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In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangement of an n-element set is called the nth derangement number. Recently, the degenerate derangement numbers and polynomials have been studied as degenerate versions. Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study probabilistic extension of the degenerate derangement numbers and polynomials, namely the probabilistic degenerate derangement numbers and polynomials associated with Y. In addition, we consider the probabilistic degenerate r-derangement numbers associated with Y and the probabilistic degenerate derangement polynomila of the second kind associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers., Comment: 13 pages

The aim of this paper is to derive a summation formula for the alternating infinite series and an expression for zeta function by using hyperbolic secant random variables. These identities involve Euler numbers and are obtained by computing the moments of the random variable and the moments of the sum of two independent such random variables., Comment: 9 pages

In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study probabilistic degenerate Bernstein polynomials associated with Y which are both probabilistic extension of the degenerate Bernstein polynomials and degenerate version of the probabilistic Bernstein polynomials associated with $Y$. We derive several explicit expressions and certain related identities for those polynomials. In addition, we treat the special cases of the Poisson random variable, the Bernoulli random variable and of the binomial random variable.

In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such functions by using elementary methods. Especially, we obtain multiple angle formulas for the degenerate cotangent and degenerate sine functions., Comment: 7 pages

In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate version of the recent probabilistic proofs on sums of powers of integers., Comment: 7 pages

Chiral magnets have garnered significant interest due to the emergence of unique phenomena prohibited in inversion-symmetric magnets. While the equilibrium characteristics of chiral magnets have been extensively explored through the Dzyaloshinskii-Moriya interaction (DMI), non-equilibrium properties like magnetic damping have received comparatively less attention. We present the inaugural direct observation of chiral damping through Brillouin light scattering (BLS) spectroscopy. Employing BLS spectrum analysis, we independently deduce the Dzyaloshinskii-Moriya interaction (DMI) and chiral damping, extracting them from the frequency shift and linewidth of the spectrum peak, respectively. The resulting linewidths exhibit clear odd symmetry with respect to the magnon wave vector, unambiguously confirming the presence of chiral damping. Our study introduces a novel methodology for quantifying chiral damping, with potential ramifications on diverse nonequilibrium phenomena within chiral magnets.

This paper introduces mhGPT, a lightweight generative pre-trained transformer trained on mental health-related social media and PubMed articles. Fine-tuned for specific mental health tasks, mhGPT was evaluated under limited hardware constraints and compared with state-of-the-art models like MentaLLaMA and Gemma. Despite having only 1.98 billion parameters and using just 5% of the dataset, mhGPT outperformed larger models and matched the performance of models trained on significantly more data. The key contributions include integrating diverse mental health data, creating a custom tokenizer, and optimizing a smaller architecture for low-resource settings. This research could advance AI-driven mental health care, especially in areas with limited computing power.

In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tanx, several expressions for log coshx and an identity for {\pi}2, from a series expansion of tan x, which gives the product expansion of the cosine function., Comment: 13 pages

Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density functional theory (TDDFT), employing the Tamm-Dancoff approximation (TDA) and Gaussian-type atomic orbitals as basis functions. We discuss GPU-efficient algorithms for the derivatives of electron repulsion integrals and exchange-correlation functionals within the range-separated scheme. As an illustrative example, we calculated the TDA-TDDFT gradient of the S1 state of a full-scale green fluorescent protein with explicit water solvent molecules, totaling 4353 atoms, at the wB97X/def2-SVP level of theory. Our algorithm demonstrates favorable parallel efficiencies on a high-speed distributed system equipped with 256 Nvidia A100 GPUs, achieving >70% with up to 64 GPUs and 31% with 256 GPUs, effectively leveraging the capabilities of modern high-performance computing systems., Comment: 13 pages, 9 figures

Let X be the Laplacian random variable with parameters (a,b)=(0,1), and let X1, X2, X3 , ...be a sequence of mutually independent copies of X$. In this note, we explicitly determine the moments of the Laplacian random variable in terms of the Bernoulli and Euler numbers., Comment: 4 pages

