A Linear Frequency Principle Model to Understand the Absence of Overfitting in Neural Networks

Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle(LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore,through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to an LFP model with quantitative prediction power.     

Investigations on the g factors of the ground and excited states for Cu2+ ions in ZnO crystal

The g factors g _// and g _⊥ of the ground Γ₆(² T ₂) and excited Γ_4,5(² E), Γ₆(² E) states for trigonal Cu²⁺ centres in ZnO crystals are calculated from three theoretical methods, the complete diagonalization (of the energy matrix) method, the second-order perturbation method (PTM-I) and the simplified second-order perturbation method (PTM-II, this method was described in an earlier paper). These methods are based on the cluster approach in which the spin-orbit coupling parameters ζ, ζ′ and the orbital reduction factors k, k′ are calculated from a semi-empirical molecular orbital method. The crystal-field parameters used in the calculations are obtained from the superposition model and so the defect structure of Cu²⁺ centres in ZnO can be acquired. The calculated g factors from the three methods are in reasonable agreement with the experimental values and the defect structure of Cu²⁺ centres in ZnO is acquired. It appears that in some cases the approximate PTM can be applied in the studies of g factors of various states. The conditions that the PTM are ineffective are discussed.     

Dielectric Barrier Discharge in Analytical Spectrometry

Abstract

Dielectric barrier discharge is a nonequilibrium plasma, and its industrial application has been on a large scale. Similarly, its prominent features of high dissociation ability at low working temperature and low power consumption, simple and adjustable configuration, ambient working conditions, and long lifetime are favorable for developing a wide array of analytical devices as well. This review addresses the basics of dielectric barrier discharge and emphasizes their analytical applications in analytical atomic spectrometry, chemiluminescence, gas chromatographic detectors, ion source for mass spectrometry, and ion mobility spectrometry with 103 references.     

3D reconstruction of objects using stereo imaging

This paper describes two stereo imaging experimental set-ups useful in measuring the 3D geometry of objects: a parallel optical-axis model and a converging optical-axis model. Digital image correlation is used to find the disparities between corresponding points in a pair of images, for each of these models, with subpixel accuracy. To show the application of the developed algorithms and the stereo imaging experimental set-ups, four different body geometries are used. For some of the objects tested a higher measuring accuracy is obtainable from the converging optical-axis experimental set-up.     

The structure and expression of power group

With the application of the topological upgrade, more and more experts are interested in the problems concerning the mathematical structure’s upgrade to its power set. This paper is a further study on the structure and interrelationship of a power group. By revealing the nature of relationship between the power group and a regular one, the present paper proves some theorems of the structure of the power group and constructs some theorems on its homomorphism and isomorphism as well, proposing an expression form and isomorphism replacement construct methods of the power group.     

A Cross‐Cultural Lesson Comparison on Teaching the Connection Between Multiplication and Division

This study compared one lesson across four U.S. “traditional” textbook series, two U.S. reform‐based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of the lesson across three dimensions (i.e., problem schemata, response requirement, and algebra readiness). In particular, the Chinese lesson's penetrating analysis or explanation of the topic is reflected in its deliberately constructed examples and wide range of problems (pertaining to problem types and difficulty levels) present in the teaching and practice sections of the lesson. None of analyzed U.S. lessons are comparable with the Chinese lesson with respect to the breadth and depth in teaching the topic. A deliberate emphasis, both arithmetically and algebraically, on problem schema acquisition as found in the Chinese lesson represents a promotion of symbolic or higher order of conceptual understanding. The findings are discussed within the context of teaching big ideas through problem schemata acquisition and the importance of symbolic level of conceptual understanding.     

Enforcing Strong Stability of Explicit Runge-Kutta Methods with Superviscosity

A time discretization method is called strongly stable(or monotone),if the norm of its numerical solution is nonincreasing.Although this property is desirable i...     

Leakage current and sub-bandgap photo-response of oxygen-plasma treated GaN Schottky barrier diodes

The effect of oxygen plasma treatment on the performance of GaN Schottky barrier diodes is studied. The GaN surface is intentionally exposed to oxygen plasma generated in an inductively coupled plasma etching system before Schottky metal deposition. The reverse leakage current of the treated diodes is suppressed in low bias range with enhanced diode ideality factor and series resistance. However, in high bias range the treated diodes exhibit higher reverse leakage current and corresponding lower breakdown voltage. The X-ray photoelectron spectroscopy analysis reveals the growth of a thin GaO_x layer on GaN surface during oxygen plasma treatment. Under sub-bandgap light illumination, the plasma-treated diodes show larger photovoltaic response compared with that of untreated diodes, suggesting that additional defect states at GaN surface are induced by the oxygen plasma treatment.     

Improved fake mode free plane wave expansion method

We analyze the origin of the fake modes introduced by the plane wave expansion method with three-dimension (3D) supercell approximation. Through the detailed analysis of the energy distribution of fake modes and real modes, we propose the plane wave expansion-three planar-slab waveguides method to remove the fake modes and obtain the fake mode free band structure of a two-dimensional air hole photonic crystal slab. To the best of our knowledge, this is the first time that such a fake mode free photonic crystal band structure is presented. Our method is also definitely useful in designing other 3D devices.