Single Peak Fitting Research Articles

Enhancing Mechanical Stimulated Brillouin Scattering Imaging with Physics‐Driven Model Selection

AbstractBrillouin microscopy (BM) is an emerging technique for all‐optical mechanical imaging without the need for physical contact with the sample or for an external mechanical stimulus. However, BM often retrieves a single Brillouin frequency shift for multiple mechanically different materials of structures and/or in regions—sufficiently larger than the phonon wavelength—inside the volume and its surroundings, resulting in significantly limited mechanical specificity in the Brillouin shift images produced. Here, a new physics‐driven model selection framework is developed based on information theory and a physical‐statistical overfit Brillouin water peak threshold that enables the robust identification of single‐ and multi‐peak Brillouin signatures in the sample pixels. The model selection framework is applied to Brillouin data of material interfaces and living NIH/3T3 cells measured by stimulated Brillouin scattering (SBS) microscopy, facilitating the quantification of the Brillouin frequency shift of materials in different regions of the sample and significantly improving mechanical specificity compared with the standard single peak fitting analysis.

Epidemiological characteristics and dynamic transmissions of COVID-19 pandemics in Chinese mainland: A trajectory clustering perspective analysis

BackgroundThe corona virus disease 2019 (COVID-19) pandemic has spread to more than 210 countries and regions around the world, with different characteristics recorded depending on the location. A systematic summarization of COVID-19 outbreaks that occurred during the “dynamic zero-COVID” policy period in Chinese mainland had not been previously conducted. In-depth mining of the big data from the past two years of the COVID-19 pandemics must be performed to clarify their epidemiological characteristics and dynamic transmissions. MethodsTrajectory clustering was used to group epidemic and time-varying reproduction number (Rt) curves of mass outbreaks into different models and reveal the epidemiological characteristics and dynamic transmissions of COVID-19. For the selected single-peak epidemic curves, we constructed a peak-point judgment model based on the dynamic slope and adopted a single-peak fitting model to identify the key time points and peak parameters. Finally, we developed an extreme gradient boosting-based prediction model for peak infection cases based on the total number of infections on the first 3, 5, and 7 days of the initial average incubation period. Results(1) A total of 7 52298 cases, including 587 outbreaks in 251 cities in Chinese mainland between June 11, 2020, and June 29, 2022, were collected, and the first wave of COVID-19 outbreaks was excluded. Excluding the Shanghai outbreak in 2022, the 586 remaining outbreaks resulted in 1 25425 infections, with an infection rate of 4.21 per 1 00000 individuals. The number of outbreaks varied based on location, season, and temperature.(2) Trajectory clustering analysis showed that 77 epidemic curves were divided into four patterns, which were dominated by two single-peak clustering patterns (63.3%). A total of 77 Rt curves were grouped into seven patterns, with the leading patterns including four downward dynamic transmission patterns (74.03%). These curves revealed that the interval from peak to the point where the Rt value dropped below 1 was approximately 5 days.(3) The peak-point judgment model achieved a better result in the area under the curve (0.96, 95% confidence interval = 0.90–1.00). The single-peak fitting results on the epidemic curves indicated that the interval from the slow-growth point to the sharp-decline point was approximately 4–6 days in more than 50% of mass outbreaks.(4) The peak-infection-case prediction model exhibited the superior clustering results of epidemic and Rt curves compared with the findings without grouping. ConclusionOverall, our findings suggest the variation in the infection rates during the “dynamic zero-COVID” policy period based on the geographic division, level of economic development, seasonal division, and temperature. Trajectory clustering can be a useful tool for discovering epidemiological characteristics and dynamic transmissions, judging peak points, and predicting peak infection cases using different patterns.

