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Nonlinear Violence in Nonlinear Oscillations at High Energy

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Applied Mathematics 2024年第1期15卷 65-95页

作者： yair Zarmi Jacob Blaustein Institutes for Desert Research Ben-Gurion University of the Negev Midreshet Ben-Gurion Israel

This paper focuses on the characteristics of solutions of nonlinear oscillatory systems in the limit of very high oscillation energy, E;specifically, systems, in which the nonlinear driving force grows with energy much faster for x(t) close to the turning point, a(E), than at any position, x(t), that is not too close to a(E). This behavior dominates important aspects of the solutions. It will be called “nonlinear violence”. In the vicinity of a turning point, the solution of a nonlinear oscillatory systems that is affected by nonlinear violence exhibits the characteristics of boundary-layer behavior (independently of whether the equation of motion of the system can or cannot be cast in the traditional form of a boundary-layer problem.): close to a(E), x(t) varies very rapidly over a short time interval (which vanishes for E → ∞). In traditional boundary layer systems this would be called the “inner” solution. Outside this interval, x(t) soon evolves into a moderate profile (e.g. linear in time, or constant)—the “outer” solution. In (1 + 1)-dimensional nonlinear energy-conserving oscillators, if the solution is reflection-invariant, nonlinear violence determines the characteristics of the whole solution. For large families of nonlinear oscillatory systems, as E → ∞, the solutions for x(t) tend to common, indistinguishable profiles, such as periodic saw-tooth profiles or step-functions. If such profiles are observed experimentally in high-energy oscillations, it may be difficult to decipher the dynamical equations that govern the motion. The solution of motion in a central field with a non-zero angular momentum exhibits extremely fast rotation around a turning point that is affected by nonlinear violence. This provides an example for the possibility of interesting phenomena in (1 + 2)-dimensional oscillatory systems.

关键词： High-Energy Oscillations Nonlinear Violence Boundary-Layer Characteristics

Unified Description of the Three Stable Particles in Self-Action Allows Determination of Their Relative Masses

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Journal of High Energy Physics, Gravitation and Cosmology 2024年第1期10卷 185-196页

作者： yair Goldin Halfon Mexico City Mexico

The Dirac equation γμ(δμ-eAμ)Ψ=mc2Ψ describes the bound states of the electron under the action of external potentials, Aμ. We assumed that the fundamental form of the Dirac equation γμ(δμ-Sμ)Ψ=0 should describe the stable particles (the electron, the proton and the dark-matter-particle (dmp)) bound to themselves under the action of their own potentials Sμ. The new equation reveals that self energy is consequence of self action, it also reveals that the spin angular momentum is consequence of the dynamic structure of the stable particles. The quantitative results are the determination of their relative masses as well as the determination of the electromagnetic coupling constant.

关键词： Electron in Self Action Electron-Dark-Matter Particle Mass Ratio Analytic Description Dark-Matter-Particle

以色列研究生教育的基本特征、内容体系与实践路径

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研究生教育研究 2024年第2期 111-117页

作者：王晨霏 Gad yair 东北师范大学思想政治教育研究中心长春130024 耶路撒冷希伯来大学创新教育研究中心耶路撒冷91905以色列

以色列以教育立国,其研究生教育为人才培养、科技创新、农业振兴、经济增长、民族复兴、国防安全作出了重大贡献。以色列研究生教育的形成和发展受意识形态、社会文化、道德习俗等多方面综合影响,经历了精英教育到大众教育的转变,形成... 详细信息

以色列以教育立国,其研究生教育为人才培养、科技创新、农业振兴、经济增长、民族复兴、国防安全作出了重大贡献。以色列研究生教育的形成和发展受意识形态、社会文化、道德习俗等多方面综合影响,经历了精英教育到大众教育的转变,形成了科研方向以国家意志为导向、教育体系以追求卓越与普及大众相结合、教育对象多元化的现实样态。以色列研究生教育以培养人才和学术卓越为根本目标,其内容体系涵盖坚定理想信念、坚守卓越学术、坚持自我完善三个维度,其实践进路包括专业课程培养、隐性思政培育、职业技能培训等主要途径。

关键词：以色列研究生研究生教育大学学术学院

Nonlinear Violence in Nonlinear Oscillations at High Energy

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Deep learning accelerates whole slide imaging for next-generation digital pathology applications

Applied Mathematics（应用数学） 2024年第1期

作者： yair Zarmi

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Light(Science & Applications) 2022年第11期11卷 2558-2560页

作者： yair Rivenson Aydogan Ozcan Pictor Labs InLos AngelesUSA Electrical and Computer Engineering Department University of CaliforniaLos Angeles 90095 CAUSA Bioengineering Department University of CaliforniaLos Angeles 90095 CAUSA California NanoSystems Institute(CNSI) University of CaliforniaLos Angeles 90095 CAUSA Department of Surgery David Geffen School of MedicineUniversity of CaliforniaLos Angeles 90095 CAUSA

Deep learning demonstrates the ability to significantly increase the scanning speed of whole slide imaging in *** transformative solution can be used to further accelerate the adoption of digital pathology.

