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Non-adiabatic molecular dynamics (NAMD) has become an essential computational technique for studying the photophysical relaxation of molecular systems after light absorption. These phenomena require approximations that go beyond the Born-Oppenheimer approximation, and the accuracy of the results heavily depends on the electronic structure theory employed. Sophisticated electronic methods, however, make these techniques computationally expensive, even for medium size systems. Consequently, simulations are often performed on simplified models to interpret experimental results. In this context, a variety of techniques have been developed to perform NAMD using approximate methods, particularly Density Functional Tight Binding (DFTB). Despite the use of these techniques on large systems where ab initio methods are computationally prohibitive, a comprehensive validation has been lacking. In this work, we present a new implementation of trajectory surface hopping (TSH) combined with DFTB, utilizing non-adiabatic coupling vectors (NACVs). We selected two different systems for validation, providing an exhaustive comparison with higher-level electronic structure methods. As a case study, we simulated a system from the class of molecular motors, which has been extensively studied experimentally but remains challenging to simulate with ab initio methods due to its inherent complexity. Our approach effectively captures the key photophysical mechanism of dihedral rotation after absorption of light. Additionally, we successfully reproduce the transition from the bright to dark states observed in the time dependent fluorescence experiments, providing valuable insights into this critical part of the photophysical behavior in molecular motors.

Causality analysis is a powerful tool for determining cause-and-effect relationships between variables in a system by quantifying the influence of one variable on another. Despite significant advancements in the field, many existing studies are constrained by their focus on unidirectional causality or Gaussian external forcing, limiting their applicability to complex real-world problems. This study proposes a novel data-driven approach to causality analysis for complex stochastic differential systems, integrating the concepts of Liang-Kleeman information flow and linear inverse modeling. Our method models environmental noise as either memoryless Gaussian white noise or memory-retaining Ornstein-Uhlenbeck colored noise, and allows for self and mutual causality, providing a more realistic representation and interpretation of the underlying system. Moreover, this LIM-based approach can identify the individual contribution of dynamics and correlation to causality. We apply this approach to re-examine the causal relationships between the El Ni\~{n}o-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), two major climate phenomena that significantly influence global climate patterns. In general, regardless of the type of noise used, the causality between ENSO and IOD is mutual but asymmetric, with the causality map reflecting an ENSO-like pattern consistent with previous studies. Notably, in the case of colored noise, the noise memory map reveals a hotspot in the Ni\~no 3 region, which is further related to the information flow. This suggests that our approach offers a more comprehensive framework and provides deeper insights into the causal inference of global climate systems., Comment: This article is to be submitted to MathTech 2024

In a recent paper [Quantum 5, 552 (2021)], the authors proposed a framework for robustly self-testing steerable quantum assemblages. In this work, we apply their method to the scenario of self-testing two-qubit entangled quantum states. The new bounds on the fidelity with the reference states are compared with other methods.

Topic modelling has become increasingly popular for summarizing text data, such as social media posts and articles. However, topic modelling is usually completed in one shot. Assessing the quality of resulting topics is challenging. No effective methods or measures have been developed for assessing the results or for making further enhancements to the topics. In this research, we propose we propose to use an iterative process to perform topic modelling that gives rise to a sense of completeness of the resulting topics when the process is complete. Using the BERTopic package, a popular method in topic modelling, we demonstrate how the modelling process can be applied iteratively to arrive at a set of topics that could not be further improved upon using one of the three selected measures for clustering comparison as the decision criteria. This demonstration is conducted using a subset of the COVIDSenti-A dataset. The early success leads us to believe that further research using in using this approach in conjunction with other topic modelling algorithms could be viable.

A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to $w$, a CAC of length $L$ with weight $w$ can provide a hard guarantee that each active user has at least one successful transmission within every consecutive $L$ slots. In this paper, we generalize some previously known constructions of constant-weight CACs, and then derive several classes of optimal CACs by the help of Kneser's Theorem and some techniques in Additive Combinatorics. Another spotlight of this paper is to relax the identical-weight constraint in prior studies to study mixed-weight CACs for the first time, for the purpose of increasing the throughput and reducing the access delay of some potential users with higher priority. As applications of those obtained optimal CACs, we derive some classes of optimal mixed-weight CACs., Comment: 32 pages

