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arXiv 2021年

作者： Huang, Jessie Busch, Erica L. Wallenstein, Tom Gerasimiuk, Michal Benz, Andrew Lajoie, Guillaume Wolf, Guy Turk-Browne, Nicholas B. Krishnaswamy, Smita Department Of Computer Science Department Of Psychology Department Of Mathematics Department Of Genetics Program In Applied Mathematics Wu Tsai Institute Yale University United States Department Of Mathematics And Statistics Université De Montréal Canada Mila Quebec AI Institute Canada

Functional magnetic resonance imaging (fMRI) is a notoriously noisy measurement of brain activity because of the large variations between individuals, signals marred by environmental differences during collection, and spatiotemporal averaging required by the measurement resolution. In addition, the data is extremely high dimensional, with the space of the activity typically having much lower intrinsic dimension. In order to understand the connection between stimuli of interest and brain activity, and analyze differences and commonalities between subjects, it becomes important to learn a meaningful embedding of the data that denoises, and reveals its intrinsic structure. Specifically, we assume that while noise varies significantly between individuals, true responses to stimuli will share common, low-dimensional features between subjects which are jointly discoverable. Similar approaches have been exploited previously but they have mainly used linear methods such as PCA and shared response modeling (SRM). In contrast, we propose a neural network called MRMD-AE (manifold-regularized multiple decoder, autoencoder), that learns a common embedding from multiple subjects in an experiment while retaining the ability to decode to individual raw fMRI signals. We show that our learned common space represents an extensible manifold (where new points not seen during training can be mapped), improves the classification accuracy of stimulus features of unseen timepoints, as well as improves cross-subject translation of fMRI signals. We believe this framework can be used for many downstream applications such as guided brain-computer interface (BCI) training in the future. Copyright © 2021, The Authors. All rights reserved.

关键词： Magnetic resonance imaging

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Fault Tolerant Quantum Error Mitigation

arXiv

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arXiv 2023年

作者： Gonzales, Alvin Babu, Anjala M. Liu, Ji Saleem, Zain Byrd, Mark Intelligence Community Postdoctoral Research Fellowship Program Argonne National Laboratory LemontIL United States School of Physics and Applied Physics Southern Illinois University CarbondaleIL United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States School of Computing Southern Illinois University CarbondaleIL United States

Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based error mitigation techniques. We also demonstrate that similar to results in fault tolerant quantum computing, code concatenation in fault-tolerant quantum error mitigation (FTQEM) can exponentially suppress the errors to arbitrary levels. For a family of circuits, we provide analytical error thresholds for FTQEM with the repetition code. These circuits include a set of quantum circuits that can generate all of reversible classical computing. The post-selection rate in FTQEM can also be increased by correcting some of the outcomes. Our threshold results can also be viewed from the perspective of quantifying the number of gate operations we can delay checking the stabilizers in a concatenated code before errors overwhelm the encoding. The benefits of FTQEM are demonstrated with numerical simulations and hardware demonstrations. Copyright © 2023, The Authors. All rights reserved.

关键词： Quantum computers

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Adaptive tikhonov strategies for stochastic ensemble Kalman inversion

arXiv

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arXiv 2021年

作者： Weissmann, Simon Chada, Neil K. Schillings, Claudia Tong, Xin T. Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg69120 Germany Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal KSA 23955 Saudi Arabia Mannheim School of Computer Science and Mathematics University of Mannheim Mannheim68131 Germany Department of Mathematics National University of Singapore Singapore119077 Singapore

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and *** Codes 65M32, 60G35, 65C35, 70F17 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems

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On the Okamoto-Uchiyama cryptosystem: (A brief essay on basic mathematics applied in cryptography) 3

On the Okamoto-Uchiyama cryptosystem: (A brief essay on basi...

引用

3rd International Conference on science, ICOS 2019

作者： Haryanto, Loeky Lawi, Armin Suhastina, Suhastina Qarynah, Putri Computer Science Study Program Mathematics Department Hasanuddin University Makassar Indonesia

The Okamoto-Uchiyama cryptosystem applies many consepts of basic abstract algebra, discrete mathematics and number theory. Many of these concepts are elementary and used in other branches of cryptography. However, those elementary concepts are not enough provided in the mathematics curriculla in under developed and developing countries despite the fact that in early stages teaching of those basic mathematics concepts, there is no need to provide sophiticated nor rigorous treatments beyond computations of integers. By exploring the basic mathematics applied in Okamoto-Uchiyama's algorithm and its re-lated concepts, this exploration should make mathematics teachers, educators and instructors to be aware of the important teaching the basic abstract algebra, discrete mathematics and number theory as early as high school senior level or at the first year in colleges and universities. © Published under licence by IOP Publishing Ltd.

