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Reducing CO$_2$ emissions is crucial to mitigating climate change. Carbon Capture and Storage (CCS) is one of the few technologies capable of achieving net-negative CO$_2$ emissions. However, predicting fluid flow patterns in CCS remains challenging due to uncertainties in CO$_2$ plume dynamics and reservoir properties. Building on existing seismic imaging methods like the Joint Recovery Method (JRM), which lacks uncertainty quantification, we propose the Probabilistic Joint Recovery Method (pJRM). By estimating posterior distributions across surveys using a shared generative model, pJRM provides uncertainty information to improve risk assessment in CCS projects.

In this article, we introduce the simplicial $d$-polytopic numbers defined on generalized Fibonacci polynomials. We establish basic identities and find $q$-identities known. Furthermore, we find generating functions for the simplicial $d$-polytopic numbers and for the squares of the generalized triangular numbers. Finally, we compute sums of reciprocals of generalized Fibonacci polynomials and generalized triangular numbers. Here we introduce the Zeta function defined on generalized Fibonacci polynomials., Comment: arXiv admin note: text overlap with arXiv:2408.08943

Combining multiple machine learning models has long been a technique for enhancing performance, particularly in distributed settings. Traditional approaches, such as model ensembles, work well, but are expensive in terms of memory and compute. Recently, methods based on averaging model parameters have achieved good results in some settings and have gained popularity. However, merging models initialized differently that do not share a part of their training trajectories can yield worse results than simply using the base models, even after aligning their neurons. In this paper, we introduce a novel approach, Non-uniform Parameter-wise Model Merging, or NP Merge, which merges models by learning the contribution of each parameter to the final model using gradient-based optimization. We empirically demonstrate the effectiveness of our method for merging models of various architectures in multiple settings, outperforming past methods. We also extend NP Merge to handle the merging of multiple models, showcasing its scalability and robustness., Comment: 9 pages, 1 figure, to be published in the Proceedings of the 9th IEEE Special Session on Machine Learning on Big Data (MLBD 2024)

Deep-learning based traffic prediction models require vast amounts of data to learn embedded spatial and temporal dependencies. The inherent privacy and commercial sensitivity of such data has encouraged a shift towards decentralised data-driven methods, such as Federated Learning (FL). Under a traditional Machine Learning paradigm, traffic flow prediction models can capture spatial and temporal relationships within centralised data. In reality, traffic data is likely distributed across separate data silos owned by multiple stakeholders. In this work, a cross-silo FL setting is motivated to facilitate stakeholder collaboration for optimal traffic flow prediction applications. This work introduces an FL framework, referred to as FedTPS, to generate synthetic data to augment each client's local dataset by training a diffusion-based trajectory generation model through FL. The proposed framework is evaluated on a large-scale real world ride-sharing dataset using various FL methods and Traffic Flow Prediction models, including a novel prediction model we introduce, which leverages Temporal and Graph Attention mechanisms to learn the Spatio-Temporal dependencies embedded within regional traffic flow data. Experimental results show that FedTPS outperforms multiple other FL baselines with respect to global model performance., Comment: 11 pages, 7 figures, 6 tables, ACM format

To tackle the global challenge of online hate speech, a large body of research has developed detection models to flag hate speech in the sea of online content. Yet, due to systematic biases in evaluation datasets, detection performance in real-world settings remains unclear, let alone across geographies. To address this issue, we introduce HateDay, the first global hate speech dataset representative of social media settings, randomly sampled from all tweets posted on September 21, 2022 for eight languages and four English-speaking countries. Using HateDay, we show how the prevalence and composition of hate speech varies across languages and countries. We also find that evaluation on academic hate speech datasets overestimates real-world detection performance, which we find is very low, especially for non-European languages. We identify several factors explaining poor performance, including models' inability to distinguish between hate and offensive speech, and the misalignment between academic target focus and real-world target prevalence. We finally argue that such low performance renders hate speech moderation with public detection models unfeasible, even in a human-in-the-loop setting which we find is prohibitively costly. Overall, we emphasize the need to evaluate future detection models from academia and platforms in real-world settings to address this global challenge.