In this paper, we introduce a method to tackle Domain Generalized Semantic Segmentation (DGSS) by utilizing domain-invariant semantic knowledge from text embeddings of vision-language models. We employ the text embeddings as object queries within a transformer-based segmentation framework (textual object queries). These queries are regarded as a domain-invariant basis for pixel grouping in DGSS. To leverage the power of textual object queries, we introduce a novel framework named the textual query-driven mask transformer (tqdm). Our tqdm aims to (1) generate textual object queries that maximally encode domain-invariant semantics and (2) enhance the semantic clarity of dense visual features. Additionally, we suggest three regularization losses to improve the efficacy of tqdm by aligning between visual and textual features. By utilizing our method, the model can comprehend inherent semantic information for classes of interest, enabling it to generalize to extreme domains (e.g., sketch style). Our tqdm achieves 68.9 mIoU on GTA5$\rightarrow$Cityscapes, outperforming the prior state-of-the-art method by 2.5 mIoU. The project page is available at https://byeonghyunpak.github.io/tqdm., Comment: ECCV 2024

Estimation of distribution algorithms (EDAs) constitute a new branch of evolutionary optimization algorithms, providing effective and efficient optimization performance in a variety of research areas. Recent studies have proposed new EDAs that employ mutation operators in standard EDAs to increase the population diversity. We present a new mutation operator, a matrix transpose, specifically designed for Bayesian structure learning, and we evaluate its performance in Bayesian structure learning. The results indicate that EDAs with transpose mutation give markedly better performance than conventional EDAs.

A novel initialization method in the fuzzy c-means (FCM) algorithm is proposed for the color clustering problem. Given a set of color points, the proposed initialization extracts dominant colors that are the most vivid and distinguishable colors. Color points closest to the dominant colors are selected as initial centroids in the FCM. To obtain the dominant colors and their closest color points, we introduce reference colors and define a fuzzy membership model between a color point and a reference color.

The research interest of this paper is focused on the efficient clustering task for an arbitrary color data. In order to tackle this problem, we have tried to model the inherent uncertainty and vagueness of color data using fuzzy color model. By taking fuzzy approach to color modeling, we could make a soft decision for the vague regions between neighboring colors. The proposed fuzzy color model defined a three dimensional fuzzy color ball and color membership computation method with two inter-color distances. With the fuzzy color model, we developed a new fuzzy clustering algorithm for an efficient partition of color data. Each fuzzy cluster set has a cluster prototype which is represented by fuzzy color centroid.

A new cluster validity index is proposed for fuzzy clusters obtained from fuzzy c-means algorithm. The proposed validity index exploits inter-cluster proximity between fuzzy clusters. Inter-cluster proximity is used to measure the degree of overlap between clusters. A low proximity value refers to well-partitioned clusters. The best fuzzy c-partition is obtained by minimizing inter-cluster proximity with respect to c. Well-known data sets are tested to show the effectiveness and reliability of the proposed index., Comment: Accepted at FIP-2002

Assume that the moment generating function of the random vari able Y exists in a neighborhood of the origin. We introduce the probabilistic multi-Stirling numbers of the second kind associated with Y and the proba bilistic multi-Lah numbers associated with Y, both of indices (k1,k2,...,kr), by means of the multiple logarithm. Those numbers are respectively probabilistic extensions of the multi-Stirling numbers of the second kind and the multi-Lah numbers which, for (k1,k2,...,kr) = (1,1,...,1), boil down respectively to the Stirling numbers of the second and the unsigned Lah numbers. The aim of this paper is to study some properties, related identities, recurrence relations and explicit expressions of those probabilistic extension numbers in connection with several other special numbers, Comment: 11 pages

Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are constructed from the degenerate cumulant generating function of Y. They are a degenerate version of the probabilistic Stirling numbers of the first kind associated with Y, which were recently introduced by Adell-Benyi. We investigate some properties, related identities, recurrence relations and explicit expressions for those numbers. In addition, we apply our results to the special cases of normal and gamma random variables., Comment: 15 pages

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. The aim of this paper is to study the probabilistic Lah numbers associated with Y and the probabilistic Lah-Bell polynomials associated with Y, as probabilistic versions of the Lah numbers and the Lah-Bell polynomials, respectively. We derive some properties, explicit expressions, recurrence relations and certain identities for those numbers and polynomials. In addition, we treat the special cases that Y is the Poisson random variable with parameter {\alpha} > 0 and the Bernoulli random variable with probability of success p., Comment: 10 pages

Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. We study the probabilistic degenerate r-Stirling numbers of the second kind associated with Y and the probabilistic degenerate r-Bell polynomials associated with Y. They are respectively probabilistic extensions of the degenerate r-Stirling numbers of the second and the degenerate r-Bell polynomials which are studied earlier. The aim of this paper is to obtain their properties, explicit expressions and related identities by means of generating functions., Comment: 10 pages

Ultra-high-Q optical resonators have facilitated recent advancements in on-chip photonics by effectively harnessing nonlinear phenomena providing useful functionalities. While these breakthroughs, primarily focused on the near-infrared region, have extended interest to longer wavelengths holding importance for monitoring and manipulating molecules, the absence of ultra-high-Q resonators in this region remains a significant challenge. Here, we have developed on-chip microresonators with a remarkable Q-factor of 38 million, surpassing previous mid-infrared records by over 30 times. Employing innovative fabrication techniques, including the spontaneous formation of light-guiding geometries during material deposition, resonators with internal multilayer structures have been seamlessly created and passivated with chalcogenide glasses within a single chamber. Major loss factors, especially airborne-chemical absorption, were thoroughly investigated and mitigated by extensive optimization of resonator geometries and fabrication procedures. This allowed us to access the fundamental loss performance offered by doubly purified chalcogenide glass sources, as demonstrated in their fiber form. Exploiting this ultra-high-Q resonator, we successfully demonstrated Brillouin lasing on a chip for the first time in the mid-infrared, with a threshold power of 91.9 {\mu}W and a theoretical Schawlow-Townes linewidth of 83.45 Hz, far surpassing carrier phase noise. Our results showcase the effective integration of cavity-enhanced optical nonlinearities into on-chip mid-infrared photonics., Comment: 10 pages, 5 figures in main script, and 1 figure in methods

We introduce HyperCLOVA X, a family of large language models (LLMs) tailored to the Korean language and culture, along with competitive capabilities in English, math, and coding. HyperCLOVA X was trained on a balanced mix of Korean, English, and code data, followed by instruction-tuning with high-quality human-annotated datasets while abiding by strict safety guidelines reflecting our commitment to responsible AI. The model is evaluated across various benchmarks, including comprehensive reasoning, knowledge, commonsense, factuality, coding, math, chatting, instruction-following, and harmlessness, in both Korean and English. HyperCLOVA X exhibits strong reasoning capabilities in Korean backed by a deep understanding of the language and cultural nuances. Further analysis of the inherent bilingual nature and its extension to multilingualism highlights the model's cross-lingual proficiency and strong generalization ability to untargeted languages, including machine translation between several language pairs and cross-lingual inference tasks. We believe that HyperCLOVA X can provide helpful guidance for regions or countries in developing their sovereign LLMs., Comment: 44 pages; updated authors list and fixed author names

In 2008, Spivey found a recurrence relation for the Bell numbers. We consider the probabilistic r-Bell polynomials associated with which are a probabilistic extension of the r-Bell polynomials. Here Y is a random variable whose moment generating function exists in some neighborhood of the origin . The aim of this paper is to generalize the relation for the Bell numbers to that for the probabilistic r-Bell polynomials associated with Y., Comment: 10 pages

Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. We consider the probabilistic bivariate Bell polynomials associated with Y and the probabilistic bivariate r-Bell polynomials associated with Y. For those polynomials, we derive the recurrence relations corresponding to the ones found by Zheng and Li for the bivariate Bell polynomials and the bivariate r-Bell polynomials., Comment: 10 pages

Clients often partner with AI experts to develop AI applications tailored to their needs. In these partnerships, careful planning and clear communication are critical, as inaccurate or incomplete specifications can result in misaligned model characteristics, expensive reworks, and potential friction between collaborators. Unfortunately, given the complexity of requirements ranging from functionality, data, and governance, effective guidelines for collaborative specification of requirements in client-AI expert collaborations are missing. In this work, we introduce AINeedsPlanner, a workbook that AI experts and clients can use to facilitate effective interchange and clear specifications. The workbook is based on (1) an interview of 10 completed AI application project teams, which identifies and characterizes steps in AI application planning and (2) a study with 12 AI experts, which defines a taxonomy of AI experts' information needs and dimensions that affect the information needs. Finally, we demonstrate the workbook's utility with two case studies in real-world settings., Comment: To appear in DIS 2024

