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Modeling of Measurement Error in Financial Returns Data

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arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Mijatović, Aleksandar School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics University of Warwick United Kingdom

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [12] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. Copyright © 2024, The Authors. All rights reserved.

关键词： Markov chains

Investigation of Automatic Part-of-Speech Tagging using CRF, HMM and LSTM on Misspelled and Edited Texts 5

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Investigation of Automatic Part-of-Speech Tagging using CRF,...

5th Artificial Intelligence and Cloud Computing Conference, AICCC 2022

作者： Aydinov, Farhad Huseynov, Igbal Sayadzada, Sofiya Rustamov, Samir Data Science University of Glasgow United Kingdom Computational Linguistics and Language Technologies Charles University Prague Czech Republic Department of Applied Mathematics and Computer Science Technical University of Denmark Copenhagen Denmark School of Information Technology and Engineering ADA University Baku Azerbaijan Institute of Control Systems BakuVarna Bulgaria Azerbaijan

ISBN: (纸本)9781450398749

Part-of-speech tagging is the process of assigning words in a given text to appropriate parts-of speech in order to reduce the disambiguation which may arise depending on the contextual usage of the words. In this paper, the problem of word sense disambiguation in Azerbaijani language is addressed by applying part of speech tagging on two varying data corpora, misspelled, and edited (clean) text using 3 different machine learning algorithms: Hidden Markov Model, Long Short-Term Memory, and Conditional Random Fields. The comparative analysis on the outcomes of the mentioned algorithms and their accuracy scores were analysed in the paper. The misspelled dataset for the experiments is provided by Unibank from their chatbot dialogues while the clean textual data was retrieved from the books and newspapers in Azerbaijani. The experiments showed that the Bidirectional LSTM has the highest accuracy scores for both edited (98.2%) and noisy (96.2%) data corpora. Suggested models can be used in the application of algorithms focuses on part of speech tags and syntactic structure of Azerbaijani language which is an agglutinative language belonging to Turkic languages family, thus enabling the research to be further investigated in other agglutinative languages with similar grammatical structure. © 2022 ACM.

关键词： Hidden Markov models

Free vibration analysis of functionally graded porous curved nanobeams on elastic foundation in hygro-thermo-magnetic environment

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Frontiers of Structural and Civil Engineering 2023年第4期17卷 584-605页

作者： Quoc-Hoa PHAM Parviz MALEKZADEH Van Ke TRAN Trung NGUYEN-THOI Faculty of Engineering and Technology Nguyen Tat Thanh UniversityHo Chi Minh City 700000Vietnam Department of Mechanical Engineering Persian Gulf UniversityBushehr ***Iran Faculty of Mechanical Engineering Le Quy Don Technical UniversityHanoi 100000Vietnam Laboratory for Applied and Industrial Mathematics Institute for Computational Science and Artificial IntelligenceVan Lang UniversityHo Chi Minh City 700000Vietnam Faculty of Mechanical-Electrical and Computer Engineering School of TechnologyVan Lang UniversityHo Chi Minh City 700000Vietnam Bualuang ASEAN Chair Professor Thammasat School of EngineeringThammasat UniversityPathumtani 12120Thailand

Herein,a two-node beam element enriched based on the Lagrange and Hermite interpolation function is proposed to solve the governing equation of a functionally graded porous(FGP)curved nanobeam on an elastic foundation in a hygro–thermo–magnetic *** material properties of curved nanobeams change continuously along the thickness via a power-law distribution,and the porosity distributions are described by an uneven porosity *** effects of magnetic fields,temperature,and moisture on the curved nanobeam are assumed to result in axial loads and not affect the mechanical properties of the *** equilibrium equations of the curved nanobeam are derived using Hamilton’s principle based on various beam theories,including the classical theory,first-order shear deformation theory,and higher-order shear deformation theory,and the nonlocal elasticity *** accuracy of the proposed method is verified by comparing the results obtained with those of previous reliable ***,the effects of different parameters on the free vibration behavior of the FGP curved nanobeams are investigated comprehensively.

关键词： functionally graded porous material curved nanobeam hygro-thermo-magnetic enriched finite element method

Multirate Time-Integration based on Dynamic ODE Partitioning through Adaptively Refined Meshes for Compressible Fluid Dynamics

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arXiv 2024年

作者： Doehring, Daniel Schlottke-Lakemper, Michael Gassner, Gregor J. Torrilhon, Manuel Applied and Computational Mathematics RWTH Aachen University Schinkelstrasse 2 North Rhine-Westphalia Aachen52062 Germany University of Stuttgart Germany High-Performance Scientific Computing Center for Advanced Analytics and Predictive Sciences University of Augsburg Germany Department of Mathematics and Computer Science Center for Data and Simulation Science University of Cologne Germany

In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. [1, 2] to dynamically partitioned systems arising from adaptive mesh refinement. The PERK schemes enable multirate time-integration with no changes in the spatial discretization methodology, making them readily implementable in existing codes that employ a method-of-lines approach. We show that speedup compared to a range of state of the art Runge-Kutta methods can be realized, despite additional overhead due to the dynamic re-assignment of flagging variables and restricting nonlinear stability properties. The effectiveness of the approach is demonstrated for a range of simulation setups for viscous and inviscid convection-dominated compressible flows for which we provide a reproducibility repository. In addition, we perform a thorough investigation of the nonlinear stability properties of the Paired-Explicit Runge-Kutta schemes regarding limitations due to the violation of monotonicity properties of the underlying spatial discretization. Furthermore, we present a novel approach for estimating the relevant eigenvalues of large Jacobians required for the optimization of stability *** Codes 65L06, 65M20, 76Mxx, 76Nxx © 2024, CC BY.

