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We explore tree-based macroeconomic regime-switching in the context of the dynamic Nelson-Siegel (DNS) yield-curve model. In particular, we customize the tree-growing algorithm to partition macroeconomic variables based on the DNS model's marginal likelihood, thereby identifying regime-shifting patterns in the yield curve. Compared to traditional Markov-switching models, our model offers clear economic interpretation via macroeconomic linkages and ensures computational simplicity. In an empirical application to U.S. Treasury bond yields, we find (1) important yield curve regime switching, and (2) evidence that macroeconomic variables have predictive power for the yield curve when the short rate is high, but not in other regimes, thereby refining the notion of yield curve ``macro-spanning".

We present an approach for generating differentially private synthetic text using large language models (LLMs), via private prediction. In the private prediction framework, we only require the output synthetic data to satisfy differential privacy guarantees. This is in contrast to approaches that train a generative model on potentially sensitive user-supplied source data and seek to ensure the model itself is safe to release. We prompt a pretrained LLM with source data, but ensure that next-token predictions are made with differential privacy guarantees. Previous work in this paradigm reported generating a small number of examples (<10) at reasonable privacy levels, an amount of data that is useful only for downstream in-context learning or prompting. In contrast, we make changes that allow us to generate thousands of high-quality synthetic data points, greatly expanding the set of potential applications. Our improvements come from an improved privacy analysis and a better private selection mechanism, which makes use of the equivalence between the softmax layer for sampling tokens in LLMs and the exponential mechanism. Furthermore, we introduce a novel use of public predictions via the sparse vector technique, in which we do not pay privacy costs for tokens that are predictable without sensitive data; we find this to be particularly effective for structured data., Comment: 12 pages main text + 15 pages appendix

In this paper, we show that a Clifford algebra valued function is slice if and only if it is in the kernel of Dunkl-spherical Dirac operator and a slice function $f$ is slice regular if and only if it is in the kernel of the Dunkl-Cauchy-Riemann operator of a certain parameter. Based on this observation and the inverse Dunkl intertwining operator, we present a new approach to construct a family of classical monogenic functions from a given holomorphic function., Comment: 15 pages

We examine the relationship between learnability and robust (or agnostic) learnability for the problem of distribution learning. We show that, contrary to other learning settings (e.g., PAC learning of function classes), realizable learnability of a class of probability distributions does not imply its agnostic learnability. We go on to examine what type of data corruption can disrupt the learnability of a distribution class and what is such learnability robust against. We show that realizable learnability of a class of distributions implies its robust learnability with respect to only additive corruption, but not against subtractive corruption. We also explore related implications in the context of compression schemes and differentially private learnability., Comment: In NeurIPS 2023

This paper presents TRACE, a tool to analyze the quality of 2D embeddings generated through dimensionality reduction techniques. Dimensionality reduction methods often prioritize preserving either local neighborhoods or global distances, but insights from visual structures can be misleading if the objective has not been achieved uniformly. TRACE addresses this challenge by providing a scalable and extensible pipeline for computing both local and global quality measures. The interactive browser-based interface allows users to explore various embeddings while visually assessing the pointwise embedding quality. The interface also facilitates in-depth analysis by highlighting high-dimensional nearest neighbors for any group of points and displaying high-dimensional distances between points. TRACE enables analysts to make informed decisions regarding the most suitable dimensionality reduction method for their specific use case, by showing the degree and location where structure is preserved in the reduced space., Comment: 4 pages, 3 figures, Accepted at ECML-PKDD 2024. For a demo video, see https://youtu.be/mtyFzXt51Jw. Code is available at https://github.com/aida-ugent/TRACE

Personalized recommendation systems often drive users towards more extreme content, exacerbating opinion polarization. While (content-aware) moderation has been proposed to mitigate these effects, such approaches risk curtailing the freedom of speech and of information. To address this concern, we propose and explore the feasibility of \emph{content-agnostic} moderation as an alternative approach for reducing polarization. Content-agnostic moderation does not rely on the actual content being moderated, arguably making it less prone to forms of censorship. We establish theoretically that content-agnostic moderation cannot be guaranteed to work in a fully generic setting. However, we show that it can often be effectively achieved in practice with plausible assumptions. We introduce two novel content-agnostic moderation methods that modify the recommendations from the content recommender to disperse user-item co-clusters without relying on content features. To evaluate the potential of content-agnostic moderation in controlled experiments, we built a simulation environment to analyze the closed-loop behavior of a system with a given set of users, recommendation system, and moderation approach. Through comprehensive experiments in this environment, we show that our proposed moderation methods significantly enhance stance neutrality and maintain high recommendation quality across various data scenarios. Our results indicate that achieving stance neutrality without direct content information is not only feasible but can also help in developing more balanced and informative recommendation systems without substantially degrading user engagement.

Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions introduces unique challenges due to its sparsity. Merely embedding nodes as trajectories in the latent space overlooks this sparsity, emphasizing the need to quantify uncertainty around the latent positions. In this paper, we propose TGNE (\textbf{T}emporal \textbf{G}aussian \textbf{N}etwork \textbf{E}mbedding), an innovative method that bridges two distinct strands of literature: the statistical analysis of networks via Latent Space Models (LSM)\cite{Hoff2002} and temporal graph machine learning. TGNE embeds nodes as piece-wise linear trajectories of Gaussian distributions in the latent space, capturing both structural information and uncertainty around the trajectories. We evaluate TGNE's effectiveness in reconstructing the original graph and modelling uncertainty. The results demonstrate that TGNE generates competitive time-varying embedding locations compared to common baselines for reconstructing unobserved edge interactions based on observed edges. Furthermore, the uncertainty estimates align with the time-varying degree distribution in the network, providing valuable insights into the temporal dynamics of the graph. To facilitate reproducibility, we provide an open-source implementation of TGNE at \url{https://github.com/aida-ugent/tgne}.

Dynamic Link Prediction (DLP) addresses the prediction of future links in evolving networks. However, accurately portraying the performance of DLP algorithms poses challenges that might impede progress in the field. Importantly, common evaluation pipelines usually calculate ranking or binary classification metrics, where the scores of observed interactions (positives) are compared with those of randomly generated ones (negatives). However, a single metric is not sufficient to fully capture the differences between DLP algorithms, and is prone to overly optimistic performance evaluation. Instead, an in-depth evaluation should reflect performance variations across different nodes, edges, and time segments. In this work, we contribute tools to perform such a comprehensive evaluation. (1) We propose Birth-Death diagrams, a simple but powerful visualization technique that illustrates the effect of time-based train-test splitting on the difficulty of DLP on a given dataset. (2) We describe an exhaustive taxonomy of negative sampling methods that can be used at evaluation time. (3) We carry out an empirical study of the effect of the different negative sampling strategies. Our comparison between heuristics and state-of-the-art memory-based methods on various real-world datasets confirms a strong effect of using different negative sampling strategies on the test Area Under the Curve (AUC). Moreover, we conduct a visual exploration of the prediction, with additional insights on which different types of errors are prominent over time.

Line-scan mode facilitates fast-speed and high-throughput imaging with developing a suitable optical transverse needle focus. Metasurface with periodic structures such as diffractive rings, ellipses, and gratings could enable discrete focus evolving into line focus under momentum conservation, but still face the challenge of extremely low light power utilization brought by inevitably multiple high-order diffractions. In addition, the designed focus requires the selection of particular optical functional materials. High dielectric constants in atomic transition metal dichalcogenides make significant phase modulation by bringing phase singularity at zero-reflection possible. However, no light power is available for use at zero-reflection and a balance between phase and amplitude modulation is needed. In this work, above issues are simultaneously solved by designing a monolayer MoS2 based Fresnel strip structure. An optical needle primary focus with a transverse length of 40 {\mu}m (~80 {\lambda}) is obtained, which is the longest value recorded so far, together with a sub-diffraction-limited lateral spot and a broad working wavelength range. This specially developed structure not only concentrates light power in primary diffraction by breaking restriction of momentum conservation, but also guarantees a consistent phase across different strips. The novel optical manipulation way provided here together with the longer focus length for flat optics will show promising applications in biology, oncology, nanofabrication, energy harvesting, and optical information processing., Comment: 22 pages, 5 figures

KamerRaad is an AI tool that leverages large language models to help citizens interactively engage with Belgian political information. The tool extracts and concisely summarizes key excerpts from parliamentary proceedings, followed by the potential for interaction based on generative AI that allows users to steadily build up their understanding. KamerRaad's front-end, built with Streamlit, facilitates easy interaction, while the back-end employs open-source models for text embedding and generation to ensure accurate and relevant responses. By collecting feedback, we intend to enhance the relevancy of our source retrieval and the quality of our summarization, thereby enriching the user experience with a focus on source-driven dialogue., Comment: 4 pages, 2 figures, submitted to 2024 ECML-PKDD demo track