YbB$_6$ is a predicted topological insulator, with experimental evidence for conducting surface states of yet-unproven origin. However, its lack of a natural cleavage plane, and resultant surface-dependent polarity, has obscured its study. We use scanning tunneling microscopy to image the cleaved surface of YbB$_6$, exhibiting several coexisting terminations with distinct atomic structures. Our spectroscopic measurements show band-bending between the terminations, resulting in both conducting and fully-gapped regions. In the conductive regions, we observe spectral peaks that are suggestive of van Hove singularities arising from Rashba spin-split quantum well states. The insulating regions rule out the possibility that YbB$_6$ is a strong topological insulator, while the spin-polarized conducting regions suggest possible utility for spintronic devices., Comment: Submitted to Physical Review Letters

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the derangement polynomials, the derangement polynomials of type 2 and the r-derangement numbers, namely the probabilistic derangement polynomials associated with Y, the probabilistic derangement polynomials of type 2 associated with Y and the probabilistic r-derangement numbers associated Y, respectively. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers. In addition, we consider the special case that Y is the gamma random variable with parameters {\alpha},\b{eta} > 0., Comment: 11 pages

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order $r$, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials., Comment: 15

The aim of this paper is to study probabilistic versions of the degenerate Whitney numbers of the second kind and those of the degenerate Dowling polynomials, namely the probabilistic degenerate Whitney numbers of the second kind associated with Y and the probabilistic degenerate Dowling polynomials associated with Y. Here Y is a random variable whose moment generating function exists in some neighborhood of the origin. We derive some properties, explicit expressions, certain identities, recurrence relations and generating functions for those numbers and polynomials. In addition, we investigate their generalizations, namely the probabilistic degenerate r-Whitney numbers of the second kind associated with Y and the probabilistic degenerate r-Dowling polynomials associated with Y, and get similar results to the aforementioned numbers and polynomials., Comment: 14 pages

We analyze a single-epoch Global mm-VLBI Array (GMVA) observation of the blazar BL Lacertae (BL Lac) at 86 GHz from April 2021. The participation of the upgraded, phased Northern Extended Millimetre Array (NOEMA) adds additional sensitivity to the GMVA, which has facilitated the imaging of BL Lac during an unprecedentedly strong $\gamma$-ray flare. We aim to explore the nature of the inner subparsec jet of BL Lac and the impact of the NOEMA participation in the observation. For the data reduction, we employed two advanced automatic pipelines: rPICARD for the flux density calibration as well as the model-agnostic signal stabilization and GPCAL for the antenna leakage calibration. The conventional hybrid imaging (CLEAN + amplitude and phase self-calibration) was applied to the calibrated visibilities to generate final VLBI images. We performed a ridge-line analysis and Gaussian model-fits on the final jet image to derive the jet parameters. In our data, the presence of NOEMA improves the image sensitivity by a factor of 2.5. The jet shows a clear wiggling structure within 0.4 mas from the core. Our ridge-line analysis suggests the presence of a helical jet structure (i.e., a sinusoidal pattern). Six circular Gaussian components were fitted to the inner jet region. We estimated an apparent brightness temperature of $\sim$3 $\times$ 10$^{12}$ K in the two innermost components. They are likely to be highly boosted by relativistic beaming effect. We find four significant polarized knots in the jet. Interestingly, two of them are located in the core region. Finally, we suggest a number of physical scenarios to interpret our results., Comment: 11 pages, 12 figures, 3 tables, accepted for publication in A&A, in press

We introduce VL2NL, a Large Language Model (LLM) framework that generates rich and diverse NL datasets using only Vega-Lite specifications as input, thereby streamlining the development of Natural Language Interfaces (NLIs) for data visualization. To synthesize relevant chart semantics accurately and enhance syntactic diversity in each NL dataset, we leverage 1) a guided discovery incorporated into prompting so that LLMs can steer themselves to create faithful NL datasets in a self-directed manner; 2) a score-based paraphrasing to augment NL syntax along with four language axes. We also present a new collection of 1,981 real-world Vega-Lite specifications that have increased diversity and complexity than existing chart collections. When tested on our chart collection, VL2NL extracted chart semantics and generated L1/L2 captions with 89.4% and 76.0% accuracy, respectively. It also demonstrated generating and paraphrasing utterances and questions with greater diversity compared to the benchmarks. Last, we discuss how our NL datasets and framework can be utilized in real-world scenarios. The codes and chart collection are available at https://github.com/hyungkwonko/chart-llm., Comment: 22 pages, 5 figures