Accurately characterizing migration velocity models is crucial for a wide range of geophysical applications, from hydrocarbon exploration to monitoring of CO2 sequestration projects. Traditional velocity model building methods such as Full-Waveform Inversion (FWI) are powerful but often struggle with the inherent complexities of the inverse problem, including noise, limited bandwidth, receiver aperture and computational constraints. To address these challenges, we propose a scalable methodology that integrates generative modeling, in the form of Diffusion networks, with physics-informed summary statistics, making it suitable for complicated imaging problems including field datasets. By defining these summary statistics in terms of subsurface-offset image volumes for poor initial velocity models, our approach allows for computationally efficient generation of Bayesian posterior samples for migration velocity models that offer a useful assessment of uncertainty. To validate our approach, we introduce a battery of tests that measure the quality of the inferred velocity models, as well as the quality of the inferred uncertainties. With modern synthetic datasets, we reconfirm gains from using subsurface-image gathers as the conditioning observable. For complex velocity model building involving salt, we propose a new iterative workflow that refines amortized posterior approximations with salt flooding and demonstrate how the uncertainty in the velocity model can be propagated to the final product reverse time migrated images. Finally, we present a proof of concept on field datasets to show that our method can scale to industry-sized problems.

In this paper, we introduce the Rogers-Szeg\"o deformed $q$-differential operators g$_{n}(bD_{q}|u)$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators g$_{n}(bD_{q})$ is that their limit turns out to be the $q$-exponential operator T$(bD_{q})$ given by Chen. The deformed homogeneous Al-Salam-Carlitz polynomials $\Psi_{m}^{(q^{-n})}(ub,x|uq^{-1})$ can easily be represented by using the operators g$_{n}(bD_{q}|u)$. Identities relating the new general Al-Salam-Carlitz polynomial, defined by Cao et al., the generalized, and homogeneous Al-Salam-Carlitz polynomials $\Phi_{m}^{(q^n)}(b,x|q)$ and basic hypergeometric series are given.

Beyond conventional productivity metrics, human interaction and collaboration dynamics merit careful consideration in our increasingly digital workspace. This research proposes a conjectural neuro-adaptive room that enhances group interactions by adjusting the physical environment to desired internal states. Drawing inspiration from previous work on collective consciousness, the system leverages computer vision and machine learning models to analyze physiological and behavioral cues, such as facial expressions and speech analysis, to infer the overall internal state of occupants. Environmental conditions of the room, such as visual projections, lighting and sound, are actively adjusted to create an optimal setting for inducing the desired state, including focus or collaboration. Our goal is to create a dynamic and responsive environment to support group needs, fostering a sense of collective consciousness and improving workplace well-being., Comment: 5 pages, 2 figures. Longevity, AI, and Cognitive Research Hackathon

In this paper, we introduce the Heine binomial operators H$_{n}(bD_{q})$ based on $q$-differential operator $D_{q}$. The motivation for introducing the operators H$_{n}(bD_{q})$ is that their limit turns out to be the $q$-exponential operator T$(bD_{q})$ given by Chen. The Hahn polynomials $\Phi_{m}^{(q^n)}(b,x|q)$ can easily be represented by using the operators H$_{n}(bD_{q})$. Here, we derive $q$-exponential and ordinary generating function, Mehler's formula, Rogers formula, and other identities for the polynomials $\Phi_{m}^{(q^n)}(b,x|q)$.

Cyanobacteria are the most frequent dominant species of algal blooms in inland waters, threatening ecosystem function and water quality, especially when toxin-producing strains predominate. Enhanced by anthropogenic activities and global warming, cyanobacterial blooms are expected to increase in frequency and global distribution. Early warning systems (EWS) for cyanobacterial blooms development allow timely implementation of management measures, reducing the risks associated to these blooms. In this paper, we propose an effective EWS for cyanobacterial bloom forecasting, which uses 6 years of incomplete high-frequency spatio-temporal data from multiparametric probes, including phycocyanin (PC) fluorescence as a proxy for cyanobacteria. A probe agnostic and replicable method is proposed to pre-process the data and to generate time series specific for cyanobacterial bloom forecasting. Using these pre-processed data, six different non-site/species-specific predictive models were compared including the autoregressive and multivariate versions of Linear Regression, Random Forest, and Long-Term Short-Term (LSTM) neural networks. Results were analyzed for seven forecasting time horizons ranging from 4 to 28 days evaluated with a hybrid system that combined regression metrics (MSE, R2, MAPE) for PC values, classification metrics (Accuracy, F1, Kappa) for a proposed alarm level of 10 ug PC/L, and a forecasting-specific metric to measure prediction improvement over the displaced signal (skill). The multivariate version of LSTM showed the best and most consistent results across all forecasting horizons and metrics, achieving accuracies of up to 90% in predicting the proposed PC alarm level. Additionally, positive skill values indicated its outstanding effectiveness to forecast cyanobacterial blooms from 16 to 28 days in advance.

