Use of Fourier-transform infrared spectroscopy to quantify immunoglobulin G concentration and an analysis of the effect of signalment on levels in canine serum

Deficiency in immunoglobulin G (IgG) is associated with an increased susceptibility to infections in humans and animals, and changes in IgG levels occur in many disease states. In companion animals, failure of transfer of passive immunity is uncommonly diagnosed but mortality rates in puppies are high and more than 30% of these deaths are secondary to septicemia. Currently, radial immunodiffusion (RID) and enzyme-linked immunosorbent assays are the most commonly used methods for quantitative measurement of IgG in dogs. In this study, a Fourier-transform infrared spectroscopy (FTIR) assay for canine serum IgG was developed and compared to the RID assay as the reference standard. Basic signalment data and health status of the dogs were also analyzed to determine if they correlated with serum IgG concentrations based on RID results. Serum samples were collected from 207 dogs during routine hematological evaluation, and IgG concentrations determined by RID. The FTIR assay was developed using partial least squares regression analysis and its performance evaluated using RID assay as the reference test. The concordance correlation coefficient was 0.91 for the calibration model data set and 0.85 for the prediction set. A Bland-Altman plot showed a mean difference of -89 mg/dL and no systematic bias. The modified mean coefficient of variation (CV) for RID was 6.67%, and for FTIR was 18.76%. The mean serum IgG concentration using RID was 1943 ± 880 mg/dL based on the 193 dogs with complete signalment and health data. When age class, gender, breed size and disease status were analyzed by multivariable ANOVA, dogs < 2 years of age (p = 0.0004) and those classified as diseased (p = 0.03) were found to have significantly lower IgG concentrations than older and healthy dogs, respectively.

Developmental covariation of human vault and base throughout postnatal ontogeny

In the present study, we analyzed postnatal ontogenetic integration among morphological traits of the human neurocranium. Particularly, the covariation between the vault and the base during postnatal life was assessed. Since the association between these regions may depend on the generalized change produced by allometry, we tested its effect on their covariation. On a sample of adults and subadults ranging from 0 to 31 years, 3D coordinates of neurocranial landmarks and semilandmarks were digitized and geometric morphometric technics were applied. Main aspects of shape variation were examined using Principal Components analysis. Covariation between the vault and the base was examined by Partial Least Squares analysis. According to our results, the vault and the base covary strongly during postnatal ontogeny and their relation depends largely on allometry. Two size variables were studied: centroid size, which was obtained from the recorded morphometric points, and endocranial volume, taken as an estimation of brain size. Although growing brain was found to be a developmental process that contributes to covariation among neurocranial traits, there would be other factors that exert their influence during ontogeny. These results lead to reconsider cranial morphological evolution taking into account the developmental constraints given by ontogenetic patterns of integration and reinforcing the idea that in human evolution a suite of relevant characters may be fuelled by few developmental processes.

Development, validation and influence factor analysis of a near-infrared method for the molecular weight determination of xanthan gum

A practical molecular weight determination model of xanthan gum (XG), based on near-infrared (NIR) spectroscopy, was built in this study. Two sample measurement modules, integrating sphere module and fiber-optic probe module, were compared, and the best partial least square (PLS) regression model was based on fiber-optic probe module. The values of coefficient of determination in calibration (R(2)c), coefficient of determination in prediction (R(2)p), residual predictive deviation (RPD) and root mean square error of prediction (RMSEP) were 0.967, 0.975, 6.028 and 0.250×10(6)Da, respectively. The molecular weight range, linearity, accuracy and precision of the established method were also validated. Furthermore, influence factors on this method were discussed in order to establish an appropriate measurement protocol. Results showed that the proposed NIR method may be suitable for practical applications in manufacturing plants and probably be accepted as a good alternative approach for fast determination of molecular weight of XG in production process.