This paper introduces prompted software engineering (PSE), which integrates prompt engineering to build effective prompts for language-based AI models, to enhance the software development process. PSE enables the use of AI models in software development to produce high-quality software with fewer resources, automating tedious tasks and allowing developers to focus on more innovative aspects. However, effective prompts are necessary to guide software development in generating accurate, relevant, and useful responses, while mitigating risks of misleading outputs. This paper describes how productive prompts should be built throughout the software development cycle., Comment: 10 pages, 1 figure

The harmonic numbers and higher-order harmonic numbers appear frequently in several areas which are related to combinatorial identities, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this paper is to study the degenerate harmonic and degenerate higher-order harmonic numbers, which are respectively degenerate versions of the harmonic and higher-order harmonic numbers, in connection with the degenerate zeta and degenerate Hurwitz zeta function. Here the degenerate zeta and degenerate Hurwitz zeta function are respectively degenerate versions of the Riemann zeta and Hurwitz zeta function. We show that several infinite sums involving the degenerate higher-order harmonic numbers can be expressed in terms of the degenerate zeta function. Furthermore, we demonstrate that an infinite sum involving finite sums of products of the degenerate harmonic numbers can be represented by using the degenerate Hurwitz zeta function., Comment: 11 pages

The aim of this paper is to study the $\lambda$-Stirling numbers of both kinds which are $\lambda$-analogues of Stirling numbers of both kinds. Those numbers have nice combinatorial interpretations when $\lambda$ are positive integers. If $\lambda$ =1, then the $\lambda$-Stirling numbers of both kinds reduce to the Stirling numbers of both kinds. We derive new types of generating functions of the $\lambda$-Stirling numbers of both kinds which are related to the reciprocals of the generalized rising factorials. Furthermore, some related identities are also derived from those generating functions. In addition, all the corresponding results to the $\lambda$-Stirling numbers of both kinds are obtained also for the $\lambda$-analogues of r-Stirling numbers of both kinds which are generalizations of those numbers., Comment: 10 pages

Visual Speech Recognition (VSR) is the task of predicting spoken words from silent lip movements. VSR is regarded as a challenging task because of the insufficient information on lip movements. In this paper, we propose an Audio Knowledge empowered Visual Speech Recognition framework (AKVSR) to complement the insufficient speech information of visual modality by using audio modality. Different from the previous methods, the proposed AKVSR 1) utilizes rich audio knowledge encoded by a large-scale pretrained audio model, 2) saves the linguistic information of audio knowledge in compact audio memory by discarding the non-linguistic information from the audio through quantization, and 3) includes Audio Bridging Module which can find the best-matched audio features from the compact audio memory, which makes our training possible without audio inputs, once after the compact audio memory is composed. We validate the effectiveness of the proposed method through extensive experiments, and achieve new state-of-the-art performances on the widely-used LRS3 dataset., Comment: Accepted by IEEE Transactions on Multimedia

Recently, Kim-Kim investigated the degenerate harmonic numbers and the degenerate hyperharmonic numbers as degenerate versions of the harmonic numbers and the hyperharmonic numbers, respectively. The aim of this paper is to study the higher-order degenerate harmonic numbers and the higher-order degenerate hyperharmonic numbers as higher-order versions for the degenerate harmonic numbers and the degenerate hyperharmonic numbers, respectively. In addition, we study the higher-order alternating degenerate hyperharmonic numbers as an `alternating version' of the higher-order degenerate hyperharmonic numbers. In more detail, we find generating functions of them, explicit expressions for them and some relations among them for those three kinds of numbe, Comment: 9 pages

