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Annual IEEE Symposium on Foundations of Computer Science

作者： Emmanuel Abbe Min Ye Mathematics Institute and the School of Computer and Communication Sciences at EPFL Switzerland Program in Applied and Computational Mathematics in Princeton University USA Department of Electrical Engineering Princeton University USA

Reed-Muller (RM) codes were introduced in 1954 and have long been conjectured to achieve Shannon's capacity on symmetric channels. The activity on this conjecture has recently been revived with the emergence of polar codes. RM codes and polar codes are generated by the same matrix G_m= [1/1 0/1] ^⊗m but using different subset of rows. RM codes select simply rows having largest weights. Polar codes select instead rows having the largest conditional mutual information proceeding top to down in G_m; while this is a more elaborate and channel-dependent rule, the top-to-down ordering allows Arikan to show that the conditional mutual information polarizes, and this gives directly a capacity-achieving code on any symmetric channel. RM codes are yet to be proved to have such a property, despite the recent success for the erasure channel. In this paper, we connect RM codes to polarization theory. We show that proceeding in the RM code ordering, i.e., not top-to-down but from the lightest to the heaviest rows in G_m, the conditional mutual information again polarizes. We further demonstrate that it does so faster than for polar codes. This implies that G_m contains another code, different than the polar code and called here the twin-RM code, that is provably capacity-achieving on any symmetric channel. This gives in particular a necessary condition for RM codes to achieve capacity on symmetric channels. It further gives a sufficient condition if the rows with largest conditional mutual information correspond to the heaviest rows, i.e., if the twin-RM code is the RM code. We demonstrate here that the two codes are at least similar and give further evidence that they are indeed the same.

关键词： Polar codes Mutual information Channel capacity Decoding Entropy Boolean functions

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Ultra-Efficient Resistance Switching between Charge Ordered Phases in 1T-TaS2 with a Single Picosecond Electrical Pulse

arXiv

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arXiv 2022年

作者： Venturini, Rok Mraz, Anže Vaskivskyi, Igor Vaskivskyi, Yevhenii Svetin, Damjan Mertelj, Tomaž Pavlovič, Leon Cheng, Jing Chen, Genyu Amarasinghe, Priyanthi Qadri, Syed B. Trivedi, Sudhir B. Sobolewski, Roman Mihailovic, Dragan Jožef Stefan Institute Jamova 39 LjubljanaSI-1000 Slovenia Faculty of Mathematics and Physics University of Ljubljana Jadranska 19 LjubljanaSI-1000 Slovenia Faculty for Electrical Engineering University of Ljubljana Tržaška 25 LjubljanaSI-1000 Slovenia CENN Nanocenter Jamova 39 LjubljanaSI-1000 Slovenia ELEP Electronics LjubljanaSI-1000 Slovenia Materials Science Program Laboratory for Laser Energetics University of Rochester New York14627 United States Brimrose Technology Corporation SparksMD21152 United States U.S. Naval Research Laboratory WashingtonDC United States Department of Electrical and Computer Engineering Department of Physics and Astronomy University of Rochester New York14627 United States

Progress in high-performance computing demands significant advances in memory technology. Among novel memory technologies that promise efficient device operation on a sub-ns timescale, resistance switching between charge ordered phases of 1T-TaS2 has shown to be potentially useful for development of high-speed, energy efficient non-volatile memory devices. Measurement of the electrical operation of such devices in the picosecond regime is technically challenging and hitherto still largely unexplored. Here we use an optoelectronic "laboratory-on-a-chip" experiment for measurements of ultrafast memory switching, enabling accurate measurement of electrical switching parameters with 100 fs temporal resolution. Photoexcitation and electro-optic sampling on a (Cd,Mn)Te substrate are used to generate and, subsequently, measure electrical pulse propagation, with intra-band excitation and sub-gap probing, respectively. We demonstrate high contrast non-volatile resistance switching from high to low resistance states of a 1T-TaS2 device using single sub-2ps electrical pulses. Using detailed modeling we find that the switching energy density per unit area is exceptionally small, EA = 9.4 fJ/µm2. The speed and energy efficiency of an electronic "write" process, place the 1T-TaS2 devices into a category of their own among new generation non-volatile memory devices. Copyright © 2022, The Authors. All rights reserved.

