A Multi-Image Encryption Based on Sinusoidal Coding Frequency Multiplexing and Deep Learning

Multi-image encryption technology is a vital branch of optical encryption technology. The traditional encryption method can only encrypt a small number of images, which greatly restricts its application in practice. In this paper, a new multi-image encryption method based on sinusoidal stripe coding frequency multiplexing and deep learning is proposed to realize the encryption of a greater number of images. In the process of encryption, several images are grouped, and each image in each group is first encoded with a random matrix and then modulated with a specific sinusoidal stripe; therefore, the dominant frequency of each group of images can be separated in the Fourier frequency domain. Each group is superimposed and scrambled to generate the final ciphertext. In the process of decryption, deep learning is used to improve the quality of decrypted image and the decryption speed. Specifically, the obtained ciphertext can be sent into the trained neural network and then the plaintext image can be reconstructed directly. Experimental analysis shows that when 32 images are encrypted, the CC of the decrypted result can reach more than 0.99. The efficiency of the proposed encryption method is proved in terms of histogram analysis, adjacent pixels correlation analysis, anti-noise attack analysis and resistance to occlusion attacks analysis. The encryption method has the advantages of large amount of information, good robustness and fast decryption speed.

Meta-Material Enhanced Spatial Mode Decomposition

Acquiring precise information about the mode content of a laser is critical for multiplexed optical communications, optical imaging with active wave-front control, and quantum-limited interferometric measurements. Hologram-based mode decomposition devices allow a fast, direct measurement of the mode content, but they have limited precision due to cross-coupling between modes. Here we report the first proof-of-principle demonstration of mode decomposition with a meta-surface, resulting in significantly enhanced precision. A mode-weight fluctuation of 0.6ppm (-62 dB) can be measured with 1 second of averaging at a Fourier frequency of 80 Hz, an improvement on the state-of-the-art by more than three orders of magnitude. The improvement is attributable to the reduction in cross-coupling enabled by the exceptional phase accuracy of the meta-surface. We show a systematic study of the limiting sources of noise, and we show that there is a promising path towards complete mode decomposition with similar precision.

On the global existence and time-decay rates for a parabolic–hyperbolic model arising from chemotaxis

In this paper, we are concerned with the study of the Cauchy problem for a parabolic–hyperbolic model arising from chemotaxis in any dimension [Formula: see text]. We first prove the global existence of the model in [Formula: see text] critical regularity framework with respect to the scaling of the associated equations. Furthermore, under a mild additional decay assumption involving only the low frequencies of the data, we also establish the time-decay rates for the constructed global solutions. Our analyses mainly rely on Fourier frequency localization technology and on a refined time-weighted energy inequalities in different frequency regimes.

Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation

This paper is concerned with the global regularity problem on the micropolar Rayleigh-Bénard problem with only velocity dissipation in $\mathbb {R}^{d}$ with $d=2\ or\ 3$ . By fully exploiting the special structure of the system, introducing two combined quantities and using the technique of Littlewood-Paley decomposition, we establish the global regularity of solutions to this system in $\mathbb {R}^{2}$ . Moreover, we obtain the global regularity for fractional hyperviscosity case in $\mathbb {R}^{3}$ by employing various techniques including energy methods, the regularization of generalized heat operators on the Fourier frequency localized functions and logarithmic Sobolev interpolation inequalities.

Linear and non-linear tidal oscillations and mode identification in the eccentric binary system KIC 3858884

ABSTRACT The phoebe code was used to analyse the Kepler light-curve and to estimate the physical and geometrical parameters of a rare pulsating binary system, KIC 3858884. The analysis indicated that the system is composed of two detached and very similar main-sequence A-type stars, in a highly eccentric orbit with e = 0.47. After disentangling the binarity effect, the residual data were subjected to Fourier frequency decomposition using period04 software. The resulting frequency spectrum consists of two moderately high-amplitude nearby frequencies, F1 = 7.232199 d−1 and $F2=7.472889\, \mathrm{d}^{-1}$, which were attributed to δ Scuti-type pulsations. In addition, 18 frequencies were identified that were exact harmonics of the orbital frequency $f_{\rm orb}= 0.038533\, \mathrm{d}^{-1}$, and also 53 anharmonics. However, it was found that many of these anharmonic frequencies coupled together non-linearly to give harmonic modes of pulsation. Furthermore, some existing theoretical models of the tidal oscillations were numerically verified in general binary systems through estimations of various modal characteristics, for example mode quantum numbers ${n, l, m,}$ energies Ei, threshold energies Ei,th, damping rates γi, growth rates Γi and stability criteria, etc. The evolution of the stars in the binary system was compared with some similar single pulsating stars on the Hertzsprung–Russell diagram and it was concluded that the evolution of a single star is more rapid. Finally, the observed rate of apsidal line displacement was estimated through eclipse timing variation analysis as Uobs = 74745.2 ± 2566 yr. This was compared with the theoretically calculated rate of the line of apsides motion, UTheo = 73588 ± 2298 yr, and found to be in good agreement within errors, hence verifying general relativity theory once again.

Modulation of contractions in the small intestine indicate desynchronization via supercritical Andronov–Hopf bifurcation

The small intestine is covered by a network of coupled oscillators, the interstitial cells of Cajal (ICC). These oscillators synchronize to generate rhythmic phase waves of contraction. At points of low coupling, oscillations desynchronise, frequency steps occur and every few waves terminates as a dislocation. The amplitude of contractions is modulated at frequency steps. The phase difference between contractions at a frequency step and a proximal reference point increased slowly at first and then, just at the dislocation, increased rapidly. Simultaneous frequency and amplitude modulation (AM/FM) results in a Fourier frequency spectrum with a lower sideband, a so called Lashinsky spectrum, and this was also seen in the small intestine. A model of the small intestine consisting of a chain of coupled Van der Pol oscillators, also demonstrated simultaneous AM/FM at frequency steps along with a Lashinsky spectrum. Simultaneous AM/FM, together with a Lashinsky spectrum, are predicted to occur when periodically-forced or mutually-coupled oscillators desynchronise via a supercritical Andronov–Hopf bifurcation and have been observed before in other physical systems of forced or coupled oscillators in plasma physics and electrical engineering. Thus motility patterns in the intestine can be understood from the viewpoint of very general dynamical principles.