关键词： Deep learning slide

All-optical information-processing capacity of diffractive surfaces

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Light(Science & Applications) 2021年第2期10卷 217-233页

作者： Onur Kulce Deniz Mengu yair Rivenson Aydogan Ozcan Electrical and Computer Engineering Department University of CaliforniaLos AngelesCA 90095USA Bioengineering Department University of CaliforniaLos AngelesCA 90095USA California NanoSystems Institute University of CaliforniaLos AngelesCA 90095USA

The precise engineering of materials and surfaces has been at the heart of some of the recent advances in optics and *** advances related to the engineering of materials with new functionalities have also opened up exciting avenues for designing trainable surfaces that can perform computation and machine-learning tasks through light-matter interactions and ***,we analyze the information-processing capacity of coherent optical networks formed by diffractive surfaces that are trained to perform an all-optical computational task between a given input and output *** show that the dimensionality of the all-optical solution space covering the complex-valued transformations between the input and output fields-of-view is linearly proportional to the number of diffractive surfaces within the optical network,up to a limit that is dictated by the extent of the input and output *** diffractive networks that are composed of larger numbers of trainable surfaces can cover a higher-dimensional subspace of the complex-valued linear transformations between a larger input field-of-view and a larger output field-of-view and exhibit depth advantages in terms of their statistical inference,learning,and generalization capabilities for different image classification tasks when compared with a single trainable diffractive *** analyses and conclusions are broadly applicable to various forms of diffractive surfaces,including,e.g.,plasmomc and/or dielectric-based metasurfaces and flat optics,which can be used to form all-optical processors.

关键词： surface. valued optics

All-optical synthesis of an arbitrary linear transformation using diffractive surfaces

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Light(Science & Applications) 2021年第10期10卷 1928-1948页

Spatially-engineered diffractive surfaces have emerged as a powerful framework to control light-matter interactions for statistical inference and the design of task-specific optical ***,we report the design of diffractive surfaces to all-optically perform arbitrary complex-valued linear transformations between an input(Ni)and output(No),where Ni and No represent the number of pixels at the input and output fields-of-view(FOVs),***,we consider a single diffractive surface and use a matrix pseudoinverse-based method to determine the complex-valued transmission coefficients of the diffractive features/neurons to all-optically perform a desired/target linear *** addition to this data-free design approach,we also consider a deep learning-based design method to optimize the transmission coefficients of diffractive surfaces by using examples of input/output fields corresponding to the target *** compared the all-optical transformation errors and diffraction efficiencies achieved using data-free designs as well as data-driven(deep learning-based)diffractive designs to all-optically perform(i)arbitrarily-chosen complex-valued transformations including unitary,nonunitary,and noninvertible transforms,(ii)2D discrete Fourier transformation,(iii)arbitrary 2D permutation operations,and(iv)high-pass filtered coherent *** analyses reveal that if the total number(N)of spatially-engineered diffractive features/neurons is≥Ni×No,both design methods succeed in all-optical implementation of the target transformation,achieving negligible ***,compared to data-free designs,deep learning-based diffractive designs are found to achieve significantly larger diffraction efficiencies for a given N and their all-optical transformations are more accurate for N

关键词： arbitrary valued unitary

Recurrent neural network-based volumetric fluorescence microscopy

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Light(Science & Applications) 2021年第4期10卷 620-635页

作者： Luzhe Huang Hanlong Chen Yilin Luo yair Rivenson Aydogan Ozcan Electrical and Computer Engineering Department University of CaliforniaLos AngelesCA 90095USA Bioengineering Department University of CaliforniaLos AngelesCA 90095USA California Nano Systems Institute(CNSI) University of CaliforniaLos AngelesCA 90095USA David Geffen School of Medicine University of CaliforniaLos AngelesCA 90095USA

Volumetric imaging of samples using fluorescence microscopy plays an important role in various fields including physical,medical and life *** we report a deep learning-based volumetric image inference framework that uses 2D images that are sparsely captured by a standard wide-field fluorescence microscope at arbitrary axial positions within the sample *** a recurrent convolutional neural network,which we term as Recurrent-MZ,2D fluorescence information from a few axial planes within the sample is explicitly incorporated to digitally reconstruct the sample volume over an extended *** experiments on *** and nanobead samples,Recurrent-MZ is demonstrated to significantly increase the depth-of-field of a 63×/1.4NA objective lens,also providing a 30-fold reduction in the number of axial scans required to image the same sample *** further illustrated the generalization of this recurrent network for 3D imaging by showing its resilience to varying imaging conditions,including e.g.,different sequences of input images,covering various axial permutations and unknown axial positioning *** also demonstrated wide-field to confocal cross-modality image transformations using Recurrent-MZ framework and performed 3D image reconstruction of a sample using a few wide-field 2D fluorescence images as input,matching confocal microscopy images of the same sample ***-MZ demonstrates the first application of recurrent neural networks in microscopic image reconstruction and provides a flexible and rapid volumetric imaging framework,overcoming the limitations of current 3D scanning microscopy tools.

关键词： neural network networks

THE IMPLICIT CONVEX FEASIBILITY PROBLEM AND ITS APPLICATION TO ADAPTIVE IMAGE DENOISING

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Journal of Computational Mathematics 2016年第6期34卷 610-625页

作者： yair Censor Aviv Gibali Frank Lenzen Christoph Schnorr Department of Mathematics University of Haifa Mr. Carmel 3498838 Haifa Israel Department of Mathematics ORT Braude College 2161002 Karmiel Israel Heidelberg Collaboratory for Image Processing Mathematikon INF 205 University of Heidelberg 69120 Heidelberg Germany

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods capable of handling such problems and demonstrate their applicability to image denoising in a specific medical imaging situation. By allowing the variable sets to undergo scaling, shifting and rotation, this work generalizes pre^ious results -vherein the implicit convex feasibility problem was used for cooperative wireless sensor network positioning where sets are balls and their centers were implicit.

关键词： Implicit convex feasibility Split feasibility projection methods Variable sets,Proximity function Image denoising.