TyPol - a new methodology for organic compounds clustering based on their molecular characteristics and environmental behavior

Following legislation, the assessment of the environmental risks of 30000-100000 chemical substances is required for their registration dossiers. However, their behavior in the environment and their transfer to environmental components such as water or atmosphere are studied for only a very small proportion of the chemical in laboratory tests or monitoring studies because it is time-consuming and/or cost prohibitive. Therefore, the objective of this work was to develop a new methodology, TyPol, to classify organic compounds, and their degradation products, according to both their behavior in the environment and their molecular properties. The strategy relies on partial least squares analysis and hierarchical clustering. The calculation of molecular descriptors is based on an in silico approach, and the environmental endpoints (i.e. environmental parameters) are extracted from several available databases and literature. The classification of 215 organic compounds inputted in TyPol for this proof-of-concept study showed that the combination of some specific molecular descriptors could be related to a particular behavior in the environment. TyPol also provided an analysis of similarities (or dissimilarities) between organic compounds and their degradation products. Among the 24 degradation products that were inputted, 58% were found in the same cluster as their parents. The robustness of the method was tested and shown to be good. TyPol could help to predict the environmental behavior of a "new" compound (parent compound or degradation product) from its affiliation to one cluster, but also to select representative substances from a large data set in order to answer some specific questions regarding their behavior in the environment.

The impacts of second generation e-prescribing usability on community pharmacists outcomes

BACKGROUND

The results from past studies about the effects of second-generation e-prescribing systems on community pharmacists' outcomes and practices are inconclusive, and the claims of effectiveness and efficiency of such systems have not been supported in all studies. There is a strong need to study the factors that lead to positive outcomes for the users of these systems.

OBJECTIVE

This paper intends to bridge the above gaps by empirically examining the impacts of user interface usability on the community pharmacists' outcomes.

METHODS

A quantitative survey research method was used and the data was collected from the community pharmacists, who use an e-prescribing system. Data from 152 questionnaires collected in a national survey were used to for the study. Partial Least Squares (PLS) path modeling was used to examine scale reliability, validity and hypotheses.

RESULTS

The scale was found to test well for reliability and validity. Examining the hypotheses illustrated that ease of use (P < 0.01, t = 5.79) and information quality (P < 0.01, t = 6.24) of an e-prescribing system improved pharmacists' outcomes (including communication, facilitation of care, reduction of workload and medical errors) while ease of use of the system was influenced by user interface consistency (P < 0.01, t = 7.35) and system error prevention (P < 0.01, t = 5.29).

CONCLUSION

To improve community pharmacists' outcomes and practices, the ease of use, information quality, consistency and error prevention features of e-prescribing systems should be improved. It was found that information quality had a stronger impact on the outcomes and hence improving the quality of the generated information would have higher impacts on users' outcomes.

Two and three way spectrophotometric-assisted multivariate determination of linezolid in the presence of its alkaline and oxidative degradation products and application to pharmaceutical formulation

Linezolid (LIN) is determined in the presence of its alkaline (ALK) and oxidative (OXD) degradation products without preliminary separation based on ultraviolet spectrophotometry using two-way chemometric methods; principal component regression (PCR) and partial least-squares (PLS), and three-way chemometric methods; parallel factor analysis (PARAFAC) and multi-way partial least squares (N-PLS). A training set of mixtures containing LIN, ALK and OXD; was prepared in the concentration ranges of 12-18, 2.4-3.6 and 1.2-1.8 μg mL(-1), respectively according to a multilevel multifactor experimental design. The multivariate calibrations were obtained by measuring the zero-order absorbance from 220 to 320 nm using the training set. The validation of the multivariate methods was realized by analyzing their synthetic mixtures. The capabilities of the chemometric analysis methods for the analysis of real samples were evaluated by determination of LIN in its pharmaceutical preparation with satisfactory results. The accuracy of the methods, evaluated through the root mean square error of prediction (RMSEP), was 0.058, 0.026, 0.101 and 0.026 for LIN using PCR, PLS, PARAFAC and N-PLS, respectively. Protolytic equilibria of LIN and its degradation products were evaluated using the corresponding absorption spectra-pH data obtained with PARAFAC. The obtained pKa values of LIN, ALK and OXD are 5.70, 8.90 and 6.15, respectively. The results obtained were statistically compared to that of a reported HPLC method, and there was no significant difference between the proposed methods and the reported method regarding both accuracy and precision.

