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A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

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arXiv 2020年

作者： Popov, Andrey A. Sandu, Adrian Nino-Ruiz, Elias D. Evensen, Geir Computational Science Laboratory Department of Computer Science Virginia Tech United States Applied Math and Computer Science Lab Universidad del Norte Colombia Norway

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamical systems

Characterization and topological behavior of homomorphism tree-shifts

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arXiv 2021年

作者： Ban, Jung-Chao Lucius, Chih-Hung Chang Hu, Wen-Guei Lai, Guan-Yu Wu, Yu-Liang Department of Mathematical Sciences National Chengchi University Taipei11605 Taiwan Math. Division National Center for Theoretical Science National Taiwan University Taipei10617 Taiwan Department of Applied Mathematics National University of Kaohsiung Kaohsiung81148 Taiwan College of Mathematics Sichuan University Chengdu610064 China Department of Applied Mathematics National Chiao Tung University Hsinchu30010 Taiwan

The purpose of this article is twofold. On one hand, we reveal the equivalence of shift of finite type between a one-sided shift X and its associated hom tree-shift τX, as well as the equivalence in the sofic shift. On the other hand, we investigate the interrelationship among the comparable mixing properties on tree-shifts as those on multidimensional shift spaces. They include irreducibility, topologically mixing, block gluing, and strong irreducibility, all of which are defined in the spirit of classical multidimensional shift, complete prefix code (CPC), and uniform CPC. In summary, the mixing properties defined in all three manners coincide for τX. Furthermore, an equivalence between irreducibility on τAand irreducibility on XAare seen, and so is one between topologically mixing on τAand mixing property on XA, where XAis the one-sided shift space induced by the matrix A and TAis the associated tree-shift. These equivalences are consistent with the mixing properties on X or XAwhen viewed as a degenerate *** Codes 37B10, 37E25 Copyright © 2021, The Authors. All rights reserved.

关键词： Topology

Qudit Dynamical Decoupling on a Superconducting Quantum Processor

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arXiv 2024年

作者： Tripathi, Vinay Goss, Noah Vezvaee, Arian Nguyen, Long B. Siddiqi, Irfan Lidar, Daniel A. Department of Physics & Astronomy University of Southern California Los AngelesCA90089 United States Center for Quantum Information Science & Technology University of Southern California Los AngelesCA90089 United States Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Applied Math and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical & Computer Engineering University of Southern California Los AngelesCA90089 United States Department of Chemistry University of Southern California Los AngelesCA90089 United States

Multi-level qudit systems are increasingly being explored as alternatives to traditional qubit systems due to their denser information storage and processing potential. However, qudits are more susceptible to decoherence than qubits due to increased loss channels, noise sensitivity, and crosstalk. To address these challenges, we develop protocols for dynamical decoupling (DD) of qudit systems based on the Heisenberg-Weyl group. We implement and experimentally verify these DD protocols on a superconducting transmon processor that supports qudit operation based on qutrits (d = 3) and ququarts (d = 4). Specifically, we demonstrate single-qudit DD sequences to decouple qutrits and ququarts from system-bath-induced decoherence. We also introduce two-qudit DD sequences designed to suppress the detrimental cross-Kerr couplings between coupled qudits. This allows us to demonstrate a significant improvement in the fidelity of time-evolved qutrit Bell states. Our results highlight the utility of leveraging DD to enable scalable qudit-based quantum computing. © 2024, CC BY.

关键词： Qubits

Large deviation principle of multidimensional multiple averages on Nd

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arXiv 2021年

作者： Ban, Jung-Chao Hu, Wen-Guei Lai, Guan-Yu Department of Mathematical Sciences National Chengchi University Taipei11605 Taiwan Math. Division National Center for Theoretical Science National Taiwan University Taipei10617 Taiwan College of Mathematics Sichuan University Chengdu610064 China Department of Applied Mathematics National Chiao Tung University Hsinchu30010 Taiwan

This paper establishs the large deviation principle (LDP) for multiple averages on Nd. We extend the previous work of [Carinci et al., Indag. math. 2012] to multidimensional lattice Nd for d ≥ 2. The same technique is also applicable to the weighted multiple average launched by Fan [Fan, Adv. math. 2021]. Finally, the boundary conditions are imposed to the multiple sum and explicit formulae of the energy functions with respect to the boundary conditions are obtained. Copyright © 2021, The Authors. All rights reserved.