Cyclostationary linear inverse models (CS-LIMs), generalized versions of the classical (stationary) LIM, are advanced data-driven techniques for extracting the first-order time-dependent dynamics and random forcing relevant information from complex non-linear stochastic processes. Though CS-LIMs lead to a breakthrough in climate sciences, their mathematical background and properties are worth further exploration. This study focuses on the mathematical perspective of CS-LIMs and introduces two variants: e-CS-LIM and l-CS-LIM. The former refines the original CS-LIM using the interval-wise linear Markov approximation, while the latter serves as an analytic inverse model for the linear periodic stochastic systems. Although relying on approximation, e-CS-LIM converges to l-CS-LIM under specific conditions and shows noise-robust performance. Numerical experiments demonstrate that each CS-LIM reveals the temporal structure of the system. The e-CS-LIM optimizes the original model for better dynamics performance, while l-CS-LIM excels in diffusion estimation due to reduced approximation reliance. Moreover, CS-LIMs are applied to real-world ENSO data, yielding a consistent result aligning with observations and current ENSO understanding.

Heart rate (HR) is a crucial physiological signal that can be used to monitor health and fitness. Traditional methods for measuring HR require wearable devices, which can be inconvenient or uncomfortable, especially during sleep and meditation. Noncontact HR detection methods employing microwave radar can be a promising alternative. However, the existing approaches in the literature usually use high-gain antennas and require the sensor to face the user's chest or back, making them difficult to integrate into a portable device and unsuitable for sleep and meditation tracking applications. This study presents a novel approach for noncontact HR detection using a miniaturized Soli radar chip embedded in a portable device (Google Nest Hub). The chip has a $6.5 \mbox{ mm} \times 5 \mbox{ mm} \times 0.9 \mbox{ mm}$ dimension and can be easily integrated into various devices. The proposed approach utilizes advanced signal processing and machine learning techniques to extract HRs from radar signals. The approach is validated on a sleep dataset (62 users, 498 hours) and a meditation dataset (114 users, 1131 minutes). The approach achieves a mean absolute error (MAE) of $1.69$ bpm and a mean absolute percentage error (MAPE) of $2.67\%$ on the sleep dataset. On the meditation dataset, the approach achieves an MAE of $1.05$ bpm and a MAPE of $1.56\%$. The recall rates for the two datasets are $88.53\%$ and $98.16\%$, respectively. This study represents the first application of the noncontact HR detection technology to sleep and meditation tracking, offering a promising alternative to wearable devices for HR monitoring during sleep and meditation., Comment: 15 pages

In a PN junction, the separation between positive and negative charges leads to diode transport. In the past few years, the intrinsic diode transport in noncentrosymmetric polar conductors has attracted great interest, because it suggests novel nonlinear applications and provides a symmetry-sensitive probe of Fermi surface. Recently, such studies have been extended to noncentrosymmetric superconductors, realizing the superconducting diode effect. Here, we show that, even in a centrosymmetric crystal without directional charge separation, the spins of an antiferromagnet (AFM) can generate a spatial directionality, leading to an AFM diode effect. We observe large second-harmonic transport in a nonlinear electronic device enabled by the compensated AFM state of even-layered MnBi2Te4. We also report a novel electrical sum-frequency generation (SFG), which has been rarely explored in contrast to the well-known optical SFG in wide-gap insulators. We demonstrate that the AFM enables an in-plane field-effect transistor and harvesting of wireless electromagnetic energy. The electrical SFG establishes a powerful method to study nonlinear electronics built by quantum materials. The AFM diode effect paves the way for potential device concepts including AFM logic circuits, self-powered AFM spintronics, and other applications that potentially bridge nonlinear electronics with AFM spintronics., Comment: 33+8 pages, 14+2 figures

Within the context of machine learning-based closure mappings for RANS turbulence modelling, physical realizability is often enforced using ad-hoc postprocessing of the predicted anisotropy tensor. In this study, we address the realizability issue via a new physics-based loss function that penalizes non-realizable results during training, thereby embedding a preference for realizable predictions into the model. Additionally, we propose a new framework for data-driven turbulence modelling which retains the stability and conditioning of optimal eddy viscosity-based approaches while embedding equivariance. Several modifications to the tensor basis neural network to enhance training and testing stability are proposed. We demonstrate the conditioning, stability, and generalization of the new framework and model architecture on three flows: flow over a flat plate, flow over periodic hills, and flow through a square duct. The realizability-informed loss function is demonstrated to significantly increase the number of realizable predictions made by the model when generalizing to a new flow configuration. Altogether, the proposed framework enables the training of stable and equivariant anisotropy mappings, with more physically realizable predictions on new data. We make our code available for use and modification by others., Comment: 44 pages, 21 figures