Determining the causal relationships among balanced scorecard perspectives on school safety performance: case of Saudi Arabia

In the public schools of many developing countries, numerous accidents and incidents occur because of poor safety regulations and management systems. To improve the educational environment in Saudi Arabia, the Ministry of Education seeks novel approaches to measure school safety performance in order to decrease incidents and accidents. The main objective of this research was to develop a systematic approach for measuring Saudi school safety performance using the balanced scorecard framework philosophy. The evolved third generation balanced scorecard framework is considered to be a suitable and robust framework that captures the system-wide leading and lagging indicators of business performance. The balanced scorecard architecture is ideal for adaptation to complex areas such as safety management where a holistic system evaluation is more effective than traditional compartmentalised approaches. In developing the safety performance balanced scorecard for Saudi schools, the conceptual framework was first developed and peer-reviewed by eighteen Saudi education experts. Next, 200 participants, including teachers, school executives, and Ministry of Education officers, were recruited to rate both the importance and the performance of 79 measurement items used in the framework. Exploratory factor analysis, followed by the confirmatory partial least squares method, was then conducted in order to operationalise the safety performance balanced scorecard, which encapsulates the following five salient perspectives: safety management and leadership; safety learning and training; safety policy, procedures and processes; workforce safety culture; and safety performance. Partial least squares based structural equation modelling was then conducted to reveal five significant relationships between perspectives, namely, safety management and leadership had a significant effect on safety learning and training and safety policy, procedures and processes, both safety learning and training and safety policy, procedures and processes had significant effects on workforce safety culture, and workforce safety culture had a significant effect on safety performance.

Near infrared spectroscopic (NIRS) analysis of drug-loading rate and particle size of risperidone microspheres by improved chemometric model

Microspheres have been developed as drug carriers in controlled drug delivery systems for years. In our present study, near infrared spectroscopy (NIRS) is applied to analyze the particle size and drug loading rate in risperidone poly(d,l-lactide-co-glycolide) (PLGA) microspheres. Various batches of risperidone PLGA microspheres were designed and prepared successfully. The particle size and drug-loading rate of all the samples were determined by a laser diffraction particle size analyzer and high performance liquid chromatography (HPLC) system. Monte Carlo algorithm combined with partial least squares (MCPLS) method was applied to identify the outliers and choose the numbers of calibration set. Furthermore, a series of preprocessing methods were performed to remove signal noise in NIR spectra. Moving window PLS and radical basis function neural network (RBFNN) methods were employed to establish calibration model. Our data demonstrated that PLS-developed model was only suitable for drug loading analysis in risperidone PLGA microspheres. Comparatively, RBFNN-based predictive models possess better fitting quality, predictive effect, and stability for both drug loading rate and particle size analysis. The correlation coefficients of calibration set (Rc(2)) were 0.935 and 0.880, respectively. The performance of optimum RBFNN models was confirmed by independent verification test with 15 samples. Collectively, our method is successfully performed to monitor drug-loading rate and particle size during risperidone PLGA microspheres preparation.

Mortality cohort effects from mid-19th to mid-20th century Britain: did they exist?

PURPOSE

Identification is a central problem with age-period-cohort analysis. Because age + cohort = period, there is no unique solution to the linear effect using generalized linear modeling, but cohort effects have caused greater controversy than age and period effects. To illustrate the magnitude of cohort effects given the presence of collinearity, we reanalyze data from the seminal study by Kermack et al, with an update.

METHODS

Relative mortality data in England and Wales between year 1845 and 1995 were analyzed using partial least squares regression. There were seven age groups ranging from 5 to 74 years old and 16 periods with 22 cohorts.

RESULTS

Our reanalysis seemed to support the existence of cohort effects in the mortality trends. Period and cohort effects were generally consistent with changes in the social, economic, and environmental factors taking place in the last two centuries. Our analysis also showed a declining trend in period effects up to 1950s.

CONCLUSIONS

Partial least squares and related methods provide intuitive pointers toward the separation of linear age, period, and cohort effects. Because statistical algorithms cannot distinguish between relative and actual mortality rates, cohort effects may be underestimated because of contamination by negative age effects.

Predictive analysis of beer quality by correlating sensory evaluation with higher alcohol and ester production using multivariate statistics methods

Sensory evaluation is regarded as a necessary procedure to ensure a reproducible quality of beer. Meanwhile, high-throughput analytical methods provide a powerful tool to analyse various flavour compounds, such as higher alcohol and ester. In this study, the relationship between flavour compounds and sensory evaluation was established by non-linear models such as partial least squares (PLS), genetic algorithm back-propagation neural network (GA-BP), support vector machine (SVM). It was shown that SVM with a Radial Basis Function (RBF) had a better performance of prediction accuracy for both calibration set (94.3%) and validation set (96.2%) than other models. Relatively lower prediction abilities were observed for GA-BP (52.1%) and PLS (31.7%). In addition, the kernel function of SVM played an essential role of model training when the prediction accuracy of SVM with polynomial kernel function was 32.9%. As a powerful multivariate statistics method, SVM holds great potential to assess beer quality.