关键词： Switching

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Multi-Signal Approaches for Repeated Sampling Schemes in Inertial Sensor Calibration

SSRN

引用

SSRN 2021年

作者： Bakalli, Gaetan Cucci, Davide A. Radi, Ahmed El-Sheimy, Naser Molinari, Roberto Scaillet, Olivier Guerrier, Stéphane Geneva School of Economics and Management Geneva School of Economics and Management University of Geneva 1205 Switzerland University of Calgary Department of Geomatics Engineering University of Calgary CalgaryABT2N 1N4 Canada Department of Mathematics & Statistics Auburn University AuburnAL36849 United States Geneva Finance Research Institute University of Geneva Swiss Finance Institute Geneva1211 Switzerland Faculty of Science & Geneva School of Economics and Management University of Geneva 1205 Switzerland

Inertial sensor calibration plays a progressively important role in many areas of research among which navigation engineering. By performing this task accurately, it is possible to significantly increase general navigation performance by correctly filtering out the deterministic and stochastic measurement errors that characterize such devices. While different techniques are available to model and remove the deterministic errors, there has been considerable research over the past years with respect to modelling the stochastic errors which have complex structures. In order to do the latter, different replicates of these error signals are collected and a model is identified and estimated based on one of these replicates. While this procedure has allowed to improve navigation performance, it has not yet taken advantage of the information coming from all the other replicates collected on the same sensor. However, it has been observed that there is often a change of error behaviour between replicates which can also be explained by different (constant) external conditions under which each replicate was taken. Whatever the reason for the difference between replicates, it appears that the model structure remains the same between replicates but the parameter values vary. In this work we therefore consider and study the properties of different approaches that allow to combine the information from all replicates considering this phenomenon, confirming their validity both in simulation settings and also when applied to real inertial sensor error signals. By taking into account parameter variation between replicates, this work highlights how these approaches can improve the average navigation precision as well as obtain reliable estimates of the uncertainty of the navigation solution. © 2021, The Authors. All rights reserved.

关键词： Extended Kalman filters

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The kikuchi hierarchy and tensor PCA

arXiv

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arXiv 2019年

作者： Wein, Alexander S. El Alaoui, Ahmed Moore, Cristopher Department of Mathematics Courant Institute of Mathematical Sciences Nyu Departments of Electrical Engineering and Statistics Stanford University Santa Fe Institute

For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (approximate message passing). Our level- algorithm can be thought of as a linearized message-passing algorithm that keeps track of -wise dependencies among the hidden variables. Specifically, our algorithms are spectral methods based on the Kikuchi Hessian, which generalizes the well-studied Bethe Hessian to the higher-order Kikuchi free energies. It is known that AMP, the flagship algorithm of statistical physics, has substantially worse performance than SOS for tensor PCA. In this work we 'redeem' the statistical physics approach by showing that our hierarchy gives a polynomial-time algorithm matching the performance of SOS. Our hierarchy also yields a continuum of subexponential-time algorithms, and we prove that these achieve the same (conjecturally optimal) tradeoff between runtime and statistical power as SOS. Our proofs are much simpler than prior work, and also apply to the related problem of refuting random k-XOR formulas. The results we present here apply to tensor PCA for tensors of all orders, and to k-XOR when k is even. Our methods suggest a new avenue for systematically obtaining optimal algorithms for Bayesian inference problems, and our results constitute a step toward unifying the statistical physics and sum-of-squares approaches to algorithm *** Codes 68Q87 Copyright © 2019, The Authors. All rights reserved.