Mutator Model with Migration

In this paper, we construct new versions of quasispecies models with mutator effect and ecological diversification. The proposed modifications are based on the Eigen and Crow–Kimura models of asexual evolution of finite population with large genome length. Our study examines the case with different fitness landscapes in the first and second habitats and migration flows. Here, the analytical investigation raises cumbersome mathematical problems. We show that the system has a rich phase structure governed by the transition and mutation rates. For single-peak fitness landscapes, the population is grouped around two peaks in the second habitat. We calculated the static characteristics of different phases. The calculation of population fractions around two peaks in wild-type and mutator types is of significant importance from our perspective.

Single-peak fitting based on wavelength recognition in FBGs spectra under quadratic strain distribution

The stress concentration appears in the form of a quadratic or higher-order strain distribution, which affects the measurement accuracy of fiber Bragg grating (FBG). The FBG spectrum presents asymmetric deterioration when the stress concentration exceeds a specific limit, making the symmetric Gaussian fitting algorithm no longer suitable for seeking its peak wavelength. In this paper, the degree of stress concentration is defined by the quadratic coefficient of the strain field. The bearing capacity of different length FBGs to the Gaussian fitting algorithm is investigated under the quadratic strain distribution. The experimental results show that the FBG with shorter length had a higher tolerance to the Gaussian peak-seeking algorithm. The Extreme fitting algorithm based on a single peak has been proposed to adapt to the asymmetric changes of FBGs spectra. The exceptional adaptability of the Extreme peak-seeking algorithm compared with Gaussian fitting has been proved, which provides a reliable reference for the accurate peak seeking of FBG reflect spectrum in a nonuniform strain field.

Quantitative texture analysis at the WAND2 and HIDRA diffractometers

Data collection and analysis strategies have been developed for efficient and reliable crystallographic texture measurements at two recently upgraded neutron diffractometers: the Wide Angle Neutron Diffractometer Squared (WAND2) and the High Intensity Diffractometer for Residual Stress Analysis (HIDRA) at the High Flux Isotope Reactor located at Oak Ridge National Laboratory. These methods are demonstrated using measurements on a variety of textured samples, including multi-phase steel composites and polycrystalline calcite (CaCO3). Reference measurements were also made at VULCAN, the engineering diffractometer located at the Spallation Neutron Source. The texture data obtained on the different instruments are in agreement, and WAND2 is more time efficient than HIDRA. Two analysis methods were investigated, single-peak fitting to obtain individual pole figures for inversion and Rietveld texture analysis using MAUD. The impact of the differences between the various textures obtained was evaluated through the calculation of diffraction elastic constants, which is one application of the texture data collected. Both instruments were found to provide texture data that are suitable for complementing other analyses, such as residual stress mapping.

On the incongruence of genotype-phenotype and fitness landscapes.

The mapping from genotype to phenotype to fitness typically involves multiple nonlinearities that can transform the effects of mutations. For example, mutations may contribute additively to a phenotype, but their effects on fitness may combine non-additively because selection favors a low or intermediate value of that phenotype. This can cause incongruence between the topographical properties of a fitness landscape and its underlying genotype-phenotype landscape. Yet, genotype-phenotype landscapes are often used as a proxy for fitness landscapes to study the dynamics and predictability of evolution. Here, we use theoretical models and empirical data on transcription factor-DNA interactions to systematically study the incongruence of genotype-phenotype and fitness landscapes when selection favors a low or intermediate phenotypic value. Using the theoretical models, we prove a number of fundamental results. For example, selection for low or intermediate phenotypic values does not change simple sign epistasis into reciprocal sign epistasis, implying that genotype-phenotype landscapes with only simple sign epistasis motifs will always give rise to single-peaked fitness landscapes under such selection. More broadly, we show that such selection tends to create fitness landscapes that are more rugged than the underlying genotype-phenotype landscape, but this increased ruggedness typically does not frustrate adaptive evolution because the local adaptive peaks in the fitness landscape tend to be nearly as tall as the global peak. Many of these results carry forward to the empirical genotype-phenotype landscapes, which may help to explain why low- and intermediate-affinity transcription factor-DNA interactions are so prevalent in eukaryotic gene regulation.