关键词： Cryptography

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Continuous Prediction of Leg Kinematics during Walking using Inertial Sensors, Smart Glasses, and Embedded Computing

Continuous Prediction of Leg Kinematics during Walking using...

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IEEE International Conference on Robotics and Automation (ICRA)

作者： Oleksii Tsepa Roman Burakov Brokoslaw Laschowski Alex Mihailidis Department of Computer Science AGE-WELL Networks of Centres of Excellence program University of Toronto and the Vector Institute for Artificial Intelligence Department of Mathematical Methods of System Analysis Igor Sikorsky Kyiv Polytechnic Institute Kyiv Ukraine Department of Computer Science University of Toronto Toronto ON Canada Department of Mathematics National University of Kyiv-Mohyla Academy Kyiv Ukraine Department of Mechanical and Industrial Engineering University of Toronto Toronto ON Canada Toronto Rehabilitation Institute University Health Network Toronto ON Canada Institute of Biomedical Engineering University of Toronto Toronto ON Canada

Unlike traditional hierarchical controllers for robotic leg prostheses and exoskeletons, continuous systems could allow persons with mobility impairments to walk more naturally in real-world environments without requiring high-level switching between locomotion modes. To support these next-generation controllers, we developed a new system called KIFNet (Kinematics and Image Fusing Network) that uses lightweight and efficient deep learning models to continuously predict the leg kinematics during walking. We tested different sensor fusion methods to combine kinematics data from inertial sensors and computer vision data from smart glasses and found that adaptive instance normalization achieved the lowest RMSE predictions for knee and ankle joint kinematics. We also deployed our model on an embedded device. Without inference optimization, our model was 20 times faster than the previous state-of-the-art and achieved 20% higher prediction accuracies, and during some locomotor activities like stair descent, decreased RMSE up to 300%. With inference optimization, our best model achieved 125 FPS on an NVIDIA Jetson Nano. These results demonstrate the potential to build fast and accurate deep learning models for continuous prediction of leg kinematics during walking based on sensor fusion and embedded computing, therein providing a foundation for real-time continuous controllers for robotic leg prostheses and exoskeletons.

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Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm

arXiv

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arXiv 2022年

作者： Gagolewski, Marek Bartoszuk, Maciej Cena, Anna Systems Research Institute Polish Academy of Sciences ul. Newelska 6 Warsaw01-447 Poland Faculty of Mathematics and Information Science Warsaw University of Technology ul. Koszykowa 75 Warsaw00-662 Poland International PhD Studies Program Institute of Computer Science Polish Academy of Sciences Poland

The time needed to apply a hierarchical clustering algorithm is most often dominated by the number of computations of a pairwise dissimilarity measure. Such a constraint, for larger data sets, puts at a disadvantage the use of all the classical linkage criteria but the single linkage one. However, it is known that the single linkage clustering algorithm is very sensitive to outliers, produces highly skewed dendrograms, and therefore usually does not reflect the true underlying data structure - unless the clusters are well-separated. To overcome its limitations, we propose a new hierarchical clustering linkage criterion called Genie. Namely, our algorithm links two clusters in such a way that a chosen economic inequity measure (e.g., the Gini- or Bonferroni-index) of the cluster sizes does not increase drastically above a given threshold. The presented benchmarks indicate a high practical usefulness of the introduced method: it most often outperforms the Ward or average linkage in terms of the clustering quality while retaining the single linkage speed. The Genie algorithm is easily parallelizable and thus may be run on multiple threads to speed up its execution further on. Its memory overhead is small: there is no need to precompute the complete distance matrix to perform the computations in order to obtain a desired clustering. It can be applied on arbitrary spaces equipped with a dissimilarity measure, e.g., on real vectors, DNA or protein sequences, images, rankings, informetric data, etc. A reference implementation of the algorithm has been included in the open source genie package for R. [See https://genieclust. gagolewski. com for a new implementation - available for both R and Python.]. © 2022, CC BY.