关键词： Tensors

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Improving the Automated Coronal Jet Identification with U-NET

arXiv

引用

arXiv 2024年

作者： Liu, Jiajia Ji, Chunyu Wang, Yimin Soós, Szabolcs Jiang, Ye Erdélyi, Robertus Korsós, M.B. Wang, Yuming Deep Space Exploration Lab School of Earth and Space Sciences University of Science and Technology of China Hefei230026 China CAS Key Laboratory of Geospace Environment CAS Center for Excellence in Comparative Planetology Mengcheng National Geophysical Observatory University of Science and Technology of China Hefei230026 China School of Data Science Qingdao University of Science and Technology Qingdao266100 China Department of Astronomy Eötvös Loránd University Pázmány P. sétány 1/A BudapestH-1117 Hungary Petőfi tér 3. GyulaH-5700 Hungary School of Information Science and Technology Qingdao University of Science and Technology Qingdao266100 China School of Mathematics and Statistics The University of Sheffield SheffieldS3 7RH United Kingdom University of Sheffield Department of Automatic Control and Systems Engineering Amy Johnson Building Portabello Street SheffieldS1 3JD United Kingdom

Coronal jets are one of the most common eruptive activities in the solar atmosphere. They are related to rich physics processes, including but not limited to magnetic reconnection, flaring, instabilities, and plasma heating. Automated identification of off-limb coronal jets has been difficult due to their abundant nature, complex appearance, and relatively small size compared to other features in the corona. In this paper, we present an automated coronal jet identification algorithm (AJIA) that utilizes true and fake jets previously detected by a laborious semi-automated jet detection algorithm (SAJIA, Liu et al. 2023) as the input of an image segmentation neural network U-NET. It is found that AJIA could achieve a much higher (0.81) detecting precision than SAJIA (0.34), meanwhile giving the possibility of whether each pixel in an input image belongs to a jet. We demonstrate that with the aid of artificial neural networks, AJIA could enable fast, accurate, and real-time coronal jet identification from SDO/AIA 304 Å observations, which are essential in studying the collective and long-term behavior of coronal jets and their relation with the solar activity cycles. Copyright © 2024, The Authors. All rights reserved.

关键词： Image segmentation

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Using Mechanistic Movement Models to Predict Geographic Range Expansions of Ticks and Tick-Borne Pathogens: Case Studies with the Ticks Ixodes Scapularis And Amblyomma Americanum in Eastern North America

SSRN

引用

SSRN 2022年

作者： Tardy, Olivia Acheson, Emily Sohanna Bouchard, Catherine Chamberland, Eric Fortin, André Ogden, Nicholas H. Leighton, Patrick A. Research Group on Epidemiology of Zoonoses and Public Health Faculty of Veterinary Medicine Université de Montréal 3200 rue Sicotte Saint-HyacintheQCJ2S 2M2 Canada Department of Mathematics and Statistics Faculty of Science and Engineering Université Laval 1045 avenue de la Médecine QuebecQCG1V 0A6 Canada Public Health Risk Sciences Division National Microbiology Laboratory Public Health Agency of Canada 3200 rue Sicotte Saint-HyacintheQCJ2S 2M2 Canada

The geographic range of the blacklegged tick, Ixodes scapularis, is expanding northward from the United States into southern Canada, and studies suggest that the lone star tick, Amblyomma americanum, will follow suit. These tick species are vectors for many zoonotic pathogens, and their northward range expansion presents a serious threat to public health. Climate change (particularly increasing temperature) has been identified as an important driver permitting northward range expansion of blacklegged ticks, but the impacts of host movement, which is essential to tick dispersal into new climatically suitable regions, have received limited investigation. Here, a mechanistic movement model was applied to landscapes of eastern North America to explore 1) relationships between multiple ecological drivers and the speed of the northward invasion of blacklegged ticks infected with the causative agent of Lyme disease, Borrelia burgdorferi, and 2) its capacity to simulate northward range expansion of the lone star tick and the Lyme disease bacterium under theoretical scenarios for increasing temperature. Results suggest that attraction of migratory birds (long-distance tick dispersal hosts) to resource-rich areas during their spring migration, and the mate-finding demographic Allee effect in tick population dynamics are key drivers of infected blacklegged tick spread. The modeled increases in temperature extended the climatically suitable areas of Canada for infected blacklegged ticks and lone star ticks towards higher latitudes by up to 31% and 1%, and with an average speed of range expansion reaching 61 km/year and 23 km/year, respectively. Differences in spatial distribution patterns of these tick species were due to differences in temperature sensitivity of tick populations, as well as the availability and attractiveness of suitable habitats for hosts. Our results indicate that the northward invasion process of lone star ticks is primarily driven by the local dispersal of

