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arXiv 2018年

作者： Brio, Moysey Caputo, Jean-Guy Gwirtz, Kyle Liu, Jinjie Maimistov, Andrei Department of Mathematics University of Arizona TucsonAZ85721 United States Laboratoire de Mathématiques INSA Rouen Normandie Saint-Etienne du Rouvray76801 France Program in Applied Mathematics University of Arizona TucsonAZ85721 United States Department of Mathematical Sciences Delaware State University DoverDE19901 United States Department of Solid State Physics and Nanostructures National Research Nuclear University Moscow Engineering Physics Institute Kashirskoe sh. 31 Moscow115409 Russia

We combine scattering theory, Fourier, traveling wave and asymptotic analyses together with numerical simulations to present interesting and practically useful properties of femtosecond pulse interaction with thin films. The dispersive material is described by a single resonance Lorentz model and its nonlinear extension with a cubic Duffing-type nonlinearity. A key feature of the Lorentz dielectric function is that its real part becomes negative between its zero and its pole, generating a forbidden region. We illustrate numerically the linear interaction of the pulse with the film using both scattering theory and Fourier analysis. Outside this region we show the generation of a sequence of pulses separated by round trips in the Fabry-Perot cavity due to multiple reflections. When the pulse spectrum is inside the forbidden region, we observe total reflection. Near the pole of the dielectric function, we demonstrate the slowing down of the pulse (group velocity tending to zero) in the medium that behaves as a high-Q cavity. We use the combination of analysis and simulations in the linear regime to validate the delta function approximation of the thin layer;this collapses the forbidden region to a single resonant point of the spectrum. We also study the single cycle pulse interaction with a thin film and show three distinct types of reflection: half-pulse, sinusoidal wave train and cosine wavelet. Finally we analyze the influence of a strong nonlinearity and observe that the film switches from reflecting to trasparent. Copyright © 2018, The Authors. All rights reserved.

关键词： Thin films

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A limited habitable zone for complex life

arXiv

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arXiv 2019年

作者： Schwieterman, Edward W. Reinhard, Christopher T. Lyons, Timoth W. Olson, Stephanie L. Harman, Chester E. Department of Earth and Planetary Sciences University of California RiversideCA United States NASA Postdoctoral Program Universities Space Research Association ColumbiaMD United States NASA Astrobiology Institute Alternative Earths Team RiversideCA United States Virtual Planetary Laboratory SeattleWA United States Bl M bl S I tit t f S i S ttl W hi t United States School of Earth and Atmospheric Sciences Georgia Institute of Technology AtlantaGA United States De artment of Geo h sical Sciences Universit of Chica o Chica o IL United States NASA Goddard Institute for S ace Studies New YorkNY United States Department of Applied Mathematics and Applied Physics Columbia University New YorkNY United States

The habitable zone (HZ) is commonly defined as the range of distances from a host star within which liquid water, a key requirement for life, may exist on a planet’s surface. Substantially more CO2 than present in Earth’s modern atmosphere is required to maintain clement temperatures for most of the HZ, with several bars required at the outer edge. However, most complex aerobic life on Earth is limited by CO2 concentrations of just fractions of a bar. At the same time, most exoplanets in the traditional HZ reside in proximity to M dwarfs, which are more numerous than Sun-like G dwarfs but are predicted to promote greater abundances of gases that can be toxic in the atmospheres of orbiting planets, such as carbon monoxide (CO). Here we show that the HZ for complex aerobic life is likely limited relative to that for microbial life. We use a 1D radiative-convective climate and photochemical models to circumscribe a Habitable Zone for Complex Life (HZCL) based on known toxicity limits for a range of organisms as a proof of concept. We find that for CO2 tolerances of 0.01, 0.1, and 1 bar, the HZCL is only 21%, 32%, and 50% as wide as the conventional HZ for a Sun-like star, and that CO concentrations may limit some complex life throughout the entire HZ of the coolest M dwarfs. These results cast new light on the likely distribution of complex life in the universe and have important ramifications for the search for exoplanet biosignatures and technosignatures. Copyright © 2019, The Authors. All rights reserved.