This paper addresses a long-standing problem in the field of accounting: mapping company-specific ledger accounts to a standardized chart of accounts. We propose a novel solution, TopoLedgerBERT, a unique sentence embedding method devised specifically for ledger account mapping. This model integrates hierarchical information from the charts of accounts into the sentence embedding process, aiming to accurately capture both the semantic similarity and the hierarchical structure of the ledger accounts. In addition, we introduce a data augmentation strategy that enriches the training data and, as a result, increases the performance of our proposed model. Compared to benchmark methods, TopoLedgerBERT demonstrates superior performance in terms of accuracy and mean reciprocal rank., Comment: 8 pages, 4 figures

In this paper we consider the kernel of the radially deformed Fourier transform introduced in the context of Clifford analysis in [10]. By adapting the Laplace transform method from [4], we obtain the Laplace domain expressions of the kernel for the cases of $m=2$ and $m > 2$ when $1+c=\frac{1}{n}, n\in \mathbb{N}_0\backslash\{1\}$ with $n$ odd. Moreover, we show that the expressions can be simplified using the Poisson kernel and the generating function of the Gegenbauer polynomials. As a consequence, the inverse formulas are used to get the integral expressions of the kernel in terms of Mittag-Leffler functions., Comment: 23 pages

Variable selection methods are required in practical statistical modeling, to identify and include only the most relevant predictors, and then improving model interpretability. Such variable selection methods are typically employed in regression models, for instance in this article for the Poisson Log Normal model (PLN, Chiquet et al., 2021). This model aim to explain multivariate count data using dependent variables, and its utility was demonstrating in scientific fields such as ecology and agronomy. In the case of the PLN model, most recent papers focus on sparse networks inference through combination of the likelihood with a L1 -penalty on the precision matrix. In this paper, we propose to rely on a recent penalization method (SIC, O'Neill and Burke, 2023), which consists in smoothly approximating the L0-penalty, and that avoids the calibration of a tuning parameter with a cross-validation procedure. Moreover, this work focuses on the coefficient matrix of the PLN model and establishes an inference procedure ensuring effective variable selection performance, so that the resulting fitted model explaining multivariate count data using only relevant explanatory variables. Our proposal involves implementing a procedure that integrates the SIC penalization algorithm (epsilon-telescoping) and the PLN model fitting algorithm (a variational EM algorithm). To support our proposal, we provide theoretical results and insights about the penalization method, and we perform simulation studies to assess the method, which is also applied on real datasets.

Medical report generation has achieved remarkable advancements yet has still been faced with several challenges. First, the inherent imbalance in the distribution of normal and abnormal cases may lead models to exhibit a biased focus on normal samples, resulting in unreliable diagnoses. Second, the frequent occurrence of common template sentences in the reports may overwhelm the critical abnormal information. Moreover, existing works focus on 2D chest X-rays, leaving CT report generation underexplored due to the high-dimensional nature of CT images and the limited availability of CT-report pairs. Recently, LLM has shown a great ability to generate reliable answers with appropriate prompts, which shed light on addressing the aforementioned challenges. In this paper, we propose Dia-LLaMA, a framework to adapt the LLaMA2-7B for CT report generation by incorporating diagnostic information as guidance prompts. Considering the high dimension of CT, we leverage a pre-trained ViT3D with perceiver to extract the visual information. To tailor the LLM for report generation and emphasize abnormality, we extract additional diagnostic information by referring to a disease prototype memory bank, which is updated during training to capture common disease representations. Furthermore, we introduce disease-aware attention to enable the model to adjust attention for different diseases. Experiments on the chest CT dataset demonstrated that our proposed method outperformed previous methods and achieved state-of-the-art on both clinical efficacy performance and natural language generation metrics. The code will be made publically available., Comment: 10 pages