The developed system using a mobile electronic device for monitoring and warnings of heart problems, when the heart rate is outside the nominal range, which ranges from 60 to 100 beats per minute. Also, a system has been developed to save and monitor in real time changes of the cardiac pulsations, through a sensor connected to a control system. The connection of the communication module for Arduino GSM/GPRS/GPS, using the GPS network to locate the user. In addition, this device connects with GSM / GPRS technology that allows text messages to be sent to the contact number configured in the device, when warnings of heart problems are issued, moreover connects to the internet to store data in the cloud., Comment: 5 pages, 13 figures

Geological Carbon Storage GCS is arguably the only scalable net-negative CO2 emission technology available While promising subsurface complexities and heterogeneity of reservoir properties demand a systematic approach to quantify uncertainty when optimizing production and mitigating storage risks which include assurances of Containment and Conformance of injected supercritical CO2 As a first step towards the design and implementation of a Digital Twin for monitoring underground storage operations a machine learning based data-assimilation framework is introduced and validated on carefully designed realistic numerical simulations As our implementation is based on Bayesian inference but does not yet support control and decision-making we coin our approach an uncertainty-aware Digital Shadow To characterize the posterior distribution for the state of CO2 plumes conditioned on multi-modal time-lapse data the envisioned Shadow combines techniques from Simulation-Based Inference SBI and Ensemble Bayesian Filtering to establish probabilistic baselines and assimilate multi-modal data for GCS problems that are challenged by large degrees of freedom nonlinear multi-physics non-Gaussianity and computationally expensive to evaluate fluid flow and seismic simulations To enable SBI for dynamic systems a recursive scheme is proposed where the Digital Shadows neural networks are trained on simulated ensembles for their state and observed data well and/or seismic Once training is completed the systems state is inferred when time-lapse field data becomes available In this computational study we observe that a lack of knowledge on the permeability field can be factored into the Digital Shadows uncertainty quantification To our knowledge this work represents the first proof of concept of an uncertainty-aware in-principle scalable Digital Shadow.

Speech pathology has impacts on communication abilities and quality of life. While deep learning-based models have shown potential in diagnosing these disorders, the use of sensitive data raises critical privacy concerns. Although differential privacy (DP) has been explored in the medical imaging domain, its application in pathological speech analysis remains largely unexplored despite the equally critical privacy concerns. This study is the first to investigate DP's impact on pathological speech data, focusing on the trade-offs between privacy, diagnostic accuracy, and fairness. Using a large, real-world dataset of 200 hours of recordings from 2,839 German-speaking participants, we observed a maximum accuracy reduction of 3.85% when training with DP with high privacy levels. To highlight real-world privacy risks, we demonstrated the vulnerability of non-private models to explicit gradient inversion attacks, reconstructing identifiable speech samples and showcasing DP's effectiveness in mitigating these risks. To generalize our findings across languages and disorders, we validated our approach on a dataset of Spanish-speaking Parkinson's disease patients, leveraging pretrained models from healthy English-speaking datasets, and demonstrated that careful pretraining on large-scale task-specific datasets can maintain favorable accuracy under DP constraints. A comprehensive fairness analysis revealed minimal gender bias at reasonable privacy levels but underscored the need for addressing age-related disparities. Our results establish that DP can balance privacy and utility in speech disorder detection, while highlighting unique challenges in privacy-fairness trade-offs for speech data. This provides a foundation for refining DP methodologies and improving fairness across diverse patient groups in real-world deployments.