关键词： Carbon monoxide

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Ten quick tips for deep learning in biology

arXiv

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arXiv 2021年

作者： Lee, Benjamin D. Gitter, Anthony Greene, Casey S. Raschka, Sebastian Maguire, Finlay Titus, Alexander J. Kessler, Michael D. Lee, Alexandra J. Chevrette, Marc G. Stewart, Paul Allen Britto-Borges, Thiago Cofer, Evan M. Yu, Kun-Hsing Carmona, Juan Jose Fertig, Elana J. Kalinin, Alexandr A. Signal, Beth Lengerich, Benjamin J. Triche, Timothy J. Boca, Simina M. In-Q-Tel Labs School of Engineering and Applied Sciences Harvard University Department of Genetics Harvard Medical School United States Department of Biostatistics and Medical Informatics University of Wisconsin-Madison MadisonWI United States Morgridge Institute for Research MadisonWI United States Department of Systems Pharmacology and Translational Therapeutics Perelman School of Medicine University of Pennsylvania PhiladelphiaPA United States Department of Biochemistry and Molecular Genetics University of Colorado School of Medicine AuroraCO United States Center for Health AI University of Colorado School of Medicine AuroraCO United States Department of Statistics University of Wisconsin Madison United States Faculty of Computer Science Dalhousie University Canada University of New Hampshire Bioeconomy.XYZ United States Department of Oncology Johns Hopkins University United States Institute for Genome Sciences University of Maryland School of Medicine United States Genomics and Computational Biology Graduate Program University of Pennsylvania United States Department of Systems Pharmacology and Translational Therapeutics University of Pennsylvania United States Wisconsin Institute for Discovery Department of Plant Pathology University of Wisconsin-Madison United States Department of Biostatistics and Bioinformatics Moffitt Cancer Center TampaFL United States Section of Bioinformatics and Systems Cardiology Klaus Tschira Institute for Integrative Computational Cardiology University Hospital Heidelberg Germany University Hospital Heidelberg Germany Lewis-Sigler Institute for Integrative Genomics Princeton University PrincetonNJ United States Graduate Program in Quantitative and Computational Biology Princeton University PrincetonNJ United States Department of Biomedical Informatics Harvard Medical School United States Department of Pathology Brigham and Women's Hospital United States Philips Healthcare CambridgeMA United States Philips Research

Machine learning is a modern approach to problem-solving and task automation. In particular, machine learning is concerned with the development and applications of algorithms that can recognize patterns in data and use them for predictive modeling. Artificial neural networks are a particular class of machine learning algorithms and models that evolved into what is now described as deep learning. Given the computational advances made in the last decade, deep learning can now be applied to massive data sets and in innumerable contexts. Therefore, deep learning has become its own subfield of machine learning. In the context of biological research, it has been increasingly used to derive novel insights from high-dimensional biological data. To make the biological applications of deep learning more accessible to scientists who have some experience with machine learning, we solicited input from a community of researchers with varied biological and deep learning interests. These individuals collaboratively contributed to this manuscript's writing using the GitHub version control platform and the Manubot manuscript generation toolset. The goal was to articulate a practical, accessible, and concise set of guidelines and suggestions to follow when using deep learning. In the course of our discussions, several themes became clear: the importance of understanding and applying machine learning fundamentals as a baseline for utilizing deep learning, the necessity for extensive model comparisons with careful evaluation, and the need for critical thought in interpreting results generated by deep learning, among others. © 2021, CC BY.

关键词： Learning algorithms

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Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator

arXiv

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arXiv 2017年

作者： Li, Qianxiao Dietrich, Felix Bollt, Erik M. Kevrekidis, Ioannis G. Institute of High Performance Computing Singapore Singapore Faculty of Mathematics Technical University of Munich Germany Department of Mathematics Clarkson University United States Department of Chemical and Biological Engineering Program in Applied and Computational Mathematics Princeton University United States

Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are becoming increasingly popular in practical applications. The EDMD improves upon the classical DMD by the inclusion of a flexible choice of dictionary of observables that spans a finite dimensional subspace on which the Koopman operator can be approximated. This enhances the accuracy of the solution reconstruction and broadens the applicability of the Koopman formalism. Although the convergence of the EDMD has been established, applying the method in practice requires a careful choice of the observables to improve convergence with just a finite number of terms. This is especially difficult for high dimensional and highly nonlinear systems. In this paper, we employ ideas from machine learning to improve upon the EDMD method. We develop an iterative approximation algorithm which couples the EDMD with a trainable dictionary represented by an artificial neural network. Using the Duffing oscillator and the Kuramoto Sivashinsky PDE as examples, we show that our algorithm can effectively and efficiently adapt the trainable dictionary to the problem at hand to achieve good reconstruction accuracy without the need to choose a fixed dictionary a priori. Furthermore, to obtain a given accuracy we require fewer dictionary terms than EDMD with fixed dictionaries. This alleviates an important shortcoming of the EDMD algorithm and enhances the applicability of the Koopman framework to practical problems. Copyright © 2017, The Authors. All rights reserved.