Gene-influx-driven evolution.

Here we analyze the evolutionary process in the presence of continuous influx of genotypes with submaximum fitness from the outside to the given habitat with finite resources. We show that strong influx from the outside allows the low-fitness genotype to win the competition with the higher fitness genotype, and in a finite population, drive the latter to extinction. We analyze a mathematical model of this phenomenon and obtain the conditions for the transition from the high-fitness to the low-fitness genotype caused by the influx of the latter. We calculate the time to extinction of the high-fitness genotype in a finite population with two alleles and find the exact analytical dynamics of extinction for the case of many genes with epistasis. We solve a related quasispecies model for a single peak (random) fitness landscape as well as for a symmetric fitness landscape. In the symmetric landscape, a nonperturbative effect is observed such that even an extremely low influx of the low-fitness genotype drastically changes the steady state fitness distribution. A similar nonperturbative phenomenon is observed for the allele fixation time as well. The identified regime of influx-driven evolution appears to be relevant for a broad class of biological systems and could be central to the evolution of prokaryotes and viruses.

Picometer-Precision Atomic Position Tracking through Electron Microscopy.

The modern aberration-corrected scanning transmission electron microscopes (AC-STEM) have successfully achieved direct visualization of atomic columns with sub-angstrom resolution. With this significant progress, advanced image quantification and analysis are still at the early stages. In this work, we present the complete pathway for the metrology of atomic resolution scanning transmission electron microscopy (STEM) images. This includes (1) tips for acquiring high-quality STEM images; (2) denoising and drift-correction for enhancing measurement accuracy; (3) obtaining initial atomic positions; (4) indexing the atoms based on unit cell vectors; (5) quantifying the atom column positions with either 2D-Gaussian single peak fitting or (6) multi-peak fitting routines for slightly overlapping atomic columns; (7) quantification of lattice distortion/strain within the crystal structures or at the defects/interfaces where the lattice periodicity is disrupted; and (8) some common methods to visualize and present the analysis. Furthermore, a simple self-developed free MATLAB app (EASY-STEM) with a graphical user interface (GUI) will be presented. The GUI can assist in the analysis of STEM images without the need for writing dedicated analysis code or software. The advanced data analysis methods presented here can be applied for the local quantification of defect relaxations, local structural distortions, local phase transformations, and non-centrosymmetry in a wide range of materials.

Picometer-Precision Atomic Position Tracking through Electron Microscopy

The modern aberration-corrected scanning transmission electron microscopes (AC-STEM) have successfully achieved direct visualization of atomic columns with sub-angstrom resolution. With this significant progress, advanced image quantification and analysis are still at the early stages. In this work, we present the complete pathway for the metrology of atomic resolution scanning transmission electron microscopy (STEM) images. This includes (1) tips for acquiring high-quality STEM images; (2) denoising and drift-correction for enhancing measurement accuracy; (3) obtaining initial atomic positions; (4) indexing the atoms based on unit cell vectors; (5) quantifying the atom column positions with either 2D-Gaussian single peak fitting or (6) multi-peak fitting routines for slightly overlapping atomic columns; (7) quantification of lattice distortion/strain within the crystal structures or at the defects/interfaces where the lattice periodicity is disrupted; and (8) some common methods to visualize and present the analysis. Furthermore, a simple self-developed free MATLAB app (EASY-STEM) with a graphical user interface (GUI) will be presented. The GUI can assist in the analysis of STEM images without the need for writing dedicated analysis code or software. The advanced data analysis methods presented here can be applied for the local quantification of defect relaxations, local structural distortions, local phase transformations, and non-centrosymmetry in a wide range of materials.