关键词： Runge Kutta methods

An Optimal Transport Approach for Network Regression

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An Optimal Transport Approach for Network Regression

Control Technology and Applications (CCTA),

作者： Alex G. Zalles Kai M. Hung Ann E. Finneran Lydia Beaudrot César A. Uribe Department of Computational Applied Mathematics and Operations Research Rice University Houston TX USA Department of Computer Science Rice University Houston TX USA Department of Biosciences Rice University Houston TX USA Department of Electrical and Computer Engineering Rice University Houston TX USA

ISBN: (数字)9798350370942

ISBN: (纸本)9798350370959

We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on Fréchet means and propose a network regression method using the Wasserstein metric. We show that when representing graphs as multivariate Gaussian distributions, the network regression problem requires the computation of a Riemannian center of mass (i.e., Fréchet means). Fréchet means with non-negative weights translates into a barycenter problem and can be efficiently computed using fixed point iterations. Although the convergence guarantees of fixed-point iterations for the computation of Wasserstein affine averages remain an open problem, we provide evidence of convergence in a large number of synthetic and real-data scenarios. Extensive numerical results show that the proposed approach improves existing procedures by accurately accounting for graph size, topology, and sparsity in synthetic experiments. Additionally, real-world experiments using the proposed approach result in higher Coefficient of Determination (R 2 ) values and lower mean squared prediction error (MSPE), cementing improved prediction capabilities in practice.

关键词： Accuracy Network topology computational modeling Cement industry Predictive models Gaussian distribution Aerospace electronics

Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman–Bucy Filters

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arXiv 2022年

作者： Álvarez Ballesteros, Miguel Ángel Chada, Neil K. Jasra, Ajay Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia

In this article we consider the development of an unbiased estimator for the ensemble Kalman–Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization, and through the number of samples at each level. Our estimator will be specific to linear and Gaussian settings, where we know that the EnKBF is consistent, in the particle limit N → ∞, with the KBF. We highlight this for two particular variants of the EnKBF, i.e. the deterministic and vanilla variants, and demonstrate this on a linear Ornstein–Uhlenbeck process. We compare this with the EnKBF and the multilevel (MLEnKBF), for experiments with varying dimension size. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods. © 2022, CC BY-NC-SA.

关键词： Continuous time systems

Multi-State-Action Tokenisation in Decision Transformers for Multi-Discrete Action Spaces

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arXiv 2024年

作者： Moodley, Perusha Kaushik, Pramod Thambi, Dhillu Trovinger, Mark Paruchuri, Praveen Hong, Xia Rosman, Benjamin School of Mathematical Physical and Computational Sciences University of Reading Reading United Kingdom TCS Research Pune India Machine Learning Lab IIIT Hyderabad Hyderabad India Department of Computer Science and Engineering Mississippi State University Mississippi United States School of Computer Science and Applied Mathematics University of Witwatersrand Johannesburg South Africa

Decision Transformers, in their vanilla form, struggle to perform on image-based environments with multi-discrete action spaces. Although enhanced Decision Transformer architectures have been developed to improve performance, these methods have not specifically addressed this problem of multi-discrete action spaces which hampers existing Decision Transformer architectures from learning good representations. To mitigate this, we propose Multi-State Action Tokenisation (M-SAT), an approach for tokenising actions in multi-discrete action spaces that enhances the model’s performance in such environments. Our approach involves two key changes: disentangling actions to the individual action level and tokenising the actions with auxiliary state information. These two key changes also improve individual action level interpretability and visibility within the attention layers. We demonstrate the performance gains of M-SAT on challenging ViZDoom environments with multi-discrete action spaces and image-based state spaces, including the Deadly Corridor and My Way Home scenarios, where M-SAT outperforms the baseline Decision Transformer without any additional data or heavy computational overheads. Additionally, we find that removing positional encoding does not adversely affect M-SAT’s performance and, in some cases, even improves it. © 2024, CC BY.

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PROOFS OF MODULO 11 AND 13 CYLINDRIC KANADE-RUSSELL CONJECTURES FOR A2 ROGERS-RAMANUJAN TYPE IDENTITIES

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arXiv 2023年

作者： Uncu, Ali Kemal Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Science Altenbergerstraße 69 LinzA-4040 Austria University of Bath Faculty of Science Department of Computer Science BathBA2 7AY United Kingdom

We present proofs of two new families of sum-product identities arising from the cylindric parti tions paradigm. Most of the presented expressions, the related sum-product identities, and the ingredients for the proofs were first conjectured by Kanade-Russell in the spirit of Andrews-Schilling-Warnaar identities o the A2 Rogers-Ramanujan type. We follow the footsteps of Kanade-Russell while we alter the computations heavily to accomplish our *** Codes 05A15, 05A17, 05A19, 11B65, 11P84, 17B65, 68R05 Copyright © 2023, The Authors. All rights reserved.

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Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems

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arXiv 2024年

作者： Anandh, Thivin Ghose, Divij Jain, Himanshu Sunkad, Pratham Ganesan, Sashikumaar John, Volker Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore India Department of Mechanical Engineering Indian Institute of Technology Tamil Nadu Madras India Weierstrass Institute for Applied Analysis and Stochastics Berlin Germany Department of Mathematics and Computer Science Freie University Berlin Germany

This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature. © 2024, CC BY-NC-SA.

关键词： Stabilization