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Improving Molecular Force Fields with Minimal Temporal Information
Authors:
Ali Mollahosseini,
Mohammed Haroon Dupty,
Wee Sun Lee
Abstract:
Accurate prediction of energy and forces for 3D molecular systems is one of fundamental challenges at the core of AI for Science applications. Many powerful and data-efficient neural networks predict molecular energies and forces from single atomic configurations. However, one crucial aspect of the data generation process is rarely considered while learning these models i.e. Molecular Dynamics (MD…
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Accurate prediction of energy and forces for 3D molecular systems is one of fundamental challenges at the core of AI for Science applications. Many powerful and data-efficient neural networks predict molecular energies and forces from single atomic configurations. However, one crucial aspect of the data generation process is rarely considered while learning these models i.e. Molecular Dynamics (MD) simulation. MD simulations generate time-ordered trajectories of atomic positions that fluctuate in energy and explore regions of the potential energy surface (e.g., under standard NVE/NVT ensembles), rather than being constructed to steadily lower the potential energy toward a minimum as in geometry relaxations. This work explores a novel way to leverage MD data, when available, to improve the performance of such predictors. We introduce a novel training strategy called FRAMES, that use an auxiliary loss function for exploiting the temporal relationships within MD trajectories. Counter-intuitively, on two atomistic benchmarks and a synthetic system we observe that minimal temporal information, captured by pairs of just two consecutive frames, is often sufficient to obtain the best performance, while adding longer trajectory sequences can introduce redundancy and degrade performance. On the widely used MD17 and ISO17 benchmarks, FRAMES significantly outperforms its Equiformer baseline, achieving highly competitive results in both energy and force accuracy. Our work not only presents a novel training strategy which improves the accuracy of the model, but also provides evidence that for distilling physical priors of atomic systems, more temporal data is not always better.
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Submitted 14 April, 2026;
originally announced April 2026.
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Wavelength and Polarization Multiplexed Nonlocal Metasurface for Quantitative Phase Microscopy
Authors:
Haiwei Wang,
Shikun Ma,
Shaban B. Sulejman,
Niken Priscilla,
Wendy S. L. Lee,
Peter Francis Matthew Elango,
Lukas Wesemann,
Elizabeth Hinde,
Ann Roberts
Abstract:
Imaging transparent samples remains an ongoing challenge in the study of unstained biological cells and material samples. Widely used methods trade off system complexity, cost and bulk, computational efficiency and information content. Here we demonstrate the use of a nonlocal metasurface located in the object plane for obtaining single-shot, low-noise differential phase contrast images visualisin…
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Imaging transparent samples remains an ongoing challenge in the study of unstained biological cells and material samples. Widely used methods trade off system complexity, cost and bulk, computational efficiency and information content. Here we demonstrate the use of a nonlocal metasurface located in the object plane for obtaining single-shot, low-noise differential phase contrast images visualising phase gradients along orthogonal directions in a sample obtained at wavelengths of 613 nm and 656 nm. Furthermore, we show that these images are sufficient to calculate the quantitative phase introduced into the transmitted optical field by the sample. We find that the recovered phase of an optical field generated by a spatial light modulator is in good agreement with specified values. We also present information-rich differential phase contrast images of unstained HeLa cells with the recovered phase excursion values consistent with the literature. Our results demonstrate the potential for metasurfaces as a platform for extracting information from an optical field for use in next-generation compact imaging systems with applications in medical diagnostics, biotechnology, and materials science.
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Submitted 2 March, 2026;
originally announced March 2026.
