Simultaneous Fit Research Articles

Logarithmic sensitivity ratio elucidates thermal transport physics in multivariate thermoreflectance experiments

We mathematically derived a sensitivity-based method that identifies the thermal transport physics and parameters suitable for multivariate nonlinear fits in a frequency-domain thermoreflectance (FDTR) experiment. Modern electronic devices often consist of heterogeneous nanolayers with multiple unknown thermal transport properties. However, simultaneous fitting in a single experiment for these unknown parameters will produce unreliable results if they are correlated. Current methods to identify such correlations are unreliable. This unreliability has impeded the accuracy and speed of characterizing the unknown thermal properties of such multilayer stacks. Our proposed logarithmic sensitivity ratio (LSR) analysis can evaluate the feasibility of fitting a pair of unknown parameters and clarify the governing thermal transport physics. The effectiveness and convenience of this analysis were studied using Monte Carlo simulations and actual FDTR experiments for fitting up to three unknown parameters. The principle behind this method can be extended to other techniques where multivariate fits are needed.

Cyanopolyyne Chemistry in the L1544 Prestellar Core: New Insights from GBT Observations

We report a comprehensive study of the cyanopolyyne chemistry in the prototypical prestellar core L1544. Using the 100 m Robert C. Byrd Green Bank Telescope, we observe three emission lines of HC3N, nine lines of HC5N, five lines of HC7N, and nine lines of HC9N. HC9N is detected for the first time toward the source. The high spectral resolution (∼0.05 km s−1) reveals double-peak spectral line profiles with the redshifted peak a factor 3–5 brighter. Resolved maps of the core in other molecular tracers indicate that the southern region is redshifted. Therefore, the bulk of the cyanopolyyne emission is likely associated with the southern region of the core, where free carbon atoms are available to form long chains, thanks to the more efficient illumination of the interstellar field radiation. We perform a simultaneous modeling of the HC5N, HC7N, and HC9N lines to investigate the origin of the emission. To enable this analysis, we performed new calculation of the collisional coefficients. The simultaneous fitting indicates a gas kinetic temperature of 5–12 K, a source size of 80″, and a gas density larger than 100 cm−3. The HC5N:HC7N:HC9N abundance ratios measured in L1544 are about 1:6:4. We compare our observations with those toward the well-studied starless core TMC-1 and with the available measurements in different star-forming regions. The comparison suggests that a complex carbon chain chemistry is active in other sources and is related to the presence of free gaseous carbon. Finally, we discuss the possible formation and destruction routes in light of the new observations.

Relativistic force-free models of the thermal X-ray emission in millisecond pulsars observed by NICER

ABSTRACTJPSeveral important properties of rotation-powered millisecond pulsars (MSPs), such as their mass-radius ratio, equation of state and magnetic field topology, can be inferred from precise observations and modelling of their X-ray light curves. In the present study, we model the thermal X-ray signals originated in MSPs, all the way from numerically solving the surrounding magnetospheres up to the ray tracing of the emitted photons and the final computation of their light curves and spectra. The magnetosphere is solved by performing general relativistic force-free simulations of a rotating neutron star (NS) endowed with a simple centred dipolar magnetic field, for many different stellar compactness and pulsar misalignments. From these solutions, we derive an emissivity map over the surface of the star, based on the electric currents in the magnetosphere. In particular, the emission regions (ERs) are determined in this model by spacelike four-currents that reach the NS. We show that this assumption, together with the inclusion of the gravitational curvature on the force-free simulations, lead to non-standard ERs facing the closed-zone of the pulsar, in addition to other ERs within the polar caps. The combined X-ray signals from these two kinds of ERs (both antipodal) allow to approximate the non-trivial interpulses found in several MSPs light curves. Our modelled X-ray signals are compared against very accurate NICER observations of four target pulsars: PSR J043-4715, PSR J1231-1411, PSR J2124-3358, and PSR J0030 + 0451; achieving very good simultaneous fits for their light curves and spectral distributions.

Proteomics biomarker discovery for individualized prevention of familial pancreatic cancer using statistical learning.