Utilizing potent representations of the large vision-language models (VLMs) to accomplish various downstream tasks has attracted increasing attention. Within this research field, soft prompt learning has become a representative approach for efficiently adapting VLMs such as CLIP, to tasks like image classification. However, most existing prompt learning methods learn text tokens that are unexplainable, which cannot satisfy the stringent interpretability requirements of Explainable Artificial Intelligence (XAI) in high-stakes scenarios like healthcare. To address this issue, we propose a novel explainable prompt learning framework that leverages medical knowledge by aligning the semantics of images, learnable prompts, and clinical concept-driven prompts at multiple granularities. Moreover, our framework addresses the lack of valuable concept annotations by eliciting knowledge from large language models and offers both visual and textual explanations for the prompts. Extensive experiments and explainability analyses conducted on various datasets, with and without concept labels, demonstrate that our method simultaneously achieves superior diagnostic performance, flexibility, and interpretability, shedding light on the effectiveness of foundation models in facilitating XAI. The code will be made publically available.

With the rapid development of power distribution systems (PDSs), the number of terminal devices and the types of delivered services involved are constantly growing. These trends make the operations of PDSs highly dependent on the support of advanced communication networks, which face two related challenges. The first is to provide sufficient flexibility, resilience, and security to meet varying demands and ensure the proper operation of gradually diversifying network services. The second is to realize the automatic identification of terminal devices, thus reducing the network maintenance burden. To solve these problems, this paper presents a novel multiservice network integration and device authentication slice-based network slicing scheme. In this scheme, the integration of PDS communication networks enables network resource sharing, and recovery from communication interruption is achieved through network slicing in the integrated network. Authentication servers periodically poll terminal devices, adjusting network slice ranges based on authentication results, thereby facilitating dynamic network slicing. Additionally, secure plug-and-play support for PDS terminal devices and network protection are achieved through device identification and dynamic adjustment of network slices. On this basis, a network optimization and upgrading methodology for load balancing and robustness enhancement is further proposed. This approach is designed to improve the performance of PDS communication networks, adapting to ongoing PDS development and the evolution of PDS services. The simulation results show that the proposed schemes endow a PDS communication network with favorable resource utilization, fault recovery, terminal device plug-and-play support, load balancing, and improved network robustness.

Grid modernization has increased the reliance of power networks on cyber networks within distribution systems (DSs), heightening their vulnerability to disasters. Communication network failures significantly impede DS load recovery by diminishing observation and control. Prior research has largely ignored the need for integrated recovery of DS power and cyber networks' centralized control. Indeed, communication network restoration is critical for speedy load recovery through DS automation based microgrid formation. This paper exploits the data routing capabilities of software-defined networking (SDN) to enhance centralized control recovery in DS communication networks, incorporating it into a comprehensive DS restoration model. This model, tailored to the control requirements of load restoration, strategically allocates limited communication resources to re-establish connections between the operation center and terminal devices. Subsequently, DS automation is employed to orchestrate DS microgrid formation for power resupply. Additionally, we introduce a cyclic algorithm designed to optimize the load recovery via a multi-step, cooperative process. The efficacy of the proposed method is demonstrated on IEEE 33-node and IEEE 123-node test feeders.

Distribution system (DS) communication failures following extreme events often degrade monitoring and control functions, thus preventing the acquisition of complete global DS component state information, on which existing post-disaster DS restoration methods are based. This letter proposes methods of inferring the states of DS components in the case of incomplete component state information. By using the known DS information, the operating states of unobservable DS branches and buses can be inferred, providing complete information for DS performance restoration before full communication recovery

The interactions between power, transportation, and information networks (PTIN), are becoming more profound with the advent of smart city technologies. Existing mobile energy storage resource (MESR)-based power distribution network (PDN) restoration schemes often neglect the interdependencies among PTIN, thus, efficient PDN restoration cannot be achieved. This paper outlines the interacting factors of power supply demand, traffic operation efficiency, communication coverage, electric vehicle (EV) deployment capability, and PDN controllability among PTIN and further develops a PTIN-interacting model to reflect the chained recovery effect of the MESR-based restoration process. On this basis, a two-stage PDN restoration scheme is proposed that utilizes three emergency resources, including EVs, mobile energy storage systems (MESSs), and unmanned aerial vehicles (UAVs), to restore the power supply and communication of PDNs. This scheme first improves the distribution automation function, EV deployment capability, and traffic operation efficiency by prioritizing the recovery of communication network (CN) and urban traffic network (UTN) loads. Then, EVs and MESSs are further scheduled to achieve a better PDN restoration effect with the support of the restored CNs and UTNs. Case studies on a PDN, CN, and UTN integrated test system are conducted to verify the effectiveness of the proposed scheme. The results show that the prioritized load recovery operation for CN and UTN facilities in this scheme greatly improves the PDN restoration effect.