In this paper, we present novel identification strategies to develop a unified framework for vortex-induced vibration (VIV) prediction based on the general semi-empirical wake oscillator. Greybox nonlinear system identification method accompanying high-fidelity computational fluid dynamics (CFD) and/or experimental data could be applied for the identification process. The proposed template of general wake oscillators contains low- to high-order damping terms to be identified for characterizing the possible flow dynamics. Two different strategies, including individual identification of single wake oscillator and overall identification of coupled VIV control equations, are proposed. VIV system consisting of an elastically-mounted circular cylinder submerged in laminar flow at Reynold number of 100 is considered. Both strategies have been tested and have exhibited high accuracy. The second strategy, i.e., overall identification of coupled VIV control equations, would be more suitable for the future framework owing that its training process considers the effect of fluid damping. A detailed mathematical introduction to future works on framework development covering the wide Reynold number range is addressed. The proposed unified framework is a landmark update of past wake oscillators both in terms of prediction accuracy and physical principles and has considerable research significance and practical engineering value., Comment: This version is not intended to be sent for peer review and is merely a summary of the preliminary work

Approximation of solutions to partial differential equations (PDE) is an important problem in computational science and engineering. Using neural networks as an ansatz for the solution has proven a challenge in terms of training time and approximation accuracy. In this contribution, we discuss how sampling the hidden weights and biases of the ansatz network from data-agnostic and data-dependent probability distributions allows us to progress on both challenges. In most examples, the random sampling schemes outperform iterative, gradient-based optimization of physics-informed neural networks regarding training time and accuracy by several orders of magnitude. For time-dependent PDE, we construct neural basis functions only in the spatial domain and then solve the associated ordinary differential equation with classical methods from scientific computing over a long time horizon. This alleviates one of the greatest challenges for neural PDE solvers because it does not require us to parameterize the solution in time. For second-order elliptic PDE in Barron spaces, we prove the existence of sampled networks with $L^2$ convergence to the solution. We demonstrate our approach on several time-dependent and static PDEs. We also illustrate how sampled networks can effectively solve inverse problems in this setting. Benefits compared to common numerical schemes include spectral convergence and mesh-free construction of basis functions., Comment: 16 pages, 15 figures

Most Mahonian statistics can be expressed as a linear combination of vincular patterns. This is not only true with statistics on the permutation set, but it can also be applied for statistics on the permutation with repetition set. By following the method extending the vincular patterns combinations presented by Kitaev and Vajnovszki, we discover 8 vincular-patterns combinations of mad and madl extensions that are possible to be Mahonian. Some of these have been proved to be Mahonian on repetitive permutations by Clarke, Steingrimsson and Zeng, while the rest are new statistics extensions. In this thesis, we determine combinations of vincular pattern extension of mad and madl in Clarke, Steingrimsson and Zeng s paper, which have been proved to be Mahonian on the repetitive permutations. This result will be used to support the proof of Mahonity of the new statistics extensions. We show that these new statistics extensions are also Mahonian by constructing an involution {\Phi} on repetitive permutations, which preserves the descents statistics and transforms new statistics extensions to Mahonian mad and madl extensions of Clarke., Comment: 90 pages, 5 themas, bachelor thesis

In this paper, we apply a novel approach based on physics-informed neural networks to the computation of quasinormal modes of black hole solutions in modified gravity. In particular, we focus on the case of Einstein-scalar-Gauss-Bonnet theory, with several choices of the coupling function between the scalar field and the Gauss-Bonnet invariant. This type of calculation introduces a number of challenges with respect to the case of General Relativity, mainly due to the extra complexity of the perturbation equations and to the fact that the background solution is known only numerically. The solution of these perturbation equations typically requires sophisticated numerical techniques that are not easy to develop in computational codes. We show that physics-informed neural networks have an accuracy which is comparable to traditional numerical methods in the case of numerical backgrounds, while being very simple to implement. Additionally, the use of GPU parallelization is straightforward thanks to the use of standard machine learning environments., Comment: 13 pages, 9 figures. v2: Matches published version