The low five-year survival rate of pancreatic ductal adenocarcinoma (PDAC) and the low diagnostic rate of early-stage PDAC via imaging highlight the need to discover novel biomarkers and improve the current screening procedures for early diagnosis. Familial pancreatic cancer (FPC) describes the cases of PDAC that are present in two or more individuals within a circle of first-degree relatives. Using innovative high-throughput proteomics, we were able to quantify the protein profiles of individuals at risk from FPC families in different potential pre-cancer stages. However, the high-dimensional proteomics data structure challenges the use of traditional statistical analysis tools. Hence, we applied advanced statistical learning methods to enhance the analysis and improve the results' interpretability. We applied model-based gradient boosting and adaptive lasso to deal with the small, unbalanced study design via simultaneous variable selection and model fitting. In addition, we used stability selection to identify a stable subset of selected biomarkers and, as a result, obtain even more interpretable results. In each step, we compared the performance of the different analytical pipelines and validated our approaches via simulation scenarios. In the simulation study, model-based gradient boosting showed a more accurate prediction performance in the small, unbalanced, and high-dimensional datasets than adaptive lasso and could identify more relevant variables. Furthermore, using model-based gradient boosting, we discovered a subset of promising serum biomarkers that may potentially improve the current screening procedure of FPC. Advanced statistical learning methods helped us overcome the shortcomings of an unbalanced study design in a valuable clinical dataset. The discovered serum biomarkers provide us with a clear direction for further investigations and more precise clinical hypotheses regarding the development of FPC and optimal strategies for its early detection.

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

A comprehensive model, i.e., a model that: (i) suitably captures the mechanical behaviour of various types of rubber-like materials; (ii) describes the constitutive behaviour of a subject rubber-like specimen under different deformation modes via a single set of model parameter values, and (iii) is parent to many of the existing models of distinct types, is presented in this paper for application to the finite deformation of incompressible isotropic rubber-like materials. The model breaks away from Rivlin’s principal invariants I_{i} and Valanis-Landel’s separable function of principal stretches lambda _{i} representations, and instead adopts a general non-separable functional form W( lambda _{1}, lambda _{2}, lambda _{3} ), subject to the incompressibility constraint. By way of example, the application of the model to extant datasets from four types of rubber-like materials that exhibit discernible mechanical behaviours, namely natural unfilled and filled rubbers, hydrogels and (extremely) soft tissue specimens, will be considered. The favourable correlation between the model predictions and the considered experimental datasets, obtained via simultaneous fitting of the model to the data of various deformations, will be demonstrated. It will be shown that most of the landmark models in the literature including the W( I_{1}, I_{2} ) form Mooney-Rivlin, the Gent-like limiting chain extensibility, the nonaffine tube and the separable principal stretches-based type Ogden models are all a special sub-set of the presented parent model, and are all recovered from this model. An important implication of the non-separable functional form of the model will be conferred, through a specific dataset, where the predictions of the separable functions prove inherently inadequate. The consequences of these improvements for a more accurate modelling of the finite deformation of incompressible isotropic rubber-like materials will also be discussed.

Use of time dependent data in Bayesian global 21-cm foreground and signal modelling

ABSTRACT Global 21-cm cosmology aims to investigate the cosmic dawn and epoch of reionization by measuring the sky averaged H i absorption signal, which requires, accurate modelling of, or correction for, the bright radio foregrounds and distortions arising from chromaticity of the antenna beam. We investigate the effect of improving foreground modelling by fitting data sets from many observation times simultaneously in a single Bayesian analysis, fitting for the same parameter set by performing these fits on simulated data. We find that for a hexagonal dipole antenna, this simultaneous fitting produces a significant improvement in the accuracy of the recovered 21-cm signal, relative to fitting a time average of the data. Furthermore, the recovered models of the foreground are also seen to become more accurate by up to a factor of ∼2–3 relative to time averaged fitting. For a less chromatic log spiral antenna, no significant improvement in signal recovery was found by this process. However, the modelling of the foregrounds was still significantly improved. We also investigate extending this technique to fit multiple data sets from different antennas simultaneously for the same parameters. This is also found to improve both 21-cm signal and foreground modelling, to a higher degree than fitting data set from multiple times from the same antenna.