The higher step Grushin operators $\Delta_{\alpha}$ are a family of sub-elliptic operators which degenerate on a sub-manifold of $\mathbb{R}^{n+m}$. This paper establishes Carleman-type inequalities for these operators. It is achieved by deriving a weighted $L^{p}-L^{q}$ estimate for the Grushin-harmonic projector. The crucial ingredient in the proof is the addition formula for Gegenbauer polynomials due to T. Koornwinder and Y. Xu. As a consequence, we obtain the strong unique continuation property for the Schr\"odinger operators $-\Delta_{\alpha}+V$ at points of the degeneracy manifold, where $V$ belongs to certain $ L^{r}_{{\rm loc}}(\mathbb{R}^{n+m})$., Comment: Comments Welcome

In one-shot federated learning (FL), clients collaboratively train a global model in a single round of communication. Existing approaches for one-shot FL enhance communication efficiency at the expense of diminished accuracy. This paper introduces FedPFT (Federated Learning with Parametric Feature Transfer), a methodology that harnesses the transferability of foundation models to enhance both accuracy and communication efficiency in one-shot FL. The approach involves transferring per-client parametric models (specifically, Gaussian mixtures) of features extracted from foundation models. Subsequently, each parametric model is employed to generate synthetic features for training a classifier head. Experimental results on eight datasets demonstrate that FedPFT enhances the communication-accuracy frontier in both centralized and decentralized FL scenarios, as well as across diverse data-heterogeneity settings such as covariate shift and task shift, with improvements of up to 20.6%. Additionally, FedPFT adheres to the data minimization principle of FL, as clients do not send real features. We demonstrate that sending real features is vulnerable to potent reconstruction attacks. Moreover, we show that FedPFT is amenable to formal privacy guarantees via differential privacy, demonstrating favourable privacy-accuracy tradeoffs., Comment: 20 pages, 12 figures

We present OpenRL, an advanced reinforcement learning (RL) framework designed to accommodate a diverse array of tasks, from single-agent challenges to complex multi-agent systems. OpenRL's robust support for self-play training empowers agents to develop advanced strategies in competitive settings. Notably, OpenRL integrates Natural Language Processing (NLP) with RL, enabling researchers to address a combination of RL training and language-centric tasks effectively. Leveraging PyTorch's robust capabilities, OpenRL exemplifies modularity and a user-centric approach. It offers a universal interface that simplifies the user experience for beginners while maintaining the flexibility experts require for innovation and algorithm development. This equilibrium enhances the framework's practicality, adaptability, and scalability, establishing a new standard in RL research. To delve into OpenRL's features, we invite researchers and enthusiasts to explore our GitHub repository at https://github.com/OpenRL-Lab/openrl and access our comprehensive documentation at https://openrl-docs.readthedocs.io.

In the field of autonomous vehicles (AVs), accurately discerning commander intent and executing linguistic commands within a visual context presents a significant challenge. This paper introduces a sophisticated encoder-decoder framework, developed to address visual grounding in AVs.Our Context-Aware Visual Grounding (CAVG) model is an advanced system that integrates five core encoders-Text, Image, Context, and Cross-Modal-with a Multimodal decoder. This integration enables the CAVG model to adeptly capture contextual semantics and to learn human emotional features, augmented by state-of-the-art Large Language Models (LLMs) including GPT-4. The architecture of CAVG is reinforced by the implementation of multi-head cross-modal attention mechanisms and a Region-Specific Dynamic (RSD) layer for attention modulation. This architectural design enables the model to efficiently process and interpret a range of cross-modal inputs, yielding a comprehensive understanding of the correlation between verbal commands and corresponding visual scenes. Empirical evaluations on the Talk2Car dataset, a real-world benchmark, demonstrate that CAVG establishes new standards in prediction accuracy and operational efficiency. Notably, the model exhibits exceptional performance even with limited training data, ranging from 50% to 75% of the full dataset. This feature highlights its effectiveness and potential for deployment in practical AV applications. Moreover, CAVG has shown remarkable robustness and adaptability in challenging scenarios, including long-text command interpretation, low-light conditions, ambiguous command contexts, inclement weather conditions, and densely populated urban environments. The code for the proposed model is available at our Github.