关键词： Clustering algorithms

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The implementation of GSTARI-X model for forecasting climate change with data mining approach

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AIP Conference Proceedings 2024年第1期3082卷

作者： Putri Monika Budi Nurani Ruchjana Atje Setiawan Abdullah Doctoral Student Mathematics Program Universitas Padjadjaran Sumedang 45363 Indonesia. Department of Mathematics Faculty of Mathematics and Natural Sciences Universitas Padjadjaran Sumedang 45363 Indonesia. Department of Computer Science Faculty of Mathematics and Natural Sciences Universitas Padjadjaran Sumedang 45363 Indonesia.

Climate change is one of Indonesia’s most widely discussed and studied environmental problems. Based on the purpose of the 13th SDGs goals, climate change urgently requires rapid action to overcome it. It becomes a challenge for researchers to forecast the state of the climate in the future. In this study, one of the climate parameters was forecasted, namely rainfall and humidity, through the Generalized Autoregressive Integrated with Exogenous Variable (GSTARI-X) model. The GSTARI-X model is a model that examines phenomena that are ordered spatially and time is simultaneously or commonly known as the Space-Time model. Applying the GSTARI-X model in forecasting rainfall with humidity as an exogenous variable used the Knowledge Discovery in Database (KDD) data mining approach. The KDD Data Mining method is needed because the climate data is sourced from NASA observation data which is big data. The function of the KDD method in this study is to describe and predict climate phenomena, especially in West Java. This study’s expected results forecast future climate phenomena, which are presented through rainfall maps using the QGIS program. The results of climate forecasts using the GSTARI-X model have an accurate forecasting capability with MAPE values of 18% and 15%. This can be a recommendation for related agencies in policy making.

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Antigenic cooperation in Viral Populations: Transformation of Functions of Intra-Host Viral Variants

arXiv

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arXiv 2022年

作者： Bunimovich, Leonid Ram, Athulya Skums, Pavel School of Mathematics Georgia Institute of Technology AtlantaGA30332 United States Interdisciplinary Graduate Program in Quantitative Biosciences Georgia Institute of Technology AtlantaGA30332 United States Department of Computer Science Georgia State University AtlantaGA30302 United States

In this paper we study intra-host viral adaptation by antigenic cooperation - a mechanism of immune escape that serves as an alternative to the standard mechanism of escape by continuous genomic diversification and allows to explain a number of experimental observations associated with the establishment of chronic infections by highly mutable viruses. Within this mechanism, the topology of a cross-immunoreactivity network forces intra-host viral variants to specialize for complementary roles and adapt to host's immune response as a quasi-social ecosystem. Here we study dynamical changes in immune adaptation caused by evolutionary and epidemiological events. First, we show that the emergence of a viral variant with altered antigenic features may result in a rapid re-arrangement of the viral ecosystem and a change in the roles played by existing viral variants. In particular, it may push the population under immune escape by genomic diversification towards the stable state of adaptation by antigenic cooperation. Next, we study the effect of a viral transmission between two chronically infected hosts, which results in merging of two intra-host viral populations in the state of stable immune-adapted equilibrium. In this case, we also describe how the newly formed viral population adapts to the host's environment by changing the functions of its members. The results are obtained analytically for minimal cross-immunoreactivity networks and numerically for larger populations. © 2022, CC BY.

关键词： Viruses

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Web-based structural identifiability analyzer

arXiv

引用

arXiv 2021年

作者： Ilmer, Ilia Ovchinnikov, Alexey Pogudin, Gleb Ph.D. Program in Computer Science CUNY Graduate Center New York United States Department of Mathematics CUNY Queens College Ph.D. Programs in Mathematics and Computer Science CUNY Graduate Center New York United States LIX CNRS École Polytechnique Institute Polytechnique de Paris France

Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to identify parameters from experimental data. In this work, we present a web-based software tool that allows to answer specific identifiability queries. Concretely, our toolbox can determine identifiability of individual parameters of the model and also provide all functions of parameters that are identifiable (also called identifiable combinations) from single or multiple experiments. The program is freely available at https://***/app/6509768948056064. © 2021, CC BY-SA.

关键词： Websites

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Correction: Unbiased and multilevel methods for a class of diffusions partially observed via marked point processes

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Statistics and Computing 2024年第6期34卷 1-1页

作者： Alvarez, Miguel Jasra, Ajay Ruzayqat, Hamza Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal Saudi Arabia School of Data Science The Chinese University of Hong Kong Shenzhen China

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