Temperature Measurements by Wavelength Modulation Diode Laser Absorption Spectroscopy with Logarithmic Conversion and 1f Signal Detection

A new version of a sensor for temperature measurements in the case of strong laser intensity fluctuation was developed. It was based on tunable diode laser absorption spectroscopy (TDLAS) with wavelength modulation, logarithmic conversion of the absorption signal, and detection of the first harmonic of the modulation frequency. The efficiency of the technique was demonstrated under experimental conditions with excess multiplicative noise. Temperature was evaluated from the ratio of integrated absorbance of two lines of the water molecule with different lower energy levels. Two algorithms of data processing were tested, simultaneous fitting of two spectral ranges with selected absorption lines and independent fitting of two absorption lines profiles. The correctness of the gas temperature evaluation was verified by simultaneous measurements with a commercial thermocouple. An error in temperature evaluation of less than 40 at 1000 K was achieved even when processing a single scan of the diode lasers.

Multi-modal mass-asymmetric fission of 178Pt from simultaneous mass-kinetic energy fitting

The observation of mass-asymmetric fission in neutron-deficient 180Hg dramatically expanded the region of mass-asymmetric fission found across the nuclide chart, and has led to intense experimental and theoretical investigations into the fission of sub-lead nuclei. In particular, two major questions have been raised: how many fission modes are present in the fission of sub-lead nuclides, and which shells dictate these modes?Notably, investigations of the fission modes of 178Pt have led to contrasting results. To solve this disparity, new high-statistics data have been measured at the lowest excitation energy to-date using the CUBE fission spectrometer at The Australian National University. A new fitting procedure was developed to fit the high-statistics two-dimensional mass-kinetic energy distribution without external constraints.The fission of 178Pt can best be described by three fission modes: one mass-symmetric and two mass-asymmetric. Comparisons to previous analyses highlight the necessity of fitting the two-dimensional mass-kinetic energy distribution, rather than fitting slices of individual one-dimensional projections of the full distribution. Systematic studies of high-statistics measurements, combined with a rigorous statistical analysis offer the best chance to determine the shell effects responsible for multi-modal mass-asymmetric fission in this region of the nuclide chart.

Evidence for an L3 phase in ternary deep eutectics: composition-induced L3-to-Lα transition of AOT.

Pure and hydrated deep eutectic solvents (DES) are proposed to form self-assembled nanostructures within the fluid bulk, similar to the bicontinuous L3 phase common for ionic liquids (ILs). Labelled choline chloride : urea : water DES were measured using small-angle neutron scattering (SANS), showing no long-range nanostructure. However, solutions of the surfactant AOT in this DES yielded scattering consistent with the L3 "sponge" phase, which was fitted using the Teubner-Strey model. A disclike model gave local structural information, namely, a linear increase in radius versus solvent water content (w = molar ratio of DES : water), eventually forming large, turbid lamellar phases at 10w; an L3-to-Lα transition was observed. Simultaneous multi-contrast SANS fits show the surfactant headgroup region is dominated by interactions with poorly-soluble Na+ at low water contents, and numerically-superior [cholinium]+ as water content increases. The modified interfacial Gaussian curvature from cation : anion volume matching stabilizes the lamellar morphology, allowing the bilayer aggregation number to increase.

First measurements of second-order frequency conversion phase-matching conditions in the new CTAS crystal

We report that Ca3TaAl3Si2O14 is a positive uniaxial crystal and provides second-order frequency conversion. Indeed, we performed direct measurements of phase-matching conditions for second-harmonic generation and sum-frequency generation up to 3.5 µm. The simultaneous fitting of recorded data provided the Sellmeier equations of the two principal refractive indices and the magnitude of the nonlinear coefficient.

A neural network potential energy surface for the Li + LiNa → Li2 + Na reaction and quantum dynamics study from ultracold to thermal energies.