This study employs deep learning techniques to segment scanning electron microscope images, enabling a quantitative analysis of carbide precipitates in lower bainite and tempered martensite steels with comparable strength. Following segmentation, carbides are investigated, and their volume percentage, size distribution, and orientations are probed within the image dataset. Our findings reveal that lower bainite and tempered martensite exhibit comparable volume percentages of carbides, albeit with a more uniform distribution of carbides in tempered martensite. Carbides in lower bainite demonstrate a tendency for better alignment than those in tempered martensite, aligning with the observations of other researchers. However, both microstructures display a scattered carbide orientation, devoid of any discernible pattern. Comparative analysis of aspect ratios and sizes of carbides in lower bainite and tempered martensite unveils striking similarities. The deep learning model achieves an impressive pixelwise accuracy of 98.0% in classifying carbide/iron matrix at the individual pixel level. The semantic segmentation derived from deep learning extends its applicability to the analysis of secondary phases in various materials, offering a time-efficient, versatile AI-powered workflow for quantitative microstructure analysis.

A physics-driven generative adversarial network (GAN) was established here for single-pixel hyperspectral imaging (HSI) in the infrared spectrum, to eliminate the extensive data training work required by traditional data-driven model. Within the GAN framework, the physical process of single-pixel imaging (SPI) was integrated into the generator, and the actual and estimated one-dimensional (1D) bucket signals were employed as constraints in the objective function to update the network's parameters and optimize the generator with the assistance of the discriminator. In comparison to single-pixel infrared HSI methods based on compressed sensing and physics-driven convolution neural networks, our physics-driven GAN-based single-pixel infrared HSI can achieve higher imaging performance but with fewer measurements. We believe that this physics-driven GAN will promote practical applications of computational imaging, especially various SPI-based techniques., Comment: 14 pages, 8 figures

In settings such as e-recruitment and online dating, recommendation involves distributing limited opportunities, calling for novel approaches to quantify and enforce fairness. We introduce \emph{inferiority}, a novel (un)fairness measure quantifying a user's competitive disadvantage for their recommended items. Inferiority complements \emph{envy}, a fairness notion measuring preference for others' recommendations. We combine inferiority and envy with \emph{utility}, an accuracy-related measure of aggregated relevancy scores. Since these measures are non-differentiable, we reformulate them using a probabilistic interpretation of recommender systems, yielding differentiable versions. We combine these loss functions in a multi-objective optimization problem called \texttt{FEIR} (Fairness through Envy and Inferiority Reduction), applied as post-processing for standard recommender systems. Experiments on synthetic and real-world data demonstrate that our approach improves trade-offs between inferiority, envy, and utility compared to naive recommendations and the baseline methods.

Current fairness toolkits in machine learning only admit a limited range of fairness definitions and have seen little integration with automatic differentiation libraries, despite the central role these libraries play in modern machine learning pipelines. We introduce a framework of fairness regularization terms (fairrets) which quantify bias as modular, flexible objectives that are easily integrated in automatic differentiation pipelines. By employing a general definition of fairness in terms of linear-fractional statistics, a wide class of fairrets can be computed efficiently. Experiments show the behavior of their gradients and their utility in enforcing fairness with minimal loss of predictive power compared to baselines. Our contribution includes a PyTorch implementation of the fairret framework., Comment: Presented at ICLR 2024

In this paper, we study the pointwise bounds for the kernel of the $(\kappa, a)$-generalized Fourier transform with $\kappa\equiv0$, introduced by Ben Sa\"id, Kobayashi and Orsted. We present explicit formulas for the case $a=4$, which show that the kernels can exhibit polynomial growth. Subsequently, we provide a polynomial bound for the even dimensional kernel for this transform, focusing on the cases with finite order. Furthermore, by utilizing an estimation for the Prabhakar function, it is found that the $(0,a)$-generalized Fourier kernel is bounded by a constant when $a>1$ and $m\ge 2$, except within an angular domain that diminishes as $a \rightarrow \infty$. As a byproduct, we prove that the $(0, 2^{\ell}/n)$-generalized Fourier kernel is uniformly bounded, when $m=2$ and $\ell, n\in \mathbb{N}$., Comment: We corrected Eq.(3.1) in this version. Main results are not changed. All comments are welcome!