关键词： Machine learning

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Physical, optical and luminescence properties of Sm 3+ doped lithium aluminium phosphate glass system

引用

Materials Today: Proceedings 2018年第7期5卷 15066-15071页

作者： N. Chanthima Y. Tariwong M. Djamal J. Kaewkhao N. Sangwaranatee Center of Excellence in Glass Technology and Materials Science (CEGM) Nakhon Pathom Rajabhat University Nakhon Pathom 73000 Thailand Physics Program Faculty of Science and Technology Nakhon Pathom Rajabhat University Nakhon Pathom 73000 Thailand Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung 40132 Indonesia Applied Physics Faculty of Science and Technology Suan Sunandha Rajabhat University Bangkok 10300 Thailand

Sm 3+ doped lithium aluminium phosphate glasses have been investigated in different concentration of Sm 3+ ions. The physical, optical and luminescence properties were studied to evaluate their potential to using as orange color emitting materials. The result of physical properties indicated that the density, the molar volume and the refractive index of glass samples were increased with an increase of Sm 2 O 3 content. The absorption spectra of glass samples were recorded in the wavelength range of 250-2000 nm. The absorption bands centered at 401, 473, 947, 1080, 1232, 1379, 1482 and 1532 nm have been observed. From the photoluminescence spectra, the glasses are showed strong emission at 597 nm which corresponds to 4 G 5/2 → 6 H 7/2 transition under excitation wavelength at 401 nm. The optimal concentration of Sm 2 O 3 in lithium aluminium phosphate glasses was 0.5 mol%.

关键词： Luminescence properties Phosphate glass Physical properties Samarium

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Signatures of quantum mechanics in chaotic systems

arXiv

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arXiv 2017年

作者： Short, Kevin M Morena, Matthew A Integrated Applied Mathematics Program University of New Hampshire DurhamNH03824 United States Division of Mathematics and Science Young Harris College Young HarrisGA30582 United States

We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system's set of cupolets, which are essentially highly-accurate stabilizations of its unstable periodic orbits. The discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external intervention. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, then the chaotic entanglement would be broken. In this paper, we further describe chaotic entanglement and go on to discuss the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, the measurement problem, the superposition of states, and to quantum entropy de_nitions. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. Copyright © 2017, The Authors. All rights reserved.

关键词： Chaotic systems

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Multi-frequency effect towards High Conductivity Overburden Responses using Vertical Coplanar (VCP) coil configuration for Landslide Instrumentation

引用

Journal of Physics: Conference Series 2018年第1期1120卷

作者： Muhammad Syukri Surbakti Bukhari Nazli Ismail Nasrullah Idris Elin Yusibani Muhammad Isa Saumi Syahreza Department of Physics Faculty of Mathematics and Natural Sciences University of Syiah Kuala Banda Aceh Indonesia 23111 Doctorate Program of Mathematics and Applied Science (DMAS) Postgraduate Program University of Syiah Kuala Banda Aceh Indonesia 23111

A novel instrumentation for landslide application has been made and calibrated using Vertical Coplanar (VCP) coil orientation. The early instrumentation and commonly used right now for landslide slopes was gradually equipped with standard and automatic instrumentation: three the piezometric cells, two deep-seated steel wire extensometers, four inclinometric tubes, a rainfall gauge, a snow gauge and an air thermometer. This novel instrumentation works in electromagnetic methods similar with electromagnetic methods in geophysics; otherwise, the system was mechanics and electronics. VCP coil orientation is a coplanar array where both coils are vertical. In VCP, the depth of sounding is about 1.5 times of the coils separation. The overburden thicknesses in the field exploration are often covering the tropical area and presented as weathering layer. The more of overburden thickness then the more of energy of electromagnetic wave will be absorbed, as the result that the electromagnetic wave becomes smaller. The electromagnetic wave that reaches the target of the subsurface is also become smaller in amplitude. The multi-frequency application would be helpful in the data interpretation of the anomaly position and the conductive overburden caused by the domination trends between out-of-phase (OP) and in-phase (IP) components could be determined. In the higher frequencies (3037.5 Hz and 1012.5 Hz), the curve of IP is raised up, with the result that the positive peak values become higher and the negative peak values become lower in levels. The multi-frequency application gives the results that in the higher frequency examinations, the anomaly response is influenced significantly by the conductive overburden. In the lower frequency measurements, the anomaly response is not influenced significantly by overburden response. In the higher frequency measurements, when the electromagnetic wave is passing through the conductive material, the amplitude attenuation and the phase shiftin

