages, 14 figures