Recent work has shown that when both the chart and caption emphasize the same aspects of the data, readers tend to remember the doubly-emphasized features as takeaways; when there is a mismatch, readers rely on the chart to form takeaways and can miss information in the caption text. Through a survey of 280 chart-caption pairs in real-world sources (e.g., news media, poll reports, government reports, academic articles, and Tableau Public), we find that captions often do not emphasize the same information in practice, which could limit how effectively readers take away the authors' intended messages. Motivated by the survey findings, we present EmphasisChecker, an interactive tool that highlights visually prominent chart features as well as the features emphasized by the caption text along with any mismatches in the emphasis. The tool implements a time-series prominent feature detector based on the Ramer-Douglas-Peucker algorithm and a text reference extractor that identifies time references and data descriptions in the caption and matches them with chart data. This information enables authors to compare features emphasized by these two modalities, quickly see mismatches, and make necessary revisions. A user study confirms that our tool is both useful and easy to use when authoring charts and captions., Comment: IEEE VIS 2023

rPPG (Remote photoplethysmography) is a technology that measures and analyzes BVP (Blood Volume Pulse) by using the light absorption characteristics of hemoglobin captured through a camera. Analyzing the measured BVP can derive various physiological signals such as heart rate, stress level, and blood pressure, which can be applied to various applications such as telemedicine, remote patient monitoring, and early prediction of cardiovascular disease. rPPG is rapidly evolving and attracting great attention from both academia and industry by providing great usability and convenience as it can measure biosignals using a camera-equipped device without medical or wearable devices. Despite extensive efforts and advances in this field, serious challenges remain, including issues related to skin color, camera characteristics, ambient lighting, and other sources of noise and artifacts, which degrade accuracy performance. We argue that fair and evaluable benchmarking is urgently required to overcome these challenges and make meaningful progress from both academic and commercial perspectives. In most existing work, models are trained, tested, and validated only on limited datasets. Even worse, some studies lack available code or reproducibility, making it difficult to fairly evaluate and compare performance. Therefore, the purpose of this study is to provide a benchmarking framework to evaluate various rPPG techniques across a wide range of datasets for fair evaluation and comparison, including both conventional non-deep neural network (non-DNN) and deep neural network (DNN) methods. GitHub URL: https://github.com/remotebiosensing/rppg, Comment: 20 pages, 10 figures

Recently, the degenerate harmonic and the degenerate hyperharmonic numbers are introduced respectively as degenerate versions of the harmonic and the hyperharmonic numbers. The aim of this paper is to introduce the degenerate harmonic-Fubini polynomials and numbers related to the degenerate harmonic numbers and to study their properties, explicit expressions and some identities. In addition, as generalizations of those polynomials and numbers, we also introduce the degenerate hyperharmonic-Fubini polynomials and numbers related to the degenerate hyperharmonic numbers and derive similar results to the degenerate harmonic-Fubini polynomials and numbers. \end{abstract}, Comment: 12 pages

This paper presents a novel reference architecture for blockchain-enabled federated learning (BCFL), a state-of-the-art approach that amalgamates the strengths of federated learning and blockchain technology.We define smart contract functions, stakeholders and their roles, and the use of interplanetary file system (IPFS) as key components of BCFL and conduct a comprehensive analysis. In traditional centralized federated learning, the selection of local nodes and the collection of learning results for each round are merged under the control of a central server. In contrast, in BCFL, all these processes are monitored and managed via smart contracts. Additionally, we propose an extension architecture to support both crossdevice and cross-silo federated learning scenarios. Furthermore, we implement and verify the architecture in a practical real-world Ethereum development environment. Our BCFL reference architecture provides significant flexibility and extensibility, accommodating the integration of various additional elements, as per specific requirements and use cases, thereby rendering it an adaptable solution for a wide range of BCFL applications. As a prominent example of extensibility, decentralized identifiers (DIDs) have been employed as an authentication method to introduce practical utilization within BCFL. This study not only bridges a crucial gap between research and practical deployment but also lays a solid foundation for future explorations in the realm of BCFL. The pivotal contribution of this study is the successful implementation and verification of a realistic BCFL reference architecture. We intend to make the source code publicly accessible shortly, fostering further advancements and adaptations within the community., Comment: 14 pages, 15 figures, 3 tables

It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results. The aim of this paper is to study the generalized degenerate (r, s)-Stirling numbers of the second and their natural extensions to polynomials, namely the generalized degenerate (r, s)-Bell polynomials, arising from certain degenerate boson normal ordering. We derive some properties, explicit expressions and generating functions for those numbers and polynomials. The generalized degenerate (r, s)-Stirling numbers of the second and the degenerate boson normal ordering are respectively degenerate versions of the generalized (r, s)-Stirling numbers of the second and the boson normal ordering studied earlier by Blasiak-Person-Solomon., Comment: 13