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Symmetry-Constrained Multi-Scale Physics-Informed Neural Networks for Graphene Electronic Band Structure Prediction
Authors:
Wei Shan Lee,
I Hang Kwok,
Kam Ian Leong,
Chi Kiu Althina Chau,
Kei Chon Sio
Abstract:
Accurate prediction of electronic band structures in two-dimensional materials remains a fundamental challenge, with existing methods struggling to balance computational efficiency and physical accuracy. We present the Symmetry-Constrained Multi-Scale Physics-Informed Neural Network (SCMS-PINN) v35, which directly learns graphene band structures while rigorously enforcing crystallographic symmetri…
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Accurate prediction of electronic band structures in two-dimensional materials remains a fundamental challenge, with existing methods struggling to balance computational efficiency and physical accuracy. We present the Symmetry-Constrained Multi-Scale Physics-Informed Neural Network (SCMS-PINN) v35, which directly learns graphene band structures while rigorously enforcing crystallographic symmetries through a multi-head architecture. Our approach introduces three specialized ResNet-6 pathways -- K-head for Dirac physics, M-head for saddle points, and General head for smooth interpolation -- operating on 31 physics-informed features extracted from k-points. Progressive Dirac constraint scheduling systematically increases the weight parameter from 5.0 to 25.0, enabling hierarchical learning from global topology to local critical physics. Training on 10,000 k-points over 300 epochs achieves 99.99\% reduction in training loss (34.597 to 0.003) with validation loss of 0.0085. The model predicts Dirac point gaps within 30.3 $μ$eV of theoretical zero and achieves average errors of 53.9 meV (valence) and 40.5 meV (conduction) across the Brillouin zone. All twelve C$_{6v}$ operations are enforced through systematic averaging, guaranteeing exact symmetry preservation. This framework establishes a foundation for extending physics-informed learning to broader two-dimensional materials for accelerated discovery.
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Submitted 14 August, 2025;
originally announced August 2025.
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Breaking the Precision Ceiling in Physics-Informed Neural Networks: A Hybrid Fourier-Neural Architecture for Ultra-High Accuracy
Authors:
Wei Shan Lee,
Chi Kiu Althina Chau,
Kei Chon Sio,
Kam Ian Leong
Abstract:
Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We break through this barrier with a hybrid Fourier-neural architecture for the Euler-Bernoulli beam equation, achieving unprecedented L2 error of…
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Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We break through this barrier with a hybrid Fourier-neural architecture for the Euler-Bernoulli beam equation, achieving unprecedented L2 error of $1.94 \times 10^{-7}$-a 17-fold improvement over standard PINNs and \(15-500\times\) better than traditional numerical methods. Our approach synergistically combines a truncated Fourier series capturing dominant modal behavior with a deep neural network providing adaptive residual corrections. A systematic harmonic optimization study revealed a counter-intuitive discovery: exactly 10 harmonics yield optimal performance, with accuracy catastrophically degrading from $10^{-7}$ to $10^{-1}$ beyond this threshold. The two-phase optimization strategy (Adam followed by L-BFGS) and adaptive weight balancing enable stable ultra-precision convergence. GPU-accelerated implementation achieves sub-30-minute training despite fourth-order derivative complexity. By addressing 12 critical gaps in existing approaches-from architectural rigidity to optimization landscapes-this work demonstrates that ultra-precision is achievable through proper design, opening new paradigms for scientific computing where machine learning can match or exceed traditional numerical methods.
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Submitted 28 July, 2025;
originally announced July 2025.
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Deep learning methods for Hamiltonian parameter estimation and magnetic domain image generation in twisted van der Waals magnets
Authors:
Woo Seok Lee,
Taegeun Song,
Kyoung-Min Kim
Abstract:
The application of twist engineering in van der Waals magnets has opened new frontiers in the field of two-dimensional magnetism, yielding distinctive magnetic domain structures. Despite the introduction of numerous theoretical methods, limitations persist in terms of accuracy or efficiency due to the complex nature of the magnetic Hamiltonians pertinent to these systems. In this study, we introdu…
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The application of twist engineering in van der Waals magnets has opened new frontiers in the field of two-dimensional magnetism, yielding distinctive magnetic domain structures. Despite the introduction of numerous theoretical methods, limitations persist in terms of accuracy or efficiency due to the complex nature of the magnetic Hamiltonians pertinent to these systems. In this study, we introduce a deep-learning approach to tackle these challenges. Utilizing customized, fully connected networks, we develop two deep-neural-network kernels that facilitate efficient and reliable analysis of twisted van der Waals magnets. Our regression model is adept at estimating the magnetic Hamiltonian parameters of twisted bilayer CrI3 from its magnetic domain images generated through atomistic spin simulations. The generative model excels in producing precise magnetic domain images from the provided magnetic parameters. The trained networks for these models undergo thorough validation, including statistical error analysis and assessment of robustness against noisy injections. These advancements not only extend the applicability of deep-learning methods to twisted van der Waals magnets but also streamline future investigations into these captivating yet poorly understood systems.
