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Influenza poses a significant risk to public health, as evidenced by the 2009 H1N1 pandemic which caused up to 203,000 deaths worldwide. Predicting the spatiotemporal information of disease in the incubation period is crucial because the prime aim of it is to provide guidance on preparing a response and avoid presumably adverse impact caused by a pandemic. This article designs and analyzes a prediction system about influenza-like illness (ILI) from the latent temporal and spatial information. In this system 1) Gaussian function model and multivariate polynomial regression are employed to investigate the temporal and spatial distribution of ILI data; 2) the phase space reconstructed by delay-coordinate embedding is used to explore the dynamical evolution behavior of the 1-D ILI series; and 3) a dynamical radial basis function neural network (DRBFNN) method which is the kernel of the system, is proposed to predict the ILI values based on the correlations between the observations space and reconstructed phase space. The performance analysis of our system shows that the regression equations coupling with spatial distribution information can be used to supplement the missing data, and the proposed DRBFNN method can predict the trends of ILI for the following one year. Furthermore, the prediction system in this article applies a model-free control schemes, i.e., there are no restriction equations between the multivariable inputs and outputs. This prediction system is expected to be used in predicting the output signals, even the chaotic output signals, in meteorology, industry, medicine, economy, and other fields. An example of predicting the Standard & Poors 500 index is given to introduce the application of our proposed system. The trend of open prices of the following eight trading days is well predicted.

How to predict the future behavior of complex systems with insufficient information, i.e., low dimensional mid-term chaotic time series prediction in mathematical terms, is not only a significant theoretical problem, but a more intricate practical problem. To address this issue, a Delay Parameterized Method (DPM) for low dimensional mid-term chaotic time series forecasting is presented. The correlation function, which immerses the low dimensional information into reconstructed space, is introduced to bridge time series and hidden order of system in DPM. Traversal algorithm and intelligent algorithm including particle swarm optimization or genetic algorithm, are used to obtain the optimal parameters for prediction. In addition, the applications of the proposed method on Lorenz chaotic time series, stress-strain signals and stock K-line maps show that it produces high quality predictions.

The internal mechanism of the social “earthquakes”- the wars burst in human society, is investigated by nonlinear theory. We explore the scaling behavior in the human activity and the historical evolution of ancient China. Based on the war chronology and history chronology from B.C.2000 to A.D.1840, using statistical analysis together with the detrended fluctuation analysis, we find that the social evolution system shows self-organized critical behavior and there exists self-similar scaling behavior during the evolution system. Based on time-delay reconstructed phase space, a modified radial basis function neural network (modified RBF-NN) is used to predict the number of wars and the transformation of the historical stage. It shows that the prediction result matches quite well with the real value for the following two historical stages. Furthermore, by singular value decomposition and the sparse identification algorithm in time-delay coordinates, the coefficients of the candidate functions in identified system can be solved from a sparse regression problem. We extracted the governing equations of big events burst in social system. The identified system fits well with the real data, and it can capture the same topology with the original system of wars. In this paper, we investigated the wars burst in social system by statistic analysis, neural network as well as sparse identification. It sheds light on the study of wars or conflicts from perspective of data science and dynamical theory.

Seldom could metals and alloys maintain excellent properties in cryogenic condition, such as the ductility, owing to the restrained dislocation motion. However, a face-centered-cubic (FCC) CoCrFeNi high-entropy alloy (HEA) with great ductility is investigated under the cryogenic environment. The tensile strength of this alloy can reach a maximum at 1,251±10 MPa, and the strain to failure can stay at as large as 62% at the liquid helium temperature. We ascribe the high strength and ductility to the low stacking fault energy at extremely low temperatures, which facilitates the activation of deformation twinning. Moreover, the FCC→HCP (hexagonal close-packed) transition and serration lead to the sudden decline of ductility below 77 K. The dynamical modeling and analysis of serrations at 4.2 and 20 K verify the unstable state due to the FCC→HCP transition. The deformation twinning together with phase transformation at liquid helium temperature produces an adequate strain-hardening rate that sustains the stable plastic flow at high stresses, resulting in the serration feature.

Chaos has been well understood in dynamic system, however, how the chaotic behavior occur in jerky flow in material, is still not clear, and is lack of specific chaotic attractor. Here the jerky evolution of lateral force and the stair-like fluctuation of lateral displacement are observed for Ni$_{62}$Nb$_{38}$(at.$%$) metallic glass film during nanoscratch process. This jerky flow is investigated by using the largest Lyapunov exponent, Kolmogorov entropy and fractal dimension, and chaotic behavior of lateral force-time and normal displacement-lateral displacement sequences is verified. In addition to time series analysis, it is found that jerk equation can be used to describe the jerky flow of the metallic-glass film during nanoscratch. More importantly, unambiguous chaotic attractor is presented by jerky dynamics using “jerk-singularities, namely the total change rate of lateral force relative to scratch time. These reveal an inner connection between jerky flow and jerky dynamics in nanoscratch of a metallic-glass film.