关键词： Boundary conditions

STEIN FILLINGS VS. MILNOR FIBERS

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arXiv 2024年

作者： Inanc Baykur, V. Némethi, András Plamenevskaya, Olga Department of Mathematics and Statistics University of Massachusetts AmherstMA01003 United States HUN-REN Alfréd Rényi Institute of Mathematics Reáltanoda utca 13-15 BudapestH-1053 Hungary ELTE - Faculty of Science Dept. of Geometry Pázmány Péter sétány 1/A Budapest1117 Hungary BBU - Babeş-Bolyai Univ. Str M. Kogalniceanu 1 Cluj-Napoca400084 Romania BCAM - Basque Center for Applied Math. Mazarredo Basque Country Bilbao14 E48009 Spain Department of Mathematics Stony Brook University Stony BrookNY11794 United States

Given a link of a normal surface singularity with its canonical contact structure, we compare the collection of its Stein fillings to its Milnor fillings (that is, Milnor fibers of possible smoothings). We prove that, unlike Stein fillings, Milnor fillings of a given link have bounded topology;for links of sandwiched singularities, we further establish that there are only finitely many Milnor fillings. We discuss some other obstructions for a Stein filling to be represented by a Milnor fiber, and for various types of singularities, including simple classes like cusps and triangle singularities, we produce Stein fillings that do not come from Milnor fibers or resolutions. Meanwhile, we discover that there are many contact 3–manifolds that admit infinitely many Stein fillings but do not admit arbitrarily large ones. Copyright © 2024, The Authors. All rights reserved.

关键词： Filling

From thermodynamics to protein design: Diffusion models for biomolecule generation towards autonomous protein engineering

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arXiv 2025年

作者： Li, Wenran Cadet, Xavier F. Medina-Ortiz, David Davari, Mehdi D. Sowdhamini, Ramanathan Damour, Cedric Li, Yu Miranville, Alain Cadet, Frederic University of Paris City University of Reunion INSERM BIGR DSIMB ParisF-75015 France Department of Computing Imperial College London United Kingdom Department of Computer Engineering University of Magallanes Punta Arenas Chile Centre for Biotechnology and Bioengineering Universidad de Chile Santiago Chile Department of Bioorganic Chemistry Leibniz Institute of Plant Biochemistry Halle06120 Germany National Centre for Biological Science TIFR Bangalore India Molecular Biophysics Unit Indian Institute of Science Bangalore India Institute of Bioinformatics and Applied Biotechnology Bangalore India EnergyLab EA 4079 Faculty of Sciences and Technology University of Reunion France School of Information Science and Technology Beijing Institute of Artificial Intelligence China Laboratoire de Mathématiques Appliquées University Le Havre Normandie le Havre France PEACCEL Artificial Intelligence Department AI for Bi-ologics Paris75013 France

Protein design with desirable properties has been a significant challenge for many decades. Generative artificial intelligence is a promising approach and has achieved great success in various protein generation tasks. Notably, diffusion models stand out for their robust math.matical foundations and impressive generative capabilities, offering unique advantages in certain applications such as protein design. In this review, we first give the definition and characteristics of diffusion models and then focus on two strategies: Denoising Diffusion Probabilistic Models (DDPM) and Score-based Generative Models (SGM), where DDPM is the discrete form of SGM. Furthermore, we discuss their applications in protein design, peptide generation, drug discovery, and protein-ligand interaction. Finally, we outline the future perspectives of diffusion models to advance autonomous protein design and engineering. The E(3) group consists of all rotations, reflections, and translations in three-dimensions. The equivariance in the E(3) group can maintain the physical stability of the N − Cα − C frame of each amino acid as much as possible, and we reflect on how to keep the diffusion model E(3) equivariant for protein generation. © 2025, CC BY.

关键词： Biomolecules

Inverse scattering on the quantum graph for graphene

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arXiv 2021年

作者： Ando, Kazunori Isozaki, Hiroshi Korotyaev, Evgeny Morioka, Hisashi Department of Electrical and Electronic Engineering and Computer Science Ehime University Matsuyama790-8577 Japan Graduate School of Pure and Applied Sciences Professor Emeritus University of Tsukuba Tsukuba305-8571 Japan Department of Math. Analysis Saint-Petersburg State University Universitetskaya nab. 7/9 St. Petersburg199034 Russia National Research University Higher School of Economics St. Petersburg Russia

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we show that the S-matrix for all energies in any given open set in the continuous spectrum determines the *** Codes 81U40, 47A40 Copyright © 2021, The Authors. All rights reserved.