Despite many attempts to leverage pre-trained text-to-image models (T2I) like Stable Diffusion (SD) for controllable image editing, producing good predictable results remains a challenge. Previous approaches have focused on either fine-tuning pre-trained T2I models on specific datasets to generate certain kinds of images (e.g., with a specific object or person), or on optimizing the weights, text prompts, and/or learning features for each input image in an attempt to coax the image generator to produce the desired result. However, these approaches all have shortcomings and fail to produce good results in a predictable and controllable manner. To address this problem, we present TiNO-Edit, an SD-based method that focuses on optimizing the noise patterns and diffusion timesteps during editing, something previously unexplored in the literature. With this simple change, we are able to generate results that both better align with the original images and reflect the desired result. Furthermore, we propose a set of new loss functions that operate in the latent domain of SD, greatly speeding up the optimization when compared to prior approaches, which operate in the pixel domain. Our method can be easily applied to variations of SD including Textual Inversion and DreamBooth that encode new concepts and incorporate them into the edited results. We present a host of image-editing capabilities enabled by our approach. Our code is publicly available at https://github.com/SherryXTChen/TiNO-Edit., Comment: Conference on Computer Vision and Pattern Recognition (CVPR) 2024

We present the first report on fabrication of Hafnium aluminum nitride chiral sculptured thin films (CSTFs) using reactive magnetron sputtering in a glancing angle deposition configuration, and the analysis of its optical polarization properties. The resulting CSTFs were designed to give interference extrema or so-called circular Bragg (CB) resonances at desired wavelengths in the region from 370 to 690 nm. This was achieved by tailoring the growth of the chiral thin films to obtain a dielectric pitch between 87 and 260.9 nm. The spectral positions of the obtained CB resonances were compared to values from analytical expressions. Contrary to the common case where the dielectric pitch is half of the growth-related rotational pitch due to a 180{\deg} symmetry, this pitch was shown to be the same as the rotational pitch. It is concluded that this is due to the c-axis of the CSTF being tilted about 45{\deg} from the substrate normal. The morphology and crystallographic characterizations were done using scanning electron microscopy and X-ray diffraction, respectively, while the tilt of the crystal lattice was corroborated using X-ray diffraction pole figures. The optical response from the CSTFs was analyzed using Mueller matrix spectroscopic ellipsometry from which the degree of circular polarization at the CB resonances was obtained. In addition, a strong non-reciprocal reflection was observed which could be attributed to the helicoidal morphology and the intrinsic crystal tilt. An optical layered model of the chiral structure including azimuthal twist and using the Cauchy dispersion relations was used to simulate the Mueller matrix elements and compare with the ellipsometry measurements. The correlation between the simulated and experimental data gave information of the morphological parameters of the CSTF and its optical properties.

Making ideal decisions as a product leader in a web-facing company is extremely difficult. In addition to navigating the ambiguity of customer satisfaction and achieving business goals, one must also pave a path forward for ones' products and services to remain relevant, desirable, and profitable. Data and experimentation to test product hypotheses are key to informing product decisions. Online controlled experiments by A/B testing may provide the best data to support such decisions with high confidence, but can be time-consuming and expensive, especially when one wants to understand impact to key business metrics such as retention or long-term value. Offline experimentation allows one to rapidly iterate and test, but often cannot provide the same level of confidence, and cannot easily shine a light on impact on business metrics. We introduce a novel, lightweight, and flexible approach to investigating hypotheses, called scenario analysis, that aims to support product leaders' decisions using data about users and estimates of business metrics. Its strengths are that it can provide guidance on trade-offs that are incurred by growing or shifting consumption, estimate trends in long-term outcomes like retention and other important business metrics, and can generate hypotheses about relationships between metrics at scale.