In this paper, periodic nanostructures were fabricated on GaAs wafers by four-beam UV pulsed laser interference patterning. Significant different results were observed on epi-ready and homo-epitaxial GaAs substrate surfaces, which suggests GaAs oxide layer has an important effect on pulsed laser irradiation process. In the case of two-pulse patterning, a noticeable morphology transformation induced by the second pulse was observed on homo-epitaxial GaAs substrate. Based on photo-thermal mode, temperature distribution on sample surface as a function of time and position was calculated by solving the heat diffusion equations.

Lightweight alloys are becoming more and more important. Based on the 5083 aluminum alloy, the effects of Zn and Cu additions on the microstructures, properties, and serration behavior were investigated. The results show that with the increase of the Zn content, the tensile and yield strengths of the alloy increase, while the elongation and the serration amplitude keep on decreasing. Moreover, different amounts of Cu are added to the high Zn content Al–Mg-6 wt.% (weight percent) Zn alloy, in which the strength and plasticity are improved firstly. When the Cu content was 6 wt%, the elongation of the alloy is about 7%, and the serration behavior of the alloy gradually disappears. The optimal mechanical property is achieved at the composition of Al–Mg-6wt.%Zn-6wt.%Cu. The serration behavior is believed to be related to the interaction between the moving dislocations and the precipitates. Furthermore, the serrated flow was analyzed using the refined composite multiscale entropy algorithm. It was found that the dynamical complexity of the serrations generally increased with an increase in the solute density, the stress-drop magnitude, the grain size, the tensile and yield strengths, and the degree of plasticity.

A single-beam of UV pulse laser (355nm/10ns) was used to irradiate the as-grown GaAs (100) surface in-situ in molecular beam epitaxy with pulse numbers from 1 to 6 at laser intensity of 52.5 mJ/cm2/pulse. It was observed that the irradiated GaAs surface morphology depended strongly on the pulse number. For single pulse irradiation, small nano-dots (NDs) with high density were produced on the surface. The size of NDs increased and nano-rings (NRs) were observed with the increasing of pulse numbers. The surface was completely dominated by NRs at 6 pulses of laser irradiating. Arsenic atoms were selectively desorbed away from GaAs surface by laser irradiation leaving plenty of naked Ga-atoms to form small metal-dots of Gallium. Ga-rich NDs transferred to Ga droplets with the increased number of the laser pulses. NRs formed just as the traditional droplet-epitaxy process when the droplet size grew up to a critical size. Nano-drill process played an important role in the process. This research was supposed to provide a novel and promising solution for more controllable nano-fabrication of various semiconductor materials of MBE growing, including but not limited to GaAs reported here.

A study of in-situ laser interference nano-patterning on InGaAs wetting layers was carried out during InAs/GaAs (001) quantum dot molecular beam epitaxy growth. Periodic nano-islands with heights of a few atomic layers were obtained via four-beam laser interference irradiation on the InGaAs wetting layer at an InAs coverage of 0.9 monolayer. The quantum dots nucleated preferentially at edges of nano-islands upon subsequent deposition of InAs on the patterned surface. When the nano-islands are sufficiently small, the patterned substrate could be spontaneously re-flattened and an ordered quantum dot array could be produced on the smooth surface. This letter discusses the mechanisms of nano-patterning and ordered quantum dot nucleation in detail. This study provides a potential technique leading to site-controlled, high-quality quantum dot fabrication.

This study investigates the plastic behavior of the Al0.5CoCrCuFeNi high-entropy alloy at cryogenic temperatures. The samples are uniaxially compressed at 4.2 K, 7.5 K, and 9 K. A jerky evolution of stress and stair-like fluctuation of strain are observed during plastic deformation. A scaling relationship is detected between the released elastic energy and strain-jump sizes. Furthermore, the dynamical evolution of serrations is characterized by the largest Lyapunov exponent. The largest Lyapunov exponents of the serrations at the three temperatures are all negative, which indicates that the dynamical regime is non-chaotic. This trend reflects an ordered slip process, and this ordered slip process exhibits a more disordered slip process, as the temperature decreases from 9 K to 4.2 K or 7.5 K.

Image registration is one of the crucial steps in detecting changes among the time series medical images. Due to variations in the imaging system over time, the impulse response of the imaging system, also known as its point spread function (PSF), exhibits a time-varying behavior. The registration is further complicated due to the subtle coordinate changes introduced by the patient. In this work, the registration problem is approached via a spatially varying multi-dimensional adaptive filtering method that relates one image in terms of an unknown linear combination of the other image and its spatially transformed versions. Using this model, we develop a scheme, which we refer to as signal subspace processing, to estimate a localized impulse response to calibrate relatively small regions. A criterion is designed to identify the localized PSFs that are not sensitive to the system noise or anatomical changes but accurately represent the spatially varying nature of the unknown miscalibration sources. Low order polynomials are used to sew the localized PSF together and construct a global spatially variant PSF. The anatomical changes between the time series images are achieved by calibrating the image with the global spatially variant PSF. Numerical experiments using MR images illustrate the effectiveness of the proposed algorithm.