关键词： Stars

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Modelling COVID-19 transmission dynamics in Ghana

arXiv

引用

arXiv 2021年

作者： Acheampong, Edward Okyere, Eric Iddi, Samuel Bonney, Joseph H.K. Wattis, Jonathan A.D. Gomes, Rachel L. School of Mathematical Sciences University of Nottingham University Park NottinghamNG7 2RD United Kingdom Food Water Waste Research Group Faculty of Engineering University of Nottingham University Park NottinghamNG7 2RD United Kingdom Department of Mathematics and Statistics University of Energy and Natural Resources P.O. Box 214 Sunyani B/A Ghana Department of Statistics and Actuarial Science University of Ghana P.O. Box LG 115 Legon Ghana Virology Department Noguchi Memorial Institute For Medical Research University of Ghana P.O. Box LG 581 Legon Ghana

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies. To understand how the infection will spread and how to limit the outbreak. We have developed a modified SEIR compartmental model with nine compartments (CoVCom9) to describe the dynamics of SARS-CoV-2 transmission in Ghana. We have carried out a detailed mathematical analysis of the CoVCom9, including the derivation of the basic reproduction number, R0. In particular, we have shown that the disease-free equilibrium is globally asymptotically stable when R0 0 since the results derived are significant in controlling the spread of SARS-CoV-2. We estimate that over this five month period, the basic reproduction number is given by R0 = 3.110, with the 95% confidence interval being 2.042 ≤ R0 ≤ 3.240, and the mean value being R0 = 2.623. Of the 32 parameters in the model, we find that just six have a significant influence on R0, these include the rate of testing, where an increasing testing rate contributes to the reduction of R0. © 2021, CC BY.

关键词： SARS

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DATA-DRIVEN FAILURE PREDICTION IN BRITTLE MATERIALS: A PHASE-FIELD BASED MACHINE LEARNING FRAMEWORK∗

arXiv

引用

arXiv 2020年

作者： Barros De Moraes, Eduardo A. Salehi, Hadi Zayernouri, Mohsen Department of Mechanical Engineering Department of Computational Mathematics Science and Engineering Michigan State University 428 S Shaw Ln East LansingMI48824 United States Department of Mechanical Engineering Michigan State University 428 S Shaw Ln East LansingMI48824 United States Department of Mechanical Engineering Department of Statistics Probability Michigan State University 428 S Shaw Ln East LansingMI48824 United States

Failure in brittle materials led by the evolution of micro- to macro-cracks under repetitive or increasing loads is often catastrophic with no significant plasticity to advert the onset of fracture. Early failure detection with respective location are utterly important features in any practical application, both of which can be effectively addressed using artificial intelligence. In this paper, we develop a supervised machine learning (ML) framework to predict failure in an isothermal, linear elastic and isotropic phase-field model for damage and fatigue of brittle materials. Time-series data of the phase-field model is extracted from virtual sensing nodes at different locations of the geometry. A pattern recognition scheme is introduced to represent time-series data/sensor nodes responses as a pattern with a corresponding label, integrated with ML algorithms, used for damage classification with identified patterns. We perform an uncertainty analysis by superposing random noise to the time-series data to assess the robustness of the framework with noise-polluted data. Results indicate that the proposed framework is capable of predicting failure with acceptable accuracy even in the presence of high noise levels. The findings demonstrate satisfactory performance of the supervised ML framework, and the applicability of artificial intelligence and ML to a practical engineering problem, i.,e, data-driven failure prediction in brittle materials. Copyright © 2020, The Authors. All rights reserved.

关键词： Neural networks

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The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores

arXiv

引用

arXiv 2022年

作者： Grant, Samuel D.T. Jess, D.B. Stangalini, M. Jafarzadeh, S. Fedun, V. Verth, G. Keys, P.H. Rajaguru, S.P. Uitenbroek, H. Macbride, C.D. Bate, W. Gilchrist-Millar, C.A. Astrophysics Research Centre School of Mathematics and Physics Queen's University Belfast BelfastBT7 1NN United Kingdom Department of Physics and Astronomy California State University Northridge NorthridgeCA91330 United States ASI Italian Space Agency Via del Politecnico snc Rome00133 Italy Schöneckstr. 6 Freiburg79104 Germany Rosseland Centre for Solar Physics University of Oslo P.O. Box 1029 Blindern Oslo0315 Norway Plasma Dynamics Group Department of Automatic Control and Systems Engineering The University of Sheffield Mappin Street SheffieldS1 3JD United Kingdom Plasma Dynamics Group School of Mathematics and Statistics The University of Sheffield Hicks Building Hounsfield Road SheffieldS3 7RH United Kingdom Indian Institute of Astrophysics Bangalore34 India National Solar Observatory University of Colorado Boulder 3665 Discovery Drive BoulderCO80303 United States