Simultaneous multicomponent spectrophotometric monitoring of methyl and propyl parabens using multivariate statistical methods after their preconcentration by robust ionic liquid-based dispersive liquid-liquid microextraction

A powerful and efficient signal-preprocessing technique that combines local and multiscale properties of the wavelet prism with the global filtering capability of orthogonal signal correction (OSC) is applied for pretreatment of spectroscopic data of parabens as model compounds after their preconcentration by robust ionic liquid-based dispersive liquid-liquid microextraction method (IL-DLLME). In the proposed technique, a mixture of a water-immiscible ionic liquid (as extraction solvent) [Hmim][PF6] and disperser solvent is injected into an aqueous sample solution containing one of the IL's ions, NaPF6, as extraction solvent and common ion source. After preconcentration, the absorbance of the extracted compounds was measured in the wavelength range of 200-700 nm. The wavelet orthogonal signal correction with partial least squares (WOSC-PLS) method was then applied for simultaneous determination of each individual compound. Effective parameters, such as amount of IL, volume of the disperser solvent and amount of NaPF6, were inspected by central composite design to identify the most important parameters and their interactions. The effect of pH on the sensitivity and selectivity was studied according to the net analyte signal (NAS) for each component. Under optimum conditions, enrichment factors of the studied compounds were 75 for methyl paraben (MP) and 71 for propyl paraben (PP). Limits of detection for MP and PP were 4.2 and 4.8 ng mL(-)(1), respectively. The root mean square errors of prediction for MP and PP were 0.1046 and 0.1275 μg mL(-)(1), respectively. The practical applicability of the developed method was examined using hygienic, cosmetic, pharmaceutical and natural water samples.

Modeling and partial least squares approaches in OODA

This is a discussion of the following paper: "Overview of object oriented data analysis" by J. Steve Marron and Andrés M. Alonso.

Simultaneous determination of caffeine, caramel and riboflavin in cola-type and energy drinks by synchronous fluorescence technique coupled with partial least squares

The aim of this work was to develop a multivariate method for the rapid determination of caffeine and Class IV caramel in cola-type soft drinks and of caffeine, Class III caramel and riboflavin in energy drinks using synchronous fluorescence spectra. The synchronous fluorescence spectra were recorded at constant wavelength difference 90 nm from 200 to 500 nm. Reference values of analyte concentrations by high performance liquid chromatography (HPLC) with fluorescence detection combined with the standard addition method were used to create the partial least squares (PLS) models. High coefficients of determination (>0.99) were obtained in 0.2-4.2, 0.25-5.25, 0.4-10.0 and 0.007-0.054 mg L(-1) range for caffeine, Class III caramel, Class IV caramel and riboflavin, respectively. The PLS models were used to determine the concentration of analytes in different drink samples. The method provided comparable results with those found using the HPLC method.

Uneven batch data alignment with application to the control of batch end-product quality

Batch processes are commonly characterized by uneven trajectories due to the existence of batch-to-batch variations. The batch end-product quality is usually measured at the end of these uneven trajectories. It is necessary to align the time differences for both the measured trajectories and the batch end-product quality in order to implement statistical process monitoring and control schemes. Apart from synchronizing trajectories with variable lengths using an indicator variable or dynamic time warping, this paper proposes a novel approach to align uneven batch data by identifying short-window PCA&PLS models at first and then applying these identified models to extend shorter trajectories and predict future batch end-product quality. Furthermore, uneven batch data can also be aligned to be a specified batch length using moving window estimation. The proposed approach and its application to the control of batch end-product quality are demonstrated with a simulated example of fed-batch fermentation for penicillin production.