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Optimal jittered sampling for two points in the unit square

arXiv

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arXiv 2017年

作者： Pausinger, Florian Rachh, Manas Steinerberger, Stefan TU Munich Germany Applied Mathematics Program Yale University New HavenCT06510 United States Department of Mathematics Yale University New HavenCT06510 United States

Jittered Sampling is a refinement of the classical Monte Carlo sampling method. Instead of picking n points randomly from [0, 1]2, one partitions the unit square into n regions of equal measure and then chooses a point randomly from each partition. Currently, no good rules for how to partition the space are available. In this paper, we present a solution for the special case of subdividing the unit square by a decreasing function into two regions so as to minimize the expected squared L2−discrepancy. The optimal partitions are given by a highly nonlinear integral equation for which we determine an approximate solution. In particular, there is a break of symmetry and the optimal partition is not into two sets of equal measure. We hope this stimulates further interest in the construction of good partitions.65C05 (primary) and 93E20 (secondary). Copyright © 2017, The Authors. All rights reserved.

关键词： Monte Carlo methods

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On singularity formation in a Hele-Shaw model

arXiv

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arXiv 2017年

作者： Constantin, Peter Elgindi, Tarek Nguyen, Huy Vicol, Vlad Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Uc San Diego San DiegoCA92093 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in [CDG+93] and widely studied since. The model consists of a single one dimensional evolution equation for the thickness 2h = 2h(x, t) of a thin neck of fluid, ∂th + ∂x(h ∂x3h) = 0, for x ∈ (−1, 1) and t ≥ 0. The boundary conditions fix the neck height and the pressure jump: h(±1, t) = 1, ∂x2h(±1, t) = P > 0. We prove that starting from smooth and positive h, as long as h(x, t) > 0, for x ∈ [−1, 1], t ∈ [0, T ], no singularity can arise in the solution up to time T. As a consequence, we prove for any P > 2 and any smooth and positive initial datum that the solution pinches off in either finite or infinite time, i.e., inf[−1,1]×[0,T∗) h = 0, for some T∗ ∈ (0, ∞]. These facts have been long anticipated on the basis of numerical and theoretical studies. August 30, 2017.35Q35, 35Q86 Copyright © 2017, The Authors. All rights reserved.

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Group synchronization on grids

arXiv

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arXiv 2017年

作者： Abbe, Emmanuel Massoulie, Laurent Montanari, Andrea Sly, Allan Srivastava, Nikhil Program in Applied and Computational Mathematics EE Department Princeton University Inria MSR-Inria Joint Centre Department of Electrical Engineering Department of Sttistics Stanford University Department of Mathematics Princeton University Department of Mathematics University of California Berkeley United States

Group synchronization requires to estimate unknown elements (θv)v∈V of a compact group G associated to the vertices of a graph G = (V, E), using noisy observations of the group differences associated to the edges. This model is relevant to a variety of applications ranging from structure from motion in computer vision to graph localization and positioning, to certain families of community detection problems. We focus on the case in which the graph G is the d-dimensional grid. Since the unknowns θv are only determined up to a global action of the group, we consider the following weak recovery question. Can we determine the group difference θ−u1θv between far apart vertices u, v better than by random guessing? We prove that weak recovery is possible (provided the noise is small enough) for d ≥ 3 and, for certain finite groups, for d ≥ 2. Viceversa, for some continuous groups, we prove that weak recovery is impossible for d = 2. Finally, for strong enough noise, weak recovery is always impossible. Copyright © 2017, The Authors. All rights reserved.

关键词： Recovery

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