Measurement Improvement of Distributed Optical Fiber Sensor via Lorenz Local Single Peak Fitting Algorithm

Brillouin frequency shift (BFS) of distributed optical fiber sensor is extracted from the Brillouin gain spectrum (BGS), which is often characterized by Lorenz type. However, in the case of complex stress and optical fiber self damage, the BGS will deviate from Lorenz type and be asymmetric, which leads to the extraction error of BFS. In order to enhance the extraction accuracy of BFS, the Lorenz local single peak fitting algorithm was developed to fit the Brillouin gain spectrum curve, which can make the BSG symmetrical with respect to the Brillouin center frequency shift. One temperature test of a fiber-reinforced polymer (FRP) packaged sensor whose BSG curve is asymmetric was conducted to verify the idea. The results show that the local region curve of BSG processed by the developed algorithm has good symmetry, and the temperature measurement accuracy obtained by the developed algorithm is higher than that directly measured by demodulation equipment. Comparison with the reference temperature, the relative measurement error measured by the developed algorithm and BOTDA are within 4% and 8%, respectively.

An in-situ neutron diffraction investigation of martensitic transformation in a metastable β Ti-10V-2Fe-3Al alloy during uniaxial tension

The deformation behaviour of a metastable β Ti-10V-2Fe-3Al (wt%) alloy containing ~10 vol% α phase was investigated via single-peak fitting and Rietveld refinement of in-situ neutron diffraction data collected during uniaxial tension. The formation of the 021α″ fibre is related to martensite variant selection during β → α″ transformation under applied load. The β lattice parameter increases by ~0.08% during tension whereas α″ accommodates deformation through a decrease and increase in a and b lattice parameters, respectively. The origin of the variation in α″ martensite lattice parameters with strain for different Ti alloys is linked to their different rhombicity values.

In-Situ XRD Study of Phase Transformation Kinetics in a Co-Cr-W-Alloy Manufactured by Laser Powder-Bed Fusion

The additive manufacturing process of laser powder-bed fusion (L-PBF) is an increasingly popular approach for patient-specific production of dental frameworks made from Co-Cr alloys. Macroscopically, frameworks produced in this way exhibit high anisotropy especially in Young’s modulus, and are missing standardized requirements. Microscopically, pronounced texture and high residual stresses are characteristic. To reduce resulting detrimental effects, the as-built (AB) parts are heat treated. Dependent on the treatment temperature, effects like the transformation of the γ-phase matrix in the AB condition to ϵ-phase, precipitation, stress relief, and grain growth were observed. While the existence of these processes was established in the past, little is known about their kinetics. To fill this gap, these effects were studied with in-situ X-ray diffraction (XRD) methods in isothermal heat treatments (HTs) at four different sample surface temperatures TS reaching from 650∘C to 900∘C. Furthermore, room temperature ex situ XRD and SEM/EDS measurements completed the analysis. An evaluation of the datasets, with single peak fitting and QXRD methods, yielded the following results. In the HTs below a certain threshold, a γ-to-ϵ transformation was observed in the sample bulk and close to the sample surface. In the latter case, evidence for a partially strain-induced transformation related to oxide formation was present. Above this threshold and possibly slightly below, σ- and Laves-phase precipitated. Additionally, peak profile evolutions hinted at a drop of inter- and intragranular stresses within the first 30 to 60 min. Therefore, an HT of about 30 to 60 min slightly above the threshold is proposed as optimal for reducing residual stresses while retaining a predominantly single-phased microstructure, possibly superior in corrosion properties and likewise in bio-compatibility.

Identifying cloud, precipitation, windshear, and turbulence by deep analysis of the power spectrum of coherent Doppler wind lidar.