An improved fundamental invariant neural network (FI-NN) approach for representing a potential energy surface (PES) involving permutation symmetry is introduced in this work. In this approach, FIs are regarded as symmetric neurons, thus avoiding complex preprocessing of training set data, especially when the training set contains gradient data. In this work, the improved FI-NN method, combined with simultaneous fitting of the energy and gradient strategy, is used for constructing a global accurate PES of a Li2Na system (root-mean-square error of 12.20 cm-1). The potential energies and the corresponding gradients are calculated by a UCCSD(T) method with effective core potentials. Based on the new PES, the vibrational energy levels and the corresponding wave functions of Li2Na molecules are calculated using an accurate quantum mechanics method. To accurately describe the cold or ultracold reaction dynamics of the Li + LiNa(v = 0, j = 0) → Li2(v', j') + Na reaction, the long-range region of the PES in both the reactant and product asymptotes is represented by an asymptotically correct form. A statistical quantum model (SQM) is used to study the dynamics of the ultracold Li + LiNa reaction. The calculated results are in good agreement with the exact quantum dynamics results (B. K. Kendrick, J. Chem. Phys., 2021, 154, 124303), which indicates that the dynamics of the ultracold Li + LiNa reaction can be well described by the SQM approach. The time-dependent wave packet calculations are performed for the Li + LiNa reaction at thermal energies, and the characteristic of differential cross-sections confirms that the reaction follows the complex-forming reaction mechanism.

Effect of hydration equilibria on the relaxometric properties of Gd(III) complexes: new insights into old systems.

We present a detailed relaxometric and computational investigation of three Gd(III) complexes that exist in solution as an equilibrium of two species with a different number of coordinated water molecules: [Gd(H2O)q]3+ (q = 8, 9), [Gd(EDTA)(H2O)q]- and [Gd(CDTA)(H2O)q]- (q = 2, 3). 1H nuclear magnetic relaxation dispersion (NMRD) data were recorded from aqueous solutions of these complexes using a wide Larmor frequency range (0.01-500 MHz). These data were complemented with 17O transverse relaxation rates and chemical shifts recorded at different temperatures. The simultaneous fit of the NMRD and 17O NMR data was guided by computational studies performed at the DFT and CASSCF/NEVPT2 levels, which provided information on Gd⋯H distances, 17O hyperfine coupling constants and the zero-field splitting (ZFS) energy, which affects electronic relaxation. The hydration equilibrium did not have a very important effect in the fits of the experimental data for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-, as the hydration equilibrium is largely shifted to the species with the lowest hydration number (q = 8 and 2, respectively). The quality of the analysis improves however considerably for [Gd(EDTA)(H2O)q]- upon considering the effect of the hydration equilibrium. As a result, this study provides for the first time an analysis of the relaxation properties of this important model system, as well as accurate parameters for [Gd(H2O)q]3+ and [Gd(CDTA)(H2O)q]-.

Modelling repetition in zDM: A single population of repeating fast radio bursts can explain CHIME data

AbstractRegardless of whether or not all fast radio bursts (FRBs) repeat, those that do form a population with a distribution of rates. This work considers a power-law model of this population, with rate distribution$\Phi_r \sim R^{{\gamma_r}}$between${R_{\rm min}}$and${R_{\rm max}}$. ThezDMcode is used to model the probability of detecting this population as either apparently once-off or repeat events as a function of redshift,z, and dispersion measure, DM. I demonstrate that in the nearby Universe, repeating sources can contribute significantly to the total burst rate. This causes an apparent deficit in the total number of observed sources (once-off and repeaters) relative to the distant Universe that will cause a bias in FRB population models. Thus instruments with long exposure times should explicitly take repetition into account when fitting the FRB population. I then fit data from The Canadian Hydrogen Intensity Mapping Experiment (CHIME). The relative number of repeat and apparently once-off FRBs, and their DM, declination, and burst rate distributions, can be well explained by 50–100% of CHIME single FRBs being due to repeaters, with${R_{\rm max}} > 0.75$d$^{-1}$above$10^{39}$erg, and${{\gamma_r}} = -2.2_{-0.8}^{+0.6}$. This result is surprisingly consistent with follow-up studies of FRBs detected by the Australian Square Kilometre Array Pathfinder (ASKAP). Thus the evidence suggests that CHIME and ASKAP view the same repeating FRB population, which is responsible not just for repeating FRBs, but the majority of apparently once-off bursts. For greater quantitative accuracy, non-Poissonian arrival times, second-order effects in the CHIME response, and a simultaneous fit to the total FRB population parameters, should be treated in more detail in future studies.