关键词： Inverse problems

A DNA Based Colour Image Encryption Scheme Using A Convolutional Autoencoder

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arXiv 2022年

作者： Ahmed, Fawad Rehman, Muneeb Ur Ahmad, Jawad Khan, Muhammad Shahbaz Boulila, Wadii Srivastava, Gautam Lin, Jerry Chun-Wei Buchanan, William J. Department of Cyber Security Pakistan Navy Engineering College NUST Karachi75350 Pakistan Department of Electrical Engineering HITEC University Taxila Pakistan School of Computing Edinburgh Napier University Edinburgh United Kingdom Department of Electrical Engineering HITEC University Taxila47080 Pakistan Robotics and Internet-of-Things Laboratory Prince Sultan University Riyadh Saudi Arabia RIADI Laboratory University of Manouba Manouba Tunisia Math and Computer Science Brandon University Brandon Canada Research Centre for Interneural Computing China Medical University Taichung Taiwan Dept of Computer Science and Math Lebanese American University Beirut Lebanon Western Norway University of Applied Sciences Bergen Norway

With the advancement in technology, digital images can easily be transmitted and stored over the Internet. Encryption is used to avoid illegal interception of digital images. Encrypting large-sized colour images in their original dimension generally results in low encryption/decryption speed along with exerting a burden on the limited bandwidth of the transmission channel. To address the aforementioned issues, a new encryption scheme for colour images employing convolutional autoencoder, DNA and chaos is presented in this paper. The proposed scheme has two main modules, the dimensionality conversion module using the proposed convolutional autoencoder, and the encryption/decryption module using DNA and chaos. The dimension of the input colour image is first reduced from N × M × 3 toP × Q gray-scale image using the encoder. Encryption and decryption are then performed in the reduced dimension space. The decrypted gray-scale image is upsampled to obtain the original colour image having dimension N × M × 3. The training and validation accuracy of the proposed autoencoder is 97% and 95%, respectively. Once the autoencoder is trained, it can be used to reduce and subsequently increase the dimension of any arbitrary input colour image. The efficacy of the designed autoencoder has been demonstrated by the successful reconstruction of the compressed image into the original colour image with negligible perceptual distortion. The second major contribution presented in this paper is an image encryption scheme using DNA along with multiple chaotic sequences and substitution boxes. The security of the proposed image encryption algorithm has been gauged using several evaluation parameters, such as histogram of the cipher image, entropy, NPCR, UACI, key sensitivity, contrast, etc. The experimental results of the proposed scheme demonstrate its effectiveness to perform colour image encryption. © 2022, CC BY.

关键词： DNA

Analysis, circuit realization and controls of an autonomous Morse jerk oscillator

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SeMA Journal 2021年第3期78卷 415-433页

作者： Ainamon, Cyrille Tamba, Victor Kamdoum Pone, Justin Roger Mboupda Kingni, Sifeu Takougang Malwe, Hubert Boudoue Orou, Jean Bio Chabi Institut de Mathématiques et de Sciences Physiques Université d’Abomey-Calavi B.P. 613 Porto Novo Benin Department of Telecommunication and Network Engineering IUT-Fotso Victor of Bandjoun University of Dschang PO Box 134 Bandjoun Cameroon Electrical Engineering Department of IUT-Fotso Victor of Bandjoun Research Unit of Automation and Applied Computer (RU-AIA) University of Dschang PO Box 134 Bandjoun Cameroon Department of Mechanical Petroleum and Gas Engineering Faculty of Mines and Petroleum Industries University of Maroua PO Box 46 Maroua Cameroon Department of Physics Faculty of Science University of Maroua PO Box 814 Maroua Cameroon

In this paper, an autonomous Morse jerk oscillator which is designed by converting an autonomous two-dimensional Morse oscillator to a jerk oscillator, is analysed. The stability of its unique equilibrium point reveals the existence of Hopf bifurcation. Periodic and chaotic oscillations, antimonotonicity, chaotic bubbles and coexisting attractors are generated in the proposed jerk oscillator. Then, this proposed jerk oscillator is implemented in PSIM software and realized in a printed circuit board to verify the numerical results. The experimental/PSIM results agree well with the numerical simulations. Moreover, it is possible to control partially or totally the amplitude of its signals by introducing two additional parameters in the rate-equations describing the proposed jerk oscillator. Furthermore based on the Routh–Hurwitz conditions and using a single linear feedback controller, the proposed jerk oscillator is controlled to its unique equilibrium point. Finally, the coexistence between periodic and chaotic attractors is destroyed and controlled to a desired trajectory thank to the linear augmentation method. © 2021, The Author(s), under exclusive licence to Sociedad Española de Matemática Aplicada.

关键词： Antimonotonicity Chaotic and coexisting attractors Control Electronic circuit realization Hopf bifurcation Morse jerk oscillator