Despite the recent broad adoption of Large Language Models (LLMs) across various domains, their potential for enriching information systems in extracting and exploring Linked Data (LD) and Resource Description Framework (RDF) triplestores has not been extensively explored. This paper examines the integration of LLMs within existing systems, emphasising the enhancement of conversational user interfaces (UIs) and their capabilities for data extraction by producing more accurate SPARQL queries without the requirement for model retraining. Typically, conversational UI models necessitate retraining with the introduction of new datasets or updates, limiting their functionality as general-purpose extraction tools. Our approach addresses this limitation by incorporating LLMs into the conversational UI workflow, significantly enhancing their ability to comprehend and process user queries effectively. By leveraging the advanced natural language understanding capabilities of LLMs, our method improves RDF entity extraction within web systems employing conventional chatbots. This integration facilitates a more nuanced and context-aware interaction model, critical for handling the complex query patterns often encountered in RDF datasets and Linked Open Data (LOD) endpoints. The evaluation of this methodology shows a marked enhancement in system expressivity and the accuracy of responses to user queries, indicating a promising direction for future research in this area. This investigation not only underscores the versatility of LLMs in enhancing existing information systems but also sets the stage for further explorations into their potential applications within more specialised domains of web information systems., Comment: This paper has been accepted at the 25th International Web Information Systems Engineering Conference (WISE 2024)

Compact Ultramassive Antenna Array (CUMA) is a pioneering paradigm that leverages the flexibility of the Fluid Antenna System (FAS) to enable a simple multiple access scheme for massive connectivity without the need for precoding, power control at the base station or interference mitigation in each user's equipment. In order to overcome the mathematical intricacy required to analyze their performance, we use an asymptotic matching approach to relax such complexity with a remarkable accuracy. First, we analyze the performance of the CUMA network in terms of the outage probability (OP) and the ergodic rate (ER), deriving simple and highly accurate closed-form approximations to the channel statistics. Then, we evaluate the potential of the CUMA scheme to provide secure multi-user communications from a physical layer security perspective. Leveraging a tight approximation to the signal-to-interference-ratio (SIR) distribution, we derive closed-form expressions for the secrecy outage probability (SOP). We observe that the baseline CUMA (without side information processing) exhibits limited performance when eavesdroppers are equipped with a CUMA of the same type. To improve their secure performance, we suggest that a simple imperfect interference cancellation mechanism at the legitimate receiver may substantially increase the secrecy performance. Monte Carlo simulations validate our approximations and demonstrate their accuracy under different CUMA-based scenarios.

This paper introduces the deformed Rogers-Szeg\"o polynomials R$_n(x,y;u,v|q)$. These polynomials are a generalization of the classical Rogers-Szeg\"o polynomials, the generalized Rogers-Szeg\"o polynomials, the Stieljes-Wigert polynomials, among others. Basic properties of the polynomial R$_n$ are given, along with recurrence relations, its $q$-difference equation, representations, and generating functions. We define the $u$-deformed $q$-exponential operator T$(tD_{q}|u)$, and we get for free the operators T$(yD_{q})$ the Chen, $\mathrm{R}(yD_{q})$ of Saad, $\mathcal{E}(yD_{q})$ of Exton, and $\mathcal{R}(yD_{q})$ of Rogers-Ramanujan, when $u=1,q,\sqrt{q},q^2$, respectively. The identities obtained here use a type of deformation for the basic hypergeometric series. Also, we find identities involving the polynomials R$_n(x,y;u,v|q)$, together with generalizations of the Mehler and Rogers formulas.

We respond to arguments against our criticism that claim to show a divergence of Assembly Theory from popular compression. We have proven that any implementation of the concept of `copy number' underlying Assembly Theory (AT) and its assembly index (Ai) is equivalent to Shannon Entropy and not fundamentally or methodologically different from algorithms like ZIP compression. We show that the weak empirical correlation between Ai and LZW, which the authors offered as a defense against the proof that the assembly index calculation method is a compression scheme, is based on an incomplete and misleading experiment. When the experiment is completed, the asymptotic convergence to LZ compression and Shannon Entropy is evident and aligned with the mathematical proof previously offered. Therefore, this completes the theoretical and empirical demonstrations that any variation of the copy-number concept underlying AT, which resorts to counting the number of object repetitions `to arrive at a measure for life,' is equivalent to statistical compression and Shannon Entropy. We demonstrate that the authors' `we-are-better-because-we-are-worse' defense argument against compression does not withstand basic scrutiny and that their empirical results separating organic from inorganic compounds have not only been previously reported -- sans claims to unify physics and biology -- but are also driven solely by molecular length, not a particular feature of life captured by their assembly index. Finally, we show that Ai is a particular case of our BDM introduced almost a decade earlier and that arguments attributing special stochastic properties to Ai are misleading, not unique, and exactly the same as those that Shannon Entropy is already not only equipped with but designed for which we have also proven to be equivalent to Ai making AT redundant even in practice when applied to their own experimental data., Comment: 12 figures, 53 pages (minor tweaks and adding new refs of previous relevant work not cited by the authors of AT)

