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Return to Book Page. Preview — Abiturwissen Deutsch by Yomb May. Get A Copy. Kindle Edition , pages. The framework we examined in this paper, i.
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In more detail, as previously noted, the OPNMF components themselves were circumscribed rather than representing a mixture of voxel-wise positive and negative weights as would be the case for PCA cf. Sotiras et al. LASSO then selected a small number of these spatially confined components for the actual prediction.
This allowed us to identify, which brain regions consistently contributed to the age estimation. As demonstrated in Fig S7 , many of the regions that were selected by the models are also the regions that show the highest correlation with age. This suggests that, to some extent, the observed contributors are consistent with age-related GMV changes. More specifically, the regions contributing to the prediction model in the BRAINS cohort older subjects included regions around the central sulcus, the inferior temporal cortex, the occipital and posterior temporal cortices and area Regions contributing to the predictions in this older adult cohort also included bilateral midline areas such as, the superior medial frontal gyrus, the medial fronto-orbital regions, the anterior and middle cingulate cortices and the retrosplenial cortex.
Furthermore, the pattern of regions weighting in the prediction model in this cohort further included bilateral subcortical regions such as the thalamus, the basal ganglia and the posterior hippocampus, as well as the bilateral cerebellum. On the lateral surface, the pattern included regions in prefrontal regions frontal areas anterior to the precentral gyrus , oribitofrontal regions and temporal poles. In contrast, the pattern of regions for age prediction in the MIXED dataset heterogeneous dataset covering the whole life span was less spatially specific, covering most of the brain lateral surface bilaterally including for example the whole bilateral middle and superior frontal gyri, as well as the bilateral posterior superior and inferior parietal cortices , almost the entire medial structures, and, the bilateral anterior hippocampus and amygdala.
In other words, the prediction models of age in this heterogeneous dataset built on most of the brain regions. Summary map of the regions that contributed in the prediction analysis when performing fold cross-validation and compressing the dataset using the components derived from the other dataset, in which brighter shade represents more frequently used parts of the brain. Plain anatomical slices are displayed as reference in the top raw. Spatial smoothing on the VBM data promotes homogeneity of the data by attenuating small differences between individuals. In turn, age prediction may rely on those subtle effects.
In this study, we showed that non-negative sparse coding through the combination of data compression using OPNMF with LASSO regression could predict age of previously unseen subjects in an unbiased manner from structural neuroimaging data. Several key observations emerged from this work. Our results showed that age prediction of unseen subjects using the full uncompressed VBM data reported only slightly better prediction accuracies than one based on the OPNMF compressed Table S1.
This comparable level of performance for compressed and uncompressed data has also been observed in previous brain age studies employing PCA compression Franke et al. However, in the current study, predicting age using sparse regularization LASSO prediction model on uncompressed VBM data is highly inefficient in terms of memory usage, especially for large datasets for example, MIXED dataset with 1, subjects. While high dimensional voxel wise data could also lead to overfitting of prediction model, due to the larger number of features than subjects i.
Beside this still open issue, the recent availability of MRI data in very large sample sizes, i. The key limitation of voxel-wise analysis, however, is the poor interpretability of the relevant features. Nevertheless, the individual anatomical correspondence of a particular voxel chosen by the prediction model, can be variable across subjects Davatzikos That is, features should be independent of each other in order to obtain reliable outcomes.
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In other words, voxel-wise sparse regression models pose a decoding problem Kampa et al. Thus, the poor interpretability of prediction models based on raw VBM data Lakkaraju et al. Any data reduction procedure aims to address the curse of dimensionality without any loss of information. In this context, both PCA and OPNMF provide low rank approximations representing the most influential structure within the original data, however, each decomposition method captures different aspects of the similar information PCA captures the components with the most variance explained across the dataset, while OPNMF captures the spatially more localized components that consistently co-vary across the dataset , leading in the present study to comparable performance of both approaches in age prediction.
Both LASSO and RVM yield sparse regression models with the advantage of performing feature selection by capitalizing only on the features that improve the prediction accuracy and allow comparable accuracies. However, an additional argument for the use of LASSO, this model allows the selection of the regularization parameter. Hence, LASSO optimizes the trade-off between stability and interpretability of the prediction model i. Zou and Hastie for more technical details.
Therefore, the LASSO regression model can convert the sparse regression model into a purely non-sparse model using the elastic net regularization model and can therefore be considered as a relatively more flexible regression model than RVM. Furthermore, Bunea et al.