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Submitted 1 June, 2024; v1 submitted 17 February, 2024;
originally announced February 2024.
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Coherent Exciton-Lattice Dynamics in a 2D Metal Organochalcogenolate Semiconductor
Authors:
Eric R. Powers,
Watcharaphol Paritmongkol,
Dillon C. Yost,
Woo Seok Lee,
Jeffrey C. Grossman,
William A. Tisdale
Abstract:
Hybrid organic-inorganic nanomaterials can exhibit transitional behavior that deviates from models developed for all-organic or all-inorganic materials systems. Here, we reveal the complexity of exciton-phonon interactions in a recently discovered 2D layered hybrid organic-inorganic semiconductor, silver phenylselenolate (AgSePh). Using femtosecond resonant impulsive vibrational spectroscopy and n…
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Hybrid organic-inorganic nanomaterials can exhibit transitional behavior that deviates from models developed for all-organic or all-inorganic materials systems. Here, we reveal the complexity of exciton-phonon interactions in a recently discovered 2D layered hybrid organic-inorganic semiconductor, silver phenylselenolate (AgSePh). Using femtosecond resonant impulsive vibrational spectroscopy and non-resonant Raman scattering, we measure multiple hybrid organic-inorganic vibrational modes and identify a subset of these modes that strongly couple to the electronic excited state. Calculations by density functional perturbation theory show that these strongly coupled modes exhibit large out-of-plane silver atomic motions and silver-selenium spacing displacements. Moreover, analysis of photoluminescence fine-structure splitting and temperature-dependent peak-shifting/linewidth-broadening suggests that light emission in AgSePh is most strongly affected by a compound 100 cm-1 mode involving the wagging motion of phenylselenolate ligands and accompanying metal-chalcogen stretching. Finally, red-shifting of vibrational modes with increasing temperature reveals a high degree of anharmonicity arising from non-covalent interactions between phenyl rings. These findings reveal the unique effects of hybrid vibrational modes in organic-inorganic semiconductors and motivate future work aimed at specifically engineering such interactions through chemical and structural modification.
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Submitted 12 October, 2023;
originally announced October 2023.
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Predator Extinction arose from Chaos of the Prey: the Chaotic Behavior of a Homomorphic Two-Dimensional Logistic Map in the Form of Lotka-Volterra Equations
Authors:
Wei Shan Lee,
Hou Fai Chan,
Ka Ian Im,
Kuan Ieong Chan,
U Hin Cheang
Abstract:
A two-dimensional homomorphic logistic map that preserves features of the Lotka-Volterra equations was proposed. To examine chaos, iteration plots of the population, Lyapunov exponents calculated from Jacobian eigenvalues of the $2$D logistic mapping, and from time series algorithms of Rosenstein and Eckmann et al. were calculated. Bifurcation diagrams may be divided into four categories depending…
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A two-dimensional homomorphic logistic map that preserves features of the Lotka-Volterra equations was proposed. To examine chaos, iteration plots of the population, Lyapunov exponents calculated from Jacobian eigenvalues of the $2$D logistic mapping, and from time series algorithms of Rosenstein and Eckmann et al. were calculated. Bifurcation diagrams may be divided into four categories depending on topological shapes. Our model not only recovered the $1$D logistic map, which exhibits flip bifurcation, for the prey when there is a nonzero initial predator population, but it can also simulate normal competition between two species with equal initial populations. Despite the possibility for two species to go into chaos simultaneously, where the Neimark-Sacker bifurcation was observed, it is also possible that with the same interspecies parameters as normal but with a predator population $10$ times more than that of the prey, the latter becomes chaotic, while the former dramatically reduces to zero with only a few iterations, indicating total annihilation of the predator species. Interpreting humans as predators and natural resources as preys in the ecological system, the above-mentioned conclusion may imply that not only excessive consumption of natural resources, but its chaotic state triggered by an overpopulation of humans may backfire in a manner of total extinction of the human species. Fortunately, there is little chance for the survival of the human race, as isolated fixed points in the bifurcation diagram of the predator reveal. Finally, two possible applications of the phenomenon of chaotic extinction are proposed: one is to inhibit viruses or pests by initiating the chaotic states of the prey on which the viruses or pests rely for existence, and the other is to achieve the superconducting state with the chaotic state of the applied magnetic field.