Quantification of animal fat biodiesel in soybean biodiesel and B20 diesel blends using near infrared spectroscopy and synergy interval support vector regression

In this work, multivariate calibration based on partial least squares (PLS) and support vector regression (SVR) using the whole spectrum and variable selection by synergy interval (siPLS and siSVR) were applied to NIR spectra for the determination of animal fat biodiesel content in soybean biodiesel and B20 diesel blends. For all models, prediction errors, bias test for systematic errors and permutation test for trends in the residuals were calculated. The siSVR produced significantly lower prediction errors compared to the full spectrum methods and siPLS, with a root mean squares error (RMSEP) of 0.18%(w/w) (concentration range: 0.00%-69.00%(w/w)) in the soybean biodiesel blend and 0.10%(w/w) in the B20 diesel (concentration range: 0.00%-13.80%(w/w)). Additionally, in the models for the determination of animal fat biodiesel in blends with soybean diesel, PLS and SVR showed evidence of systematic errors, and PLS/siPLS presented trends in residuals based on the permutation test. For the B20 diesel, PLS presented evidence of systematic errors, and siPLS presented trends in the residuals.

Cumulative area pre-processing (CAP): a new treatment of UV data for the analysis of complex pharmaceutical mixtures

A new approach to pre-processing of the UV spectral data in combination with chemometric techniques, aiming to obtain a significant amplification of the analytical information, is proposed. The single areas under the curve between two consecutive wavelengths were calculated along the full spectrum and therefore their cumulative sum was carried out. The method was called "cumulative area pre-processing" (CAP) and applied to multicomponent pharmaceutical formulations to test its performance in improving the accuracy of the analysis. The proposed procedure has demonstrated high ability in the quantitative determination of the components present in very low amount compared to other. Three multicomponent drug formulations were analyzed by applying the partial least squares (PLS) algorithm to the UV data processed by CAP and the results compared with those carried out by using the same data without treatment and after derivative transformation. The best results in the determination of the components present in lower concentrations were obtained by applying the PLS models calculated on data processed by CAP and confirmed in the analysis of marketed drug products.

A novel algorithm for linear multivariate calibration based on the mixed model of samples

We present a novel algorithm for linear multivariate calibration that can generate good prediction results. This is accomplished by the idea of that testing samples are mixed by the calibration samples in proper proportion. The algorithm is based on the mixed model of samples and is therefore called MMS algorithm. With both theoretical support and analysis of two data sets, it is demonstrated that MMS algorithm produces lower prediction errors than partial least squares (PLS2) model, has similar prediction performance to PLS1. In the anti-interference test of background, MMS algorithm performs better than PLS2. At the condition of the lack of some component information, MMS algorithm shows better robustness than PLS2.

Oxygenated weathering products of Deepwater Horizon oil come from surprising precursors

Following the release of crude oil from the Macondo well in 2010, a wide range of weathering processes acted on the spilled oil. A recent study revealed that samples from this spill were oxidized into oxygenated hydrocarbons (OxHC) comprising more than 50% of the extracted hydrocarbons. The precursors of these compounds were not identified despite using a wide range of analytical tools, including gas chromatography (GC). To search for these precursors, over 40 samples were analyzed by comprehensive two-dimensional gas chromatography (GC×GC), one of the largest studies of its kind to date. Partial least squares regression was employed to elucidate the GC×GC peaks that could be the precursors of OxHC in our samples. We found that the formation of OxHC correlated with the disappearance of saturated hydrocarbons, including alkylcyclopentanes, alkyl cyclohexanes, alkylated bicyclic saturated compounds, tricyclic terpanpoids, and alkylbenzenes. These results indicate a previously under-reported chemodynamic process in oil spill weathering.

Modeling the chiral resolution ability of highly sulfated β-cyclodextrin for basic compounds in electrokinetic chromatography

Despite the fact that extensive research in the field of enantioseparations by capillary electrophoresis has been carried out, it is difficult to predict whether a concrete chiral selector would be useful for the separation of a racemic compound. Hence, several experimental effort is necessary to test the abilities of individual chiral selectors, usually by trial and error procedures. Thus, the enantioseparation of a new racemate becomes a time- and money-consuming task. In this work, the ability of highly sulfated β-cyclodextrin (HS-β-CD) as chiral selector in electrokinetic chromatography (EKC) is modeled for the first time, using exclusively directly-available structural data of forty compounds (structurally unrelated basic drugs and pesticides). A discriminant partial least squares (PLS)-based quantitative structure-property relationship (QSPR) approach is simplified, resulting in a consistent, predictive and descriptive model. It is converted into an explicit equation able to predict the enantioresolution level (Rs) of new compounds, from four structure properties available in an on-line open database: logarithm of octanol-water partition coefficient estimated at pH 7.4 (lgD), polar surface area (PSA), number of hydrogen bond donors (HBD) and acceptors (HBA). For the cases in which the model predicts good Rs only in concrete experimental conditions, a Box-Behnken experimental design is proposed for the fast PLS-based optimization of the most influential experimental variables: cyclodextrin concentration, temperature and pH.