This work presents the results of modelling the ion dynamics in the ART-MS (Autoresonant Trap Mass Spectrometry) device in the quasi-static approximation. This instrument utilizes an anharmonic, purely electrostatic trap for ion confinement and a radio frequency (RF) voltage source with decrementally varying frequency for selective ion extraction. The autoresonant interaction between the oscillatory motion of the ion and the RF voltage causes an increase in the amplitude of certain confined ions, allowing their selective extraction. Numerical modelling shows that the extraction of ions with a given mass occurs not only at the fundamental frequency but also at its harmonics. This effect reduces the selective properties of devices of this type because along with the main mass component for a given frequency, it is possible to enter the detector channel of ions with another mass, for which this frequency corresponds to the second or higher harmonics, even a superposition of some of these harmonics of different ions., Comment: 9 pages, 6 figures

This paper introduces the deformed Rogers-Szeg\"o functions ${\rm R}_{\alpha}(x,y;u,v|q)$. When $\alpha=-n$ is a negative integer, these functions are related to the $q$-derivatives of Ramanujan's partial Theta function. Basic properties of the polynomial ${\rm R}_{\alpha}$ are given, along with recurrence relations, its representations, and generating functions. We use the $u$-deformed $q$-exponential operator ${\rm T}(qD_{q}|u)$ to obtain identities for Rogers-Szeg\"o functions, in particular, Rogers-type formulas., Comment: 16 pages

We developed SaludConectaMX as a comprehensive system to track and understand the determinants of complications throughout chemotherapy treatment for children with cancer in Mexico. SaludConectaMX is unique in that it integrates patient clinical indicators with social determinants and caregiver mental health, forming a social-clinical perspective of the patient's evolving health trajectory. The system is composed of a web application (for hospital staff) and a mobile application (for family caregivers), providing the opportunity for cooperative patient monitoring in both hospital and home settings. This paper presents the system's preliminary design and usability evaluation results from a 1.5-year pilot study. Our findings indicate that while the hospital web app demonstrates high completion rates and user satisfaction, the family mobile app requires additional improvements for optimal accessibility; statistical and qualitative data analysis illuminate pathways for system improvement. Based on this evidence, we formalize suggestions for health system development in LMICs, which HCI researchers may leverage in future work.

This letter illustrates the opinion of the molecular dynamics (MD) community on the need to adopt a new FAIR paradigm for the use of molecular simulations. It highlights the necessity of a collaborative effort to create, establish, and sustain a database that allows findability, accessibility, interoperability, and reusability of molecular dynamics simulation data. Such a development would democratize the field and significantly improve the impact of MD simulations on life science research. This will transform our working paradigm, pushing the field to a new frontier. We invite you to support our initiative at the MDDB community (https://mddbr.eu/community/)

The dynamics of non-equilibrium closed quantum systems and their route to thermalization are of fundamental interest to several fields, from cosmology to particle physics. However, a comprehensive description of non-equilibrium phenomena still presents a significant challenge. In this work, we report the observation of distinct stages during the relaxation of the decaying turbulence in trapped Bose-Einstein condensates. Our findings show a direct particle cascade from low to high momenta, a consequence of the energy injection in the system, exhibiting a characteristic universal scaling. This stage is followed by an inverse particle cascade responsible for repopulating the previously depleted condensate. Both cascades can be explained through self-similar solutions provided by wave turbulence theory. These findings provide important insights into the relaxation stages of out-of-equilibrium quantum many-body systems.