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Submitted 24 February, 2024; v1 submitted 27 January, 2023;
originally announced January 2023.
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Thin film notch filters as platforms for biological image processing
Authors:
Shaban B. Sulejman,
Niken Priscilla,
Lukas Wesemann,
Wendy S. L. Lee,
Jieqiong Lou,
Elizabeth Hinde,
Timothy J. Davis,
Ann Roberts
Abstract:
Many image processing operations involve the modification of the spatial frequency content of images. Here we demonstrate object-plane spatial frequency filtering utilizing the angular sensitivity of a commercial spectral bandstop filter. This approach to all-optical image processing is shown to generate real-time pseudo-3D images of transparent biological and other samples, such as human cervical…
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Many image processing operations involve the modification of the spatial frequency content of images. Here we demonstrate object-plane spatial frequency filtering utilizing the angular sensitivity of a commercial spectral bandstop filter. This approach to all-optical image processing is shown to generate real-time pseudo-3D images of transparent biological and other samples, such as human cervical cancer cells. This work demonstrates the potential of non-local, non-interferometric approaches to image processing for uses in label-free biological cell imaging and dynamical monitoring.
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Submitted 20 September, 2022;
originally announced September 2022.
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Optimal Layout Plan of Stands at the Macao Food Festival via Minimizing the Electrostatic Potential Energy with the Effective Charge as Popularity of Stands
Authors:
Ka Ian Im,
In Kio Choi,
Pak Kio Lei,
Hou Fai Chan,
U In Ian,
Wei Shan Lee
Abstract:
We proposed a mathematical model for designing the layout diagram of stand locations at the Macao Food Festival. The optimal layout diagram may be defined in such a way that, while requiring the distance between every pair of stands should not be too far away from each other, the crowd control is well managed so that people may patronize stands more effectively. More popular stands may have larger…
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We proposed a mathematical model for designing the layout diagram of stand locations at the Macao Food Festival. The optimal layout diagram may be defined in such a way that, while requiring the distance between every pair of stands should not be too far away from each other, the crowd control is well managed so that people may patronize stands more effectively. More popular stands may have larger patronage, resulting in higher pedestrian flow nearby. Therefore, to avoid customers from packing shoulder to shoulder around more popular stands, we may treat every stand as a charged particle carrying an effective charge: the more popular a stand is, the higher the effective charge it carries. Under this assumption, the problem is then converted to the minimization problem of Coulomb electrostatic potential energy on a specific configuration of charge locations, with which the global minimum may be found by the Simulated Annealing and Metropolis Algorithm. Electrostatic energy density is interpreted as density of customers, while electric field the reversed crowd flow. Therefore, at a certain location we are able to predict the customer density by calculating the energy density and the net crowd flow with electric field lines. We also concluded that even though the required computation time to obtain a configuration of stand locations with the energy value close to the global minimum with a tolerable difference may be irrelevant to the randomly generated initial configuration of stand locations, setting up an appropriate initial configuration could be one of the key issues to find out the actual global minimum.
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Submitted 16 February, 2022; v1 submitted 17 January, 2022;
originally announced January 2022.
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Applications of Traveling Salesman Problem on the Optimal Sightseeing Orders of Macao World Heritage Sites with Real Time or Distance Values Between Every Pair of Sites
Authors:
Kin Neng Tong,
Iat In Fong,
In Iat Li,
Chi Him Anthony Cheng,
Soi Chak Choi,
Hau Xiang Ye,
Wei Shan Lee
Abstract:
The optimal route of sightseeing orders for visiting every Macao World Heritage Site at exactly once was calculated with Simulated Annealing and Metropolis Algorithm(SAMA) after considering real required time or traveling distance between pairs of sites by either driving a car, taking a bus, or on foot. We found out that, with the optimal tour path, it took roughly 78 minutes for driving a car, 11…
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The optimal route of sightseeing orders for visiting every Macao World Heritage Site at exactly once was calculated with Simulated Annealing and Metropolis Algorithm(SAMA) after considering real required time or traveling distance between pairs of sites by either driving a car, taking a bus, or on foot. We found out that, with the optimal tour path, it took roughly 78 minutes for driving a car, 115 minutes on foot, while 117 minutes for taking a bus. On the other hand, the optimal total distance for driving a car would be 13.918 km while for pedestrians to walk, 7.844 km. These results probably mean that there is large space for the improvement on public transportation in this city. Comparison of computation time demanded between the brute-force enumeration of all possible paths and SAMA was also presented, together with animation of the processes for the algorithm to find out the optimal route. It is expected that computation time is astronomically increasing for the brute-force enumeration with more number of sites, while it only takes SAMA much less order of magnitude in time to calculate the optimal solution for larger number of sites. Several optimal options of routes were also provided in each transportation method. However, it is possible that in some types of transportation there could be only one optimal route having no circular or mirrored duplicates.