We propose a novel data-driven linear inverse model, called Colored-LIM, to extract the linear dynamics and diffusion matrix that define a linear stochastic process driven by an Ornstein-Uhlenbeck colored-noise. The Colored-LIM is a new variant of the classical linear inverse model (LIM) which relies on the white noise assumption. Similar to LIM, the Colored-LIM approximates the linear dynamics from a finite realization of a stochastic process and then solves the diffusion matrix based on, for instance, a generalized fluctuation-dissipation relation, which can be done by solving a system of linear equations. The main difficulty is that in practice, the colored-noise process can be hardly observed while it is correlated to the stochastic process of interest. Nevertheless, we show that the local behavior of the correlation function of the observable encodes the dynamics of the stochastic process and the diffusive behavior of the colored-noise. In this article, we review the classical LIM and develop Colored-LIM with a mathematical background and rigorous derivations. In the numerical experiments, we examine the performance of both LIM and Colored-LIM. Finally, we discuss some false attempts to build a linear inverse model for colored-noise driven processes, and investigate the potential misuse and its consequence of LIM in the appendices., Comment: 23 pages, 3 figures

In this study, we propose a volume-to-point framework for quantitative precipitation estimation (QPE) based on the Quantitative Precipitation Estimation and Segregation Using Multiple Sensor (QPESUMS) Mosaic Radar data set. With a data volume consisting of the time series of gridded radar reflectivities over the Taiwan area, we used machine learning algorithms to establish a statistical model for QPE in weather stations. The model extracts spatial and temporal features from the input data volume and then associates these features with the location-specific precipitations. In contrast to QPE methods based on the Z-R relation, we leverage the machine learning algorithms to automatically detect the evolution and movement of weather systems and associate these patterns to a location with specific topographic attributes. Specifically, we evaluated this framework with the hourly precipitation data of 45 weather stations in Taipei during 2013-2016. In comparison to the operational QPE scheme used by the Central Weather Bureau, the volume-to-point framework performed comparably well in general cases and excelled in detecting heavy-rainfall events. By using the current results as the reference benchmark, the proposed method can integrate the heterogeneous data sources and potentially improve the forecast in extreme precipitation scenarios., Comment: 22 pages, 11 figures. Published in Earth and Space Science

We study a natural stratification of certain affine slices of univariate hyperbolic polynomials. We look into which posets of strata can be realized and show that the dual of the poset of strata is a shellable simplicial complex and in particular a combinatorial sphere. From this we obtain a g-theorem and an upper bound theorem on the number of strata. We use these results to design smaller test sets to improve upon Timofte's degree principle and give bounds on how much the degree principle can be improved., Comment: 35 pages, 1 figure

Constructing earth-fixed cells with low-earth orbit (LEO) satellites in non-terrestrial networks (NTNs) has been the most promising paradigm to enable global coverage. The limited computing capabilities on LEO satellites however render tackling resource optimization within a short duration a critical challenge. Although the sufficient computing capabilities of the ground infrastructures can be utilized to assist the LEO satellite, different time-scale control cycles and coupling decisions between the space- and ground-segments still obstruct the joint optimization design for computing agents at different segments. To address the above challenges, in this paper, a multi-time-scale deep reinforcement learning (DRL) scheme is developed for achieving the radio resource optimization in NTNs, in which the LEO satellite and user equipment (UE) collaborate with each other to perform individual decision-making tasks with different control cycles. Specifically, the UE updates its policy toward improving value functions of both the satellite and UE, while the LEO satellite only performs finite-step rollout for decision-makings based on the reference decision trajectory provided by the UE. Most importantly, rigorous analysis to guarantee the performance convergence of the proposed scheme is provided. Comprehensive simulations are conducted to justify the effectiveness of the proposed scheme in balancing the transmission performance and computational complexity.

Non-terrestrial networks (NTNs) with low-earth orbit (LEO) satellites have been regarded as promising remedies to support global ubiquitous wireless services. Due to the rapid mobility of LEO satellite, inter-beam/satellite handovers happen frequently for a specific user equipment (UE). To tackle this issue, earth-fixed cell scenarios have been under studied, in which the LEO satellite adjusts its beam direction towards a fixed area within its dwell duration, to maintain stable transmission performance for the UE. Therefore, it is required that the LEO satellite performs real-time resource allocation, which however is unaffordable by the LEO satellite with limited computing capability. To address this issue, in this paper, we propose a two-time-scale collaborative deep reinforcement learning (DRL) scheme for beam management and resource allocation in NTNs, in which LEO satellite and UE with different control cycles update their decision-making policies through a sequential manner. Specifically, UE updates its policy subject to improving the value functions of both the agents. Furthermore, the LEO satellite only makes decisions through finite-step rollouts with a reference decision trajectory received from the UE. Simulation results show that the proposed scheme can effectively balance the throughput performance and computational complexity over traditional greedy-searching schemes.