The ability of Language Models (LMs) to understand natural language makes them a powerful tool for parsing human instructions into task plans for autonomous robots. Unlike traditional planning methods that rely on domain-specific knowledge and handcrafted rules, LMs generalize from diverse data and adapt to various tasks with minimal tuning, acting as a compressed knowledge base. However, LMs in their standard form face challenges with long-horizon tasks, particularly in partially observable multi-agent settings. We propose an LM-based Long-Horizon Planner for Multi-Agent Robotics (LLaMAR), a cognitive architecture for planning that achieves state-of-the-art results in long-horizon tasks within partially observable environments. LLaMAR employs a plan-act-correct-verify framework, allowing self-correction from action execution feedback without relying on oracles or simulators. Additionally, we present MAP-THOR, a comprehensive test suite encompassing household tasks of varying complexity within the AI2-THOR environment. Experiments show that LLaMAR achieves a 30% higher success rate than other state-of-the-art LM-based multi-agent planners in MAP-THOR and Search \& Rescue tasks. Code can be found at https://github.com/nsidn98/LLaMAR, Comment: 27 pages, 4 figures, 5 tables

Combining the predictions of multiple trained models through ensembling is generally a good way to improve accuracy by leveraging the different learned features of the models, however it comes with high computational and storage costs. Model fusion, the act of merging multiple models into one by combining their parameters reduces these costs but doesn't work as well in practice. Indeed, neural network loss landscapes are high-dimensional and non-convex and the minima found through learning are typically separated by high loss barriers. Numerous recent works have been focused on finding permutations matching one network features to the features of a second one, lowering the loss barrier on the linear path between them in parameter space. However, permutations are restrictive since they assume a one-to-one mapping between the different models' neurons exists. We propose a new model merging algorithm, CCA Merge, which is based on Canonical Correlation Analysis and aims to maximize the correlations between linear combinations of the model features. We show that our alignment method leads to better performances than past methods when averaging models trained on the same, or differing data splits. We also extend this analysis into the harder setting where more than 2 models are merged, and we find that CCA Merge works significantly better than past methods. Our code is publicly available at https://github.com/shoroi/align-n-merge, Comment: Proceedings of the Forty-first International Conference on Machine Learning (ICML 2024)

Noise resilience of quantum information processing is a crucial precondition to reach the fault-tolerance threshold. While resilience to many types of noise can be achieved through suitable control schemes, resilience to amplitude noise seems to be elusive within the common harmonic approximation for the bus mode of trapped ions. We show that weak an-harmonicities admit control schemes that achieve amplitude noise-resilience consistent with state-of-the-art experimental requirements, and that the required an-harmonicities can be achieved with current standards of micro-structured traps or even the intrinsically an-harmonic Coulomb interaction.

Jet point cloud images are high dimensional data structures that needs to be transformed to a separable feature space for machine learning algorithms to distinguish them with simple decision boundaries. In this article, the authors focus on jet category separability by particle and jet feature extraction, resulting in more efficient training of a simple deep neural network, resulting in a computational efficient interpretable model for jet classification. The methodology is tested with three to five categories of jets from the JetNet benchmark jet tagging dataset, resulting in comparable performance to particle flow network. This work demonstrates that high dimensional datasets represented in separable latent spaces lead to simpler architectures for jet classification., Comment: 9 pages, y figures

This work is concerned with devising a robust Parkinson's (PD) disease detector from speech in real-world operating conditions using (i) foundational models, and (ii) speech enhancement (SE) methods. To this end, we first fine-tune several foundational-based models on the standard PC-GITA (s-PC-GITA) clean data. Our results demonstrate superior performance to previously proposed models. Second, we assess the generalization capability of the PD models on the extended PC-GITA (e-PC-GITA) recordings, collected in real-world operative conditions, and observe a severe drop in performance moving from ideal to real-world conditions. Third, we align training and testing conditions applaying off-the-shelf SE techniques on e-PC-GITA, and a significant boost in performance is observed only for the foundational-based models. Finally, combining the two best foundational-based models trained on s-PC-GITA, namely WavLM Base and Hubert Base, yielded top performance on the enhanced e-PC-GITA., Comment: Accepted at INTERSPEECH 2024

In this paper, we define the deformed Euler $(s,t)$-numbers ${\rm e}_{s,t,u}$ Furthermore, we prove that ${\rm e}_{as,a^2t,u^{-1}}$ and ${\rm e}_{as,a^2t,u^{-1}}^{-1}$ are irrational numbers when $a,u\in\mathbb{Q}$ and $\vert au\vert>1$, thus providing a countable infinite family of irrational numbers. This is the first step in a program to study the irrationality of $(s,t)$-analog of known numbers., Comment: 24 pages