Dual stacked partial least squares for analysis of near-infrared spectra

A new ensemble learning algorithm is presented for quantitative analysis of near-infrared spectra. The algorithm contains two steps of stacked regression and Partial Least Squares (PLS), termed Dual Stacked Partial Least Squares (DSPLS) algorithm. First, several sub-models were generated from the whole calibration set. The inner-stack step was implemented on sub-intervals of the spectrum. Then the outer-stack step was used to combine these sub-models. Several combination rules of the outer-stack step were analyzed for the proposed DSPLS algorithm. In addition, a novel selective weighting rule was also involved to select a subset of all available sub-models. Experiments on two public near-infrared datasets demonstrate that the proposed DSPLS with selective weighting rule provided superior prediction performance and outperformed the conventional PLS algorithm. Compared with the single model, the new ensemble model can provide more robust prediction result and can be considered an alternative choice for quantitative analytical applications.

Effects of mnemonic load on cortical activity during visual working memory: linking ongoing brain activity with evoked responses

The mechanisms generating task-locked changes in cortical potentials remain poorly understood, despite a wealth of research. It has recently been proposed that ongoing brain oscillations are not symmetric, so that task-related amplitude modulations generate a baseline shift that does not average out, leading to slow event-related potentials. We test this hypothesis using multivariate methods to formally assess the co-variation between task-related evoked potentials and spectral changes in scalp EEG during a visual working memory task, which is known to elicit both evoked and sustained cortical activities across broadly distributed cortical regions. 64-channel EEG data were acquired from eight healthy human subjects who completed a visuo-spatial associative working memory task as memory load was parametrically increased from easy to hard. As anticipated, evoked activity showed a complex but robust spatio-temporal waveform maximally expressed bilaterally in the parieto-occipital and anterior midline regions, showing robust effects of memory load that were specific to the stage of the working memory trial. Similarly, memory load was associated with robust spectral changes in the theta and alpha range, throughout encoding in posterior regions and through maintenance and retrieval in anterior regions, consistent with the additional resources required for decision making in prefrontal cortex. Analysis of the relationship between event-related changes in slow potentials and cortical rhythms, using partial least squares, is indeed consistent with the notion that the former make a causal contribution to the latter.

Remembering what could have happened: neural correlates of episodic counterfactual thinking

Recent evidence suggests that our capacities to remember the past and to imagine what might happen in the future largely depend on the same core brain network that includes the middle temporal lobe, the posterior cingulate/retrosplenial cortex, the inferior parietal lobe, the medial prefrontal cortex, and the lateral temporal cortex. However, the extent to which regions of this core brain network are also responsible for our capacity to think about what could have happened in our past, yet did not occur (i.e., episodic counterfactual thinking), is still unknown. The present study examined this issue. Using a variation of the experimental recombination paradigm (Addis, Pan, Vu, Laiser, & Schacter, 2009. Neuropsychologia. 47: 2222-2238), participants were asked both to remember personal past events and to envision alternative outcomes to such events while undergoing functional magnetic resonance imaging. Three sets of analyses were performed on the imaging data in order to investigate two related issues. First, a mean-centered spatiotemporal partial least square (PLS) analysis identified a pattern of brain activity across regions of the core network that was common to episodic memory and episodic counterfactual thinking. Second, a non-rotated PLS analysis identified two different patterns of brain activity for likely and unlikely episodic counterfactual thoughts, with the former showing significant overlap with the set of regions engaged during episodic recollection. Finally, a parametric modulation was conducted to explore the differential engagement of brain regions during counterfactual thinking, revealing that areas such as the parahippocampal gyrus and the right hippocampus were modulated by the subjective likelihood of counterfactual simulations. These results suggest that episodic counterfactual thinking engages regions that form the core brain network, and also that the subjective likelihood of our counterfactual thoughts modulates the engagement of different areas within this set of regions.