Researches on the atmospheric boundary layer (ABL) need accurate measurements with high temporal and spatial resolutions from a series of different instruments. Here, a method for identifying cloud, precipitation, windshear, and turbulence in the ABL using a single coherent Doppler wind lidar (CDWL) is proposed and demonstrated. Based on deep analysis of the power spectrum of the backscattering signal, multiple lidar products, such as carrier-to-noise (CNR), spectrum width, spectrum skewness, turbulent kinetic energy dissipation rate (TKEDR), and shear intensity are derived for weather identification. Firstly, the cloud is extracted by Haar wavelet covariance transform (HWCT) algorithm based on the CNR after range correction. Secondly, since the spectrum broadening may be due to turbulence, windshear or precipitation, the spectrum skewness is introduced to distinguish the precipitation from two other conditions. Whereas wind velocity is obtained by single peak fitting in clear weather condition, the double-peak fitting is used to retrieve wind and rainfall velocities simultaneously in the precipitation condition. Thirdly, judging from shear intensity and TKEDR, turbulence and windshear are classified. As a double check, the temporal continuity is used. Stable wind variances conditions such as low-level jets are identified as windshear, while arbitrary wind variances conditions are categorized as turbulence. In the field experiment, the method is implemented on a micro-pulse CDWL to provide meteorological services for the 70th anniversary of the China's National Day, in Inner Mongolia, China (43°54'N, 115°58'E). All weather conditions are successfully classified. By comparing lidar results to that of microwave radiometer (MWR), the spectrum skewness is found be more accurate to indicate precipitation than spectrum width or vertical speed. Finally, the parameter relationships and distributions are analyzed statistically in different weather conditions.

Mpfit: a robust method for fitting atomic resolution images with multiple Gaussian peaks

The standard technique for sub-pixel estimation of atom positions from atomic resolution scanning transmission electron microscopy images relies on fitting intensity maxima or minima with a two-dimensional Gaussian function. While this is a widespread method of measurement, it can be error prone in images with non-zero aberrations, strong intensity differences between adjacent atoms or in situations where the neighboring atom positions approach the resolution limit of the microscope. Here we demonstrate mpfit, an atom finding algorithm that iteratively calculates a series of overlapping two-dimensional Gaussian functions to fit the experimental dataset and then subsequently uses a subset of the calculated Gaussian functions to perform sub-pixel refinement of atom positions. Based on both simulated and experimental datasets presented in this work, this approach gives lower errors when compared to the commonly used single Gaussian peak fitting approach and demonstrates increased robustness over a wider range of experimental conditions.

Determination of the Zn Content in Zincian Malachite by X-ray Diffraction

A method for determining Zn content in zincian malachite from a relative location of reflections in an x-ray diffraction (XRD) pattern is reported. Based on the standard samples prepared by a micro-reactor, the (220) reflection of zincian malachite is selected as the reference peak to calculate the relative location of other reflections within the 2θ-range from 10° to 35°. After establishing the relationship between the Zn content and the relative location, the shifts of these reflections are considered comprehensively to determine the Zn content by multi-peak fitting. The new method takes full advantage of the XRD pattern, avoiding the interference of adjacent reflections in single-peak fitting, eliminating the systematic deviation among different instruments that causes the overall shift of the pattern. Comparing with the Rietveld refinement, the method is more convenient for ordinary user.

Influence of dislocations and grain boundaries on diffraction line profiles of nano-crystalline materials: A numerical study

In the present paper, the contributions of dislocations and grain boundaries to the broadening of diffraction line profile have been delineated. Contribution of each factor is studied on single as well as poly crystalline ‘virtual samples’ containing different dislocation configurations generated by molecular dynamics and evaluating the simulated X-ray diffraction line profiles of these samples. Individual contributions to diffraction line profiles by different sample features, such as domain size, dislocations, grain boundaries, have been isolated by deconvoluting the evaluated diffraction line profiles. The diffraction line profiles exhibited significant asymmetry and peak splitting in the case of dislocations with predominantly edge character. It has been shown that splitting of diffraction peaks carries information about the magnitude of Burger’s vectors of the dislocations. Application of the variance method based on single peak fitting and Wilkens method based on whole powder pattern fitting of line profile analysis on the computed diffraction line profiles, showed that while accurate domain size estimation was possible, there was an under estimation of dislocation density at the high dislocation density and small grain size regime considered in the present study.