We propose a generalization of Haiman's conjecture on the diagonal coinvariant rings of real reflection groups to the context of irreducible quaternionic reflection groups (also known as symplectic reflection groups). For a reflection group $W$ acting on a quaternionic vector space $V$, by regarding $V$ as a complex vector space we consider the scheme-theoretic fiber over zero of the quotient map $\pi:V \to V/W$. For $W$ an irreducible reflection group of (quaternionic) rank at least $6$, we show that the ring of functions on this fiber admits a $(g+1)^n$-dimensional quotient arising from an irreducible representation of a symplectic reflection algebra, where $g=2N/n$ with $N$ the number of reflections in $W$ and $n=\mathrm{dim}_\mathbf{H}(V)$, and we conjecture that this holds in general. We observe that in fact the degree of the zero fiber is precisely $g+1$ for the rank one groups (corresponding to the Kleinian singularities). In an appendix, we give a proof that three variants of the Coxeter number, including $g$, are integers., Comment: 18 pages; v3 contains an appendix with a classification-free proof that three variants of the Coxeter number, including g, are integers

Deep learning for tabular data has garnered increasing attention in recent years, yet employing deep models for structured data remains challenging. While these models excel with unstructured data, their efficacy with structured data has been limited. Recent research has introduced retrieval-augmented models to address this gap, demonstrating promising results in supervised tasks such as classification and regression. In this work, we investigate using retrieval-augmented models for anomaly detection on tabular data. We propose a reconstruction-based approach in which a transformer model learns to reconstruct masked features of \textit{normal} samples. We test the effectiveness of KNN-based and attention-based modules to select relevant samples to help in the reconstruction process of the target sample. Our experiments on a benchmark of 31 tabular datasets reveal that augmenting this reconstruction-based anomaly detection (AD) method with sample-sample dependencies via retrieval modules significantly boosts performance. The present work supports the idea that retrieval module are useful to augment any deep AD method to enhance anomaly detection on tabular data., Comment: Accepted at CIKM 2024

Recent experimental findings reveal non-conventional fluorescence emission in biological systems devoid of conjugated bonds or aromatic compounds, termed \textit{Non-Aromatic Fluorescence} (NAF). This phenomenon is exclusive to aggregated or solid states, remaining absent in monomeric solutions. Previous studies focused on small model systems in vacuum show that the carbonyl stretching mode along with strong interaction of short hydrogen bonds (SHBs) remain the primary vibrational mode explaining NAF in these systems. In order to simulate larger model systems taking into account the effects of the surrounding environment, in this work we propose using the density functional tight-binding (DFTB) method in combination with non-adiabatic molecular dynamics (NAMD) and the mixed quantum/molecular mechanics (QM/MM) approach. We investigate the mechanism behind NAF in the crystal structure of L-pyroglutamine-ammonium, comparing it with the related non-fluorescent amino acid L-glutamine. Our results extend our previous findings to more realistic systems, demonstrating the efficiency and robustness of the proposed DFTB method in the context of NAMD in biological systems. Furthemore, due to its inherent low computational cost, this method allows for a better sampling on the non-radiative events at the conical intersection which is crucial for a complete understanding of this phenomenon. Beyond contributing to the ongoing exploration of NAF, this work paves the way for future application of this method in more complex biological systems such as amyloid aggregates, biomaterials and non-aromatic proteins.

The digital era has seen a marked increase in financial fraud. edge ML emerged as a promising solution for smartphone payment services fraud detection, enabling the deployment of ML models directly on edge devices. This approach enables a more personalized real-time fraud detection. However, a significant gap in current research is the lack of a robust system for monitoring data distribution shifts in these distributed edge ML applications. Our work bridges this gap by introducing a novel open-source framework designed for continuous monitoring of data distribution shifts on a network of edge devices. Our system includes an innovative calculation of the Kolmogorov-Smirnov (KS) test over a distributed network of edge devices, enabling efficient and accurate monitoring of users behavior shifts. We comprehensively evaluate the proposed framework employing both real-world and synthetic financial transaction datasets and demonstrate the framework's effectiveness.