Solar pores are efficient magnetic conduits for propagating magnetohydrodynamic wave energy into the outer regions of the solar atmosphere. Pore observations often contain isolated and/or unconnected structures, preventing the statistical examination of wave activity as a function of atmospheric height. Here, using high resolution observations acquired by the Dunn Solar Telescope, we examine photospheric and chromospheric wave signatures from a unique collection of magnetic pores originating from the same decaying sunspot. Wavelet analysis of high cadence photospheric imaging reveals the ubiquitous presence of slow sausage mode oscillations, coherent across all photospheric pores through comparisons of intensity and area fluctuations, producing statistically significant in-phase relationships. The universal nature of these waves allowed an investigation of whether the wave activity remained coherent as they propagate. Utilizing bi-sector Doppler velocity analysis of the Ca II 8542 Å line, alongside comparisons of the modeled spectral response function, we find fine-scale 5 mHz power amplification as the waves propagate into the chromosphere. Phase angles approaching zero degrees between co-spatial line depths spanning different line depths indicate standing sausage modes following reflection against the transition region boundary. Fourier analysis of chromospheric velocities between neighboring pores reveals the annihilation of the wave coherency observed in the photosphere, with examination of the intensity and velocity signals from individual pores indicating they behave as fractured wave guides, rather than monolithic structures. Importantly, this work highlights that wave morphology with atmospheric height is highly complex, with vast differences observed at chromospheric layers, despite equivalent wave modes being introduced into similar pores in the photosphere. © 2022, CC BY.

关键词： Magnetohydrodynamics

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Investigation of the Middle Corona with SWAP and a Data-Driven Non-Potential Coronal Magnetic Field Model

arXiv

引用

arXiv 2020年

作者： Meyer, Karen A. Mackay, Duncan H. Talpeanu, Dana-Camelia Upton, Lisa A. West, Matthew J. Mathematics School of Science & Engineering University of Dundee Nethergate DundeeDD1 4HN United Kingdom Division of Computing and Mathematics Abertay University Kydd Building Bell Street Dundee DD1 1HG United Kingdom School of Mathematics and Statistics University of St Andrews North Haugh St Andrews KY16 9SS United Kingdom Department of Mathematics KU Leuven Celestijnenlaan 200B Leuven3001 Belgium Ringlaan 3 Brussels1180 Belgium Space Systems Research Corporation AlexandriaVA22314 United States

The large field-of-view of the Sun Watcher using Active Pixel System detector and Image Processing (SWAP) instrument on board the PRoject for Onboard Autonomy 2 (PROBA2) spacecraft provides a unique opportunity to study extended coronal structures observed in EUV in conjunction with global coronal magnetic field simulations. A global non-potential magnetic field model is used to simulate the evolution of the global corona from 1 September 2014 to 31 March 2015, driven by newly emerging bipolar active regions determined from Helioseismic and Magnetic Imager (HMI) magnetograms. We compare the large-scale structure of the simulated magnetic field with structures seen off-limb in SWAP EUV observations. In particular, we investigate how successful the model is in reproducing regions of closed and open structures;the scale of structures;and compare the evolution of a coronal fan observed over several rotations. The model is found to accurately reproduce observed large-scale off-limb structures. When discrepancies do arise they mainly occur off the east solar limb due to active regions emerging on the far side of the Sun, which cannot be incorporated into the model until they are observed on the Earth-facing side. When such "late" active region emergences are incorporated into the model, we find that the simulated corona self-corrects within a few days, so that simulated structures off the west limb more closely match what is observed. Where the model is less successful, we consider how this may be addressed, through model developments or additional observational products. Copyright © 2020, The Authors. All rights reserved.

关键词： Magnetic fields

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