Performance of global retention models in the optimisation of the chromatographic separation (I): Simple multi-analyte samples

Conventional retention models lead to accurate descriptions of the elution behaviour from the fitting of data for single solutes or from a set of solutes, one by one. However, the simultaneous fitting of several solutes through a regression process that separates the contributions of column and solvent from those of each solute is also possible. The result is a global retention model constituted by a set of equations with some common parameters (those associated with column and solvent), whereas others, specific to each solute, differ for each equation. This work explores the possibilities, advantages, and limitations of global models when they are applied to the optimisation of chromatographic resolution. A set constituted by 13 drugs (diuretics and β-blockers) and a training experimental design of seven multi-linear gradients are considered. Since standards for all compounds were available, the optimisation based on global models could be compared with the conventional optimisation, which is based on individual models. In their current state, global models do not predict changes in elution order, but they do allow for incorporating additional solutes (e.g., new analytes or matrix peaks) with only one new experiment. This possibility is explored by extending the model for the 13 analytes to include 26 peaks associated with a contamination in the injector. The combination of individual and global models allows an optimisation where the effects of matrix peaks on the separation of analytes can be integrated.

Vibrational Raman Spectroscopy of the Hydration Shell of Ions

Ionic perturbation of water has important implications in various chemical, biological and environmental processes. Previous studies revealed the structural and dynamical perturbation of water in the presence of ions, mainly with concentrated electrolyte solutions having significant interionic interactions. These investigations highlighted the need of selective extraction of the hydration shell water from a dilute electrolyte solution that is largely free from interionic interactions. Double-difference infrared (DDIR) and Raman multivariate curve resolution (Raman-MCR), as well as MD simulation, provided valuable insight in this direction, suggesting that the perturbed water mainly resides in the immediate vicinity of the ion, called the hydration shell. Recently, we have introduced Raman difference spectroscopy with simultaneous curve fitting (Raman-DS-SCF) analysis that can quantitatively extract the vibrational response of the perturbed water pertaining to the hydration shell of fully hydrated ions/solute. The DS-SCF analysis revealed novel hydrogen-bond (H-bond) structural features of hydration water, such as the existence of extremely weakly interacting water–OH (νmax ~ 3600 cm−1) in the hydration shell of high-charge-density metal ions (Mg2+, Dy3+). In addition, Raman-DS-SCF retrieves the vibrational response of the shared water in the water–shared-ion pair (WSIP), which is different from the hydration shell water of either the interacting cation and anion. Herein, we discuss the perturbation of water H-bonding in the immediate vicinity of cation, anion, zwitterion and hydrophobes and also the inter-ionic interactions, with a focus on the recent results from our laboratory using Raman-DS-SCF spectroscopy.

Self-interacting superfluid dark matter droplets

ABSTRACT We assume dark matter to be a cosmological self-gravitating Bose–Einstein condensate of non-relativistic ultralight scalar particles with competing gravitational and repulsive contact interactions and investigate the observational implications of such model. The system is unstable to the formation of stationary self-bound structures that minimize the energy functional. These cosmological superfluid droplets, which are the smallest possible gravitationally bound dark matter structures, exhibit a universal mass profile and a corresponding universal rotation curve. Assuming a hierarchical structure formation scenario where granular dark matter haloes grow around these primordial stationary droplets, the model predicts cored haloes with rotation curves that obey a single universal equation in the inner region ($r\, \lesssim \, 1$ kpc). A simultaneous fit to a selection of galaxies from the SPARC data base chosen with the sole criterion of being strongly dark matter dominated even within the innermost region, indicates that the observational data are consistent with the presence of a Bose–Einstein condensate of ultralight scalar particles of mass m ≃ 2.2 × 10−22 eV c−2 and repulsive self-interactions characterized by a scattering length as ≃ 7.8 × 10−77 m. Such small self-interactions have profound consequences on cosmological scales. They induce a natural minimum scale length for the size of dark matter structures that makes all cores similar in length (∼1 kpc) and contributes to lower their central densities.