Using Variant Selection to Facilitate Accurate Fitting of \u03b3\u2033 Peaks in Neutron Diffraction

γ″ diffraction peaks are hard to discern in neutron/X-ray diffraction patterns, hindering studies on the γ″-strengthened superalloys using in-situ diffraction. In this study, we propose a variant selection method to increase the intensity of γ″ peaks and to facilitate accurate fitting. The specific variants of γ″ are controlled by applying a 300 MPa tensile stress during aging at 790 °C for 5 hours. The interaction energy between the applied stress and the transformation strain of each γ″ variant differs, leading to an increase in the amount of the variants with a greater energy reduction at the expense of other variants. The enhanced variants result in greater γ″ peak intensities in neutron diffraction patterns, allowing both the Pawley refinement and single peak fitting to be performed. Lattice parameters of γ″ and γ phases, and lattice misfit between the two phases and volume fraction of γ″ are acquired. The uncertainties associated with the fitting maintain an acceptable level corresponding to 150 microstrains. The proposed variant selection method shows potential for studying the role of γ″ phase in Ni-base superalloys.

The quasars’ redshift estimation method based on piecewise Gaussian fitting

To solve the problem that high-redshift and broad emission lines weaken the quasar discovery and observation severely, a new redshift calculation method based on piecewise Gaussian fitting is proposed. The denoised and normalized spectrum is divided into two regions, peak and non-peak, by mean square error threshold segmentation first. Then, the non-peak region spectrum is applied to fit the continuous spectrum, removal of which gains access to the residual spectrum. And, the peak of each segment in the residual spectrum is precisely fitted by single-peak Gaussian fitting to replace the original multi-peak Gaussian fitting. Finally, through matching the accurate peak value with the stationary template, the redshift value is acquired. Compared with traditional methods, the method proposed improves the precision of continuous spectrum fitting and redshift calculation. The effectiveness and accuracy of this method have been verified by experiments based on the Sloan Digital Sky Survey data.

Cascaded-Microrings Biosensors Fabricated on a Polymer Platform.

Polymer-based single-microring biosensors usually have a small free spectral range (FSR) that hampers the tracing of the spectrum shifting in the measurement. A cascade of two microring resonators based on the Vernier effect, is applied in this article in order to make up for this defect. A small FSR difference between the reference microring and the sensing microring is designed, in order to superpose the periodic envelope signal onto the constituent peaks, which makes it possible to continuously track the spectrum of the sensor. The optical polymer material, Ormocore, which has a large transparent window, is used in the fabrication. The biosensor is fabricated by using an UV-based soft imprint technique, which is considered to be cost-effective and suitable for mass production. By optimizing the volume ratio of Ormocore and the maT thinner, the device can be fabricated almost without a residual layer. The device works at a wavelength of 840 nm, where water absorption loss is much lower than at the infrared wavelengths. A two-step fitting method, including single-peak fitting and whole-envelope fitting, is applied in order to trace the spectral shift accurately. Finally, the two-cascaded-microrings biosensor is characterized, and the obtained FSR is 4.6 nm, which is 16 times larger than the FSR of the single microring biosensor demonstrated in our previous work. Moreover, the sensitivity can also be amplified by 16-fold, thanks to the Vernier effect.

Eigen model version of evolution with directed migration

We consider the two-habitat quasispecies model, which describes evolutionary process with migration on the basis of the Eigen model. In the first habitat there is only one genotype, and here is an influx of the replicators from the first habitat to the second one with the rate h. We solve exactly the case of a single-peak fitness landscape in both habitats, when in the first habitat there are no mutations. The Eigen model version of the model is more adequately describes the real biological experiments than the Crow-Kimura model, as can be related to the serial transfer experiments in chemical reactor.