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Submitted 29 August, 2021;
originally announced September 2021.
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O-Band Subwavelength Grating Filters in a Monolithic Photonics Technology
Authors:
Francis O. Afzal,
Yusheng Bian,
Bo Peng,
Shuren Hu,
Kevin Dezfulian,
Karen Nummy,
Andy Stricker,
Abdelsalam Aboketaf,
Crystal Hedges,
Zoey Sowinski,
Michal Rakowski,
Won Suk Lee,
Rod Augur,
Dave Riggs,
Ken Giewont,
Sharon M. Weiss
Abstract:
The data communications industry has begun transitioning from electrical to optical interconnects in datacenters in order to overcome performance bottlenecks and meet consumer needs. To mitigate the costs associated with this change and achieve performance for 5G and beyond, it is crucial to explore advanced photonic devices that can enable high-bandwidth interconnects via wavelength-division mult…
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The data communications industry has begun transitioning from electrical to optical interconnects in datacenters in order to overcome performance bottlenecks and meet consumer needs. To mitigate the costs associated with this change and achieve performance for 5G and beyond, it is crucial to explore advanced photonic devices that can enable high-bandwidth interconnects via wavelength-division multiplexing (WDM) in photonic integrated circuits. Subwavelength grating (SWG) filters have shown great promise for WDM applications. However, the small feature sizes necessary to implement these structures have prohibited them from penetrating into industrial applications. To explore the manufacturability and performance of SWG filters in an industrial setting, we fabricate and characterize O-band subwavelength grating filters using the monolithic photonics technology at GLOBALFOUNDRIES (GF). We demonstrate a low drop channel loss of -1.2 dB with a flat-top response, a high extinction ratio of -30 dB, a 3 dB channel width of 5 nm and single-source thermal tunability without shape distortion. This filter structure was designed using elements from the product design kit provided by GF and functions in a compact footprint of 0.002 mm2 with a minimum feature size of 150 nm.
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Submitted 30 April, 2020;
originally announced May 2020.
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Deep Learning of Chaos Classification
Authors:
Woo Seok Lee,
Sergej Flach
Abstract:
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need to evaluate the Lyapunov exponent. The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional…
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We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need to evaluate the Lyapunov exponent. The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional Lyapunov exponent computation is far from converging. We show the robustness of the neural network to varying control parameters, in particular we train with one set of control parameters, and successfully test in a complementary set. Furthermore, we use the neural network to successfully test the dynamics of discrete maps in different dimensions, e.g. the one-dimensional logistic map and a three-dimensional discrete version of the Lorenz system. Our results demonstrate that a convolutional neural network can be used as an excellent chaos indicator.
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Submitted 23 April, 2020;
originally announced April 2020.
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Fast frequency discrimination and phoneme recognition using a biomimetic membrane coupled to a neural network
Authors:
Woo Seok Lee,
Hyunjae Kim,
Andrew N. Cleland,
Kang-Hun Ahn
Abstract:
In the human ear, the basilar membrane plays a central role in sound recognition. When excited by sound, this membrane responds with a frequency-dependent displacement pattern that is detected and identified by the auditory hair cells combined with the human neural system. Inspired by this structure, we designed and fabricated an artificial membrane that produces a spatial displacement pattern in…
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In the human ear, the basilar membrane plays a central role in sound recognition. When excited by sound, this membrane responds with a frequency-dependent displacement pattern that is detected and identified by the auditory hair cells combined with the human neural system. Inspired by this structure, we designed and fabricated an artificial membrane that produces a spatial displacement pattern in response to an audible signal, which we used to train a convolutional neural network (CNN). When trained with single frequency tones, this system can unambiguously distinguish tones closely spaced in frequency. When instead trained to recognize spoken vowels, this system outperforms existing methods for phoneme recognition, including the discrete Fourier transform (DFT), zoom FFT and chirp z-transform, especially when tested in short time windows. This sound recognition scheme therefore promises significant benefits in fast and accurate sound identification compared to existing methods.