As reduction techniques have shown best prediction accuracies at higher level of granularity and given previous considerations, we focused on LASSO for subsequent prediction analyses. Of note, the used RS-parcellations have both been extensively evaluated in their respective studies, namely with regards to stability and convergence with histological mapping and alternative parcellations Bellec et al.
The RS-parcellations also define spatially homogenous regions, suggesting that the structural representations identified here capture segregated patterns of brain functional organization Sporns Similar observations have been reported recently by Sotiras et al. Together, these findings thus suggest that OPNMF of VBM data to some extend captures meaningful patterns of brain functional organization, both at the network and areal level. This is in line with the few multi-modal mapping studies showing that brain maps from different features such as structure and function converge towards similar brain partition schemes, but also suggesting that each feature targeting a specific aspect of the brain tissue, each feature can capture an unique aspect of brain organization Kelly et al.
In other words, different features i. From the perspective of data compression, the most efficient partitions should thus come from the same modality. And indeed, RS-parcellations provides more homogeneous parcels when assessing resting-state images than histologically defined brain regions Craddock et al. This leaves the question, whether the amount of transferable information is still sufficient for a useful representation. Our results also provided evidence that this is the case by showing that a more accurate age prediction model is built from VBM data when this data is compressed directly as compared to representing it based on a functional parcellation of the brain Fig 5 even if the latter yields very good accuracies.
Overall, in the context of multivariate pattern analysis, we suggest that brain parcellation derived from one modality is transferable to another modality for data reduction even though it does not reach within-modality performance. As the granularity increases, the resolution of structural covariance increases resulting in a finer representation of covariance patterns, but that are, in turn, more influenced by covariance trends specific to the dataset used.
Thus, we assumed that the difference in sample characteristics between the two cohorts could explain the slight differences in the brain topographical pattern of the factorizations. Importantly, our study showed that despite the fact that reproducibility may decrease at high level of granularity Sotiras et al. Our results demonstrated that when the number of components reaches approximately —, prediction accuracy remains largely stable, particularly when the factorization is derived from the same dataset.
However, when the factorization is derived from an independent dataset, a somewhat higher granularity i. At a level of granularity around — components, OPNMF seemed to factorize the entire voxel-wise data into efficient subdivisions, which allowed the LASSO regression model to capture only the relevant features i. Our finding converges with the study of Franke et al. These authors found that the lowest mean absolute error of the prediction analysis was reached at around components. Of note, this level of granularity or factorization seems also convergent with the range of subdivisions of the brain that emerged as stable in functional MRI data, which lies between and parcels Tucholka et al.
We could assume that a lower level of subdivision i. Eickhoff et al. Thus, the current study suggests that a factorization of VBM data into to components optimally organizes voxel-wise structural data into homogeneous brain regions for age prediction.
In the model validation within the same dataset, our study showed that the performance of the brain age prediction using the framework of non-negative sparse coding i. It is important to note that predicting the age of subjects compressed using the components derived from the same dataset violates the test set independence. Even though the subjects in the test dataset were separated from the training dataset at the prediction level, the used factorization reflects the best factorization of the entire dataset, including the test dataset Yuan et al.
Therefore, in this study we compared the performance of the proposed prediction framework with this later over-optimal approach. Our results demonstrated that the LASSO regression, when applied on the dataset compressed with components derived from an independent dataset, estimated the brain age with a precision comparable to that achieved when compressing the dataset with its own factorization. Our results showed that the differences between the factorizations derived from the two datasets cf. Furthermore, our supplementary results Fig S3 illustrated that the pattern of regions selected by the prediction approach remained similar when the factorization was derived from another dataset.
That is, the prediction model recollected the same anatomical regions regardless of which factorization scheme was applied. Again, this pattern of findings converges with what has been previously observed in data reduction of fMRI data for subsequent functional connectivity analyses. Those parcellation studies have observed that at an optimal resolution, parcellation from one dataset can provide a relevant spatial representation of the functional signal in other datasets, despite the topographical pattern of the parcellation between the datasets being different Bellec et al.
Similarly, OPNMF factorization based on a different dataset did not prevent an optimal compression of the data for age prediction or the selection of the relevant anatomical features. Thus, overall, our results demonstrated that despite the fact that factorization results from different datasets may comprise slightly different spatial components, any of the stable factorizations offers an efficient data compression for prediction analyses.