Application of distance field-based algorithm to adjacent spline surfaces for composite structures boundary modeling

The complex boundary modeling required for simulating composite materials was applied to a broad range of problems, including surface overlap and gap. A novel method for the simultaneous fitting of adjacent spline surfaces based on a distance field has been devised. The fitting method for spline surfaces was constructed using offline spline surface, facet simplification, and residual solid reconstruction. The distance field-based approach of simultaneous fitting of neighboring spline surfaces included producing a distance field for a spline surface and then applying that distance field to nearby spline surfaces. There would be junction and separation issues if neighboring spline surfaces were fitted individually. By simultaneously fitting the nearby spline surfaces with the aid of the equivalence surface of the distance field, it was feasible to avoid overlap and gap.

The location of the low-energy states in Lhca1 favors excitation energy transfer to the core in the plant PSI-LHCI supercomplex.

Lhca1 is one of the four pigment-protein complexes composing the outer antenna of plant Photosystem I-light-havesting I supercomplex (PSI-LHCI). It forms a functional dimer with Lhca4 but, differently from this complex, it does not contain 'red-forms,' i.e., pigments absorbing above 700nm. Interestingly, the recent PSI-LHCI structures suggest that Lhca1 is the main point of delivering the energy harvested by the antenna to the core. To identify the excitation energy pathways in Lhca1, we developed a structure-based exciton model based on the simultaneous fit of the low-temperature absorption, linear dichroism, and fluorescence spectra of wild-type Lhca1 and two mutants, lacking chlorophylls contributing to the long-wavelength region of the absorption. The model enables us to define the locations of the lowest energy pigments in Lhca1 and estimate pathways and timescales of energy transfer within the complex and to the PSI core. We found that Lhca1 has a particular energy landscape with an unusual (compared to Lhca4, LHCII, and CP29) configuration of the low-energy states. Remarkably, these states are located near the core, facilitating direct energy transfer to it. Moreover, the low-energy states of Lhca1 are also coupled to the red-most state (red forms) of the neighboring Lhca4 antenna, providing a pathway for effective excitation energy transfer from Lhca4 to the core.

Generalized Modeling of Photoluminescence Transients

Time‐resolved photoluminescence (TRPL) measurements and the extraction of meaningful parameters involve four key ingredients: a suitable sample such as a semiconductor double heterostructure, a state‐of‐the‐art measurement setup, a kinetic model appropriate for the description of the sample behavior, and a general analysis method to extract the model parameters of interest from the measured TRPL transients. Until now, the last ingredient is limited to single curve fits, which are mostly based on simple models and least‐squares fits. These are often insufficient for the parameter extraction in real‐world applications. The goal of this article is to give the community a universal method for the analysis of TRPL measurements, which accounts for the Poisson distribution of photon counting events. The method can be used to fit multiple TRPL transients simultaneously using general kinematic models, but should also be used for single transient fits. To demonstrate this approach, multiple TRPL transients of a GaAs/AlGaAs heterostructure are fitted simultaneously using coupled rate equations. It is shown that the simultaneous fits of several TRPL traces supplemented by systematic error estimations allow for a more meaningful and more robust parameter determination. The statistical methods also quantify the quality of the description by the underlying physical model.

"Dead" Exciton Layer and Exciton Anisotropy of Bulk MoS2 Extracted from Optical Measurements.

Excitons (electron-hole pairs bound by the Coulomb potential) play an important role in optical and electronic properties of layered materials. They can be used to modulate light with high frequencies due to the optical Pauli blocking. The properties of excitons in 2D materials are extremely anisotropic. However, due to nanometre sizes of excitons and their short life times, reliable tools to study this anisotropy are lacking. Here, we show how direct optical reflection measurements can be used to evaluate anisotropy of excitons in transition metal dichalcogenides MoS2. Using focused beam spectroscopic ellipsometry, we have measured the polarized optical reflection of bulk MoS2 for two crystal orientations: c-axis being perpendicular to the surface from which reflection is measured and c-axis being parallel to the surface from which reflection is measured. We found that for the parallel configuration the optical reflection near excitonic transitions is strongly affected by the presence of the exciton "dead" layer such that the excitonic reflection peaks become the excitonic dips due to light interference. At the same time, the optical reflection for the perpendicular orientation is not significantly altered by the exciton "dead" layer due to large anisotropy of exciton properties. Performing simultaneous Fresnel fitting for both geometries, we were able to evaluate exciton anisotropy in layered materials from simple optical measurements.