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Submitted 9 April, 2020;
originally announced April 2020.
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A low-cost cryogenic temperature measurement system using Arduino microcontroller
Authors:
Woong Sung Lee
Abstract:
We developed a simple, flexible, low-cost, and computer-controlled cryogenic temperature measurement system for undergraduate instructional laboratories. An Arduino microcontroller board measures the voltage across a silicon diode to calculate its temperature. Resistors and a voltage regulator provide constant current into the silicon diode. We present a graphical user interface based on the open-…
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We developed a simple, flexible, low-cost, and computer-controlled cryogenic temperature measurement system for undergraduate instructional laboratories. An Arduino microcontroller board measures the voltage across a silicon diode to calculate its temperature. Resistors and a voltage regulator provide constant current into the silicon diode. We present a graphical user interface based on the open-source Processing language. The cost of the complete temperature measurement system is thus only a small fraction of any highly-developed commercial system. Our performance test shows that the system works at a reasonable accuracy from 297.15 K (typical room temperature) down to 77 K (liquid nitrogen temperature).
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Submitted 20 October, 2019;
originally announced October 2019.
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Simplifying the vacuum bazooka
Authors:
Junghwan Lee,
Woong Sung Lee,
Eunsoo Shin
Abstract:
This paper provides a simplified explanation of the vacuum bazooka through diagrams and builds a theoretical model only using concepts found in introductory mechanics. Our theory suggests that the velocity of the projectile is proportional to the hyperbolic tangent of time, and experimental measurements support this claim. We also find that the vacuum bazooka could be used to demonstrate the conce…
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This paper provides a simplified explanation of the vacuum bazooka through diagrams and builds a theoretical model only using concepts found in introductory mechanics. Our theory suggests that the velocity of the projectile is proportional to the hyperbolic tangent of time, and experimental measurements support this claim. We also find that the vacuum bazooka could be used to demonstrate the concept of terminal velocity in a classroom setting.
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Submitted 19 March, 2019; v1 submitted 17 January, 2019;
originally announced January 2019.
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A modified porous titanium sheet prepared by plasma activated sintering for biomedical applications
Authors:
Yukimichi Tamaki,
Won Sik Lee,
Yu Kataoka,
Takashi Miyazaki
Abstract:
This study aimed to develop a contamination free porous titanium scaffold by a plasma activated sintering within an originally developed TiN coated graphite mold. The surface of porous titanium sheet with or without a coated graphite mold was characterized. The cell adhesion property of porous titanium sheet was also evaluated in this study. The peak of TiC was detected on the titanium sheet proce…
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This study aimed to develop a contamination free porous titanium scaffold by a plasma activated sintering within an originally developed TiN coated graphite mold. The surface of porous titanium sheet with or without a coated graphite mold was characterized. The cell adhesion property of porous titanium sheet was also evaluated in this study. The peak of TiC was detected on the titanium sheet processed with the graphite mold without a TiN coating. Since the titanium fiber elements were directly in contact with the carbon graphite mold during processing, surface contamination was unavoidable event in this condition. The TiC peak was not detectable on the titanium sheet processed within the TiN coated carbon graphite mold. This modified plasma activated sintering with the TiN coated graphite mold would be useful to fabricate a contamination free titanium sheet. The number of adherent cells on the modified titanium sheet was greater than that of the bare titanium plate. Stress fiber formation and the extension of the cells were observed on the titanium sheets. This modified titanium sheet is expected to be a new tissue engineering material in orthopedic bone repair.
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Submitted 7 May, 2010; v1 submitted 22 April, 2010;
originally announced April 2010.