Thus, our study supported Liem et al. In other words, heterogeneous datasets allow the model to encounter a wider range of variations, helping it to disentangle non-relevant inter-individual variations from relevant variations for prediction. Surprisingly, model trained on single-site study also performed efficiently, when predicting the age of highly heterogeneous dataset OldMIXED. To note, the single-site study consists of subjects between 55 to 75 years Fig 1A.
Therefore, the model trained on this dataset encountered a wide range of variation at each age point. We suppose that this exposure to wide range of variation might have allowed overcoming the scanner effects with a robust regression model. Thus, we would recommend to train a given prediction model on a heterogeneous dataset either with multi-sited examples or with multiple examples, ideally both to ensure that true relevant variations are learned, which in turn may support good prediction performance. Importantly, the two cohorts also differed in their age distribution.
Together, these observations further confirmed the general recommendation for the prediction model to be trained on data comprising variations due to distinct parameters such as the acquisition protocol and demographic characteristic. Despite the fact that this recommendation might sound trivial, it actually complements previous recommendations emphasizing the importance of sample size for good prediction performance Varoquaux et al. When applied in a clinical context, i. More specifically, the dramatic atrophy of AD patients was reflected by a mean BrainAGE score of almost 10 years, which is comparable to the findings of a previous study conducted by Franke et al.
The sensitivity of our framework to brain structural changes in clinical populations was underscored by the likewise elevated BrainAGE for MCI participants, which was lower than for those with AD but still on average in the rage of 5—6 years, i. In other words, our framework accurately ranked the HC, MCI and AD groups with regards to their clinical progression from healthy to demented considering MCI as a transitional stage between normal aging and dementia; Petersen, While a classification approach could be more powerful for such purpose than age prediction Franke and Gaser ; Wang et al.
Overall, our results demonstrate that models trained on highly heterogeneous life span sample MIXED can predict the age of any unseen subject with a precision of 6 years irrespective of approach i. Given the broad age range of the training sample 18 to 81 years , a precision of 6 years can be considered as a good performance from the technical side. Importantly, all previous brain age prediction studies likewise reported a precision of approximately 5 — 6 years in the context of life-span samples. The relationship between GMV and the chronological age is modulated by many factors both environmental and genetic factors Burgmans et al.
When aiming to identify the relationship between brain structural pattern and age, those factors may introduce noise obscuring the systematic effects of age on brain structure. In addition to these factors, inclusion of participant with certain characteristics such as, participants in younger age with unidentified subclinical brain alterations, or older adults representing above-normal i. Accordingly, these factors and the noise they introduce could account for the precision gap of 5 — 6 years in brain age prediction studies.
However, this hypothesis might not hold true for all life periods. For instance, one can observe dramatic age-related structural changes in childhood cf. Erus et al. Further examinations of these issues in future studies could provide better understanding of neurobiological aging. Nevertheless, in the scope of the present study, these confounding factors do not prevent our framework combining OPNMF with sparse regression model to accurately capture normal variations related to age and deviance from normal variations in clinical populations.
Such a pattern could argue for a more complex pattern of grey matter variations across the whole adult life span than in the later life periods. Furthermore, as aforementioned, several factors may induce brain structural variations in the young and middle-aged adult brain, such as life style and environmental factors Miller et al.
In our study, in addition to the regions highlighted for age prediction in older sample, some regions, such as the amygdala, and the superior parietal lobule further contributed to age prediction when the model was trained on the young and middle age adults MIXED dataset. Interestingly, the amygdala is one region where GMV has been found to increase with age in relatively younger samples 8 to 30 years old; Ostby et al. Furthermore, structural covariance of the amygdala with other brain regions is known to be modulated by several factors such as gender Mechelli Thus, we could assume that, in a prediction model mixing genders, the amygdala could be selected as an indicator modulating the pattern of relationship between other brain regions and age, despite this region per se does not show a strong, linear and universal GMV decrease with age.
Accordingly, when examining the pattern of association between GMV and age, we observed a mild general linear decline of grey matter volume with age, but with a high variance across the subjects in the MIXED sample see Fig S4 suggesting that very different age-related grey matter change patterns might be observed in this brain region. Such a pattern allows us to assume that the GMV in the amygdala, taken as isolated information, cannot significantly contribute to the age prediction, particularly in the case of older participants. In other words, we assume that the grey matter changes in the amygdala are diverse and occur mainly in the young and middle age adult lifespan rendering this specific region informative for predicting age in the whole adult life span sample in combination with information from other regions.
However, on its own, this region would not be particularly informative for age prediction in older populations. The superior parietal cortex is another example of regions contributing to the prediction analysis when the training sample consisted of young adults in addition to the older adults, but not when the model was trained on older adults only. Terribilli et al. The non-linear trend reported by the authors could be explained by a quadratic fit, that is, GMV followed a linear decline until the end of the fourth decade and then showed a mild increase. When examining the relationship between GMV and age in the superior parietal region in our study, we observed a similar trend see Fig S4 , in which the mean GMV of the superior parietal region showed a sharp decrease until 40 years of age, but less pronounced change with age in later life.
Thus, despite the fact that prediction models in general, specially LASSO regression models are inherently linear, identification of GMV in the superior parietal cortex as relevant for age prediction converges with previous data demonstrating that structural changes in this region occur mainly in the first decades of adult life, but not in periods later in life. Thus, visually examining the pattern of associations between GMV and age in regions contributing to the prediction in MIXED suggest that some regions may be informative for their relatively systematic changes in the first period of adult life such as the superior parietal cortex while others regions could contribute by introducing complementary information such as the amygdala despite not exhibiting a clear linear relationship with age across the sample.
The pattern of regions consistently contributing to the prediction in the older sample appeared more spatially specific. Many of the regions highlighted by these analyses such as the hippocampus, the temporo-occipital region and the medial superior frontal gyrus have been shown to be strongly affected by aging in the older life period and more specifically, to follow a strong linear decrease in this life period after 40—50 years old; Raz et al. However, some other regions, such as the regions around the central sulcus are not known to show systematic change with age in later life period.
Thus, the pattern of regions contributing to the predictions in BRAINS suggests that when the training sample is restricted to older populations, the model can be restricted to a few regions, whose grey matter volumes is systematically affected by the aging process in the later life period, as well as other regions that might not appear particularly informative form a neurobiological point of view but complement the information conveyed by the former regions.
Interpreting the multivariate brain pattern weighting in the prediction is usually not recommended e. Haufe et al. However, we would argue that the relationship between the brain and the predicted variable should not be kept as a conceptually locked black box, that is, the multivariate aspect of the prediction does not imply that we should not at least try to understand why the given pattern is relevant for the model.
Hence, examining the combination of those two variables for predicting the age of a person can provide us more insight by suggesting that the relationship between age and the number of children is modulated by cultural factors. Similarly, the pattern of relationship between grey matter volume and age is assumed to be modulated by several factors, but whose influence remained relatively poorly understood.
However, the current framework promoting relatively localized component as relevant features could help to explore this issue in future studies such as how the complex pattern of structural variations in the amygdala influenced by gender can contribute to age prediction in healthy adults. In conclusion, our study, which evaluated OPNMF-based compression of VBM data for age prediction in two different healthy adult cohorts, opens several new perspectives. First, we demonstrated that OPNMF compression allows age prediction with a precision that is well comparable to that achieved following PCA compression but yields substantially more interpretable results.
It also outperformed an atlas-based approach based on resting-state whole-brain parcellation, even though the precision obtained by cross-model atlas based data compression is in itself remarkable. Considering the declining return of investment when going to higher granularities, we would thus suggest that OPNMF at a granularity of and components may provide the optimal data compression for age prediction. Winterreise is about the exile of the human heart, and its bitter and gloomy self-reconciliation. Thus Heine casts his secret and 'illegal thoughts', so that the darts of his satire and humour fly out from the tragic vortex of his own exile.
In Aachen Heine first comes in contact again with the Prussian military:. Still always that wooden pedantic race, Still always a right angle In every movement and every face The frozen conceit. In Section IV on the winter-journey to Cologne he mocks the anachronistic German society , that more readily with archaic skills builds the Cologne Cathedral , unfinished since the Middle Ages, than addressing itself to the Present Age. That the anachronistic building works came to be discontinued in the course of the Reformation indicated for the poet a positive advance: the overcoming of traditional ways of thought and the end of spiritual juvenility or adolescence.
The River-god however shows himself as a sorrowful old man, disgusted with the babble about Germanic identity. His transformation of Europe had called awake in Heine the hope for universal freedom.
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However: the Emperor is dead. Heine had been an eye-witness in Paris of his burial in at Les Invalides. This Heine offers as a metaphoric statement of the critical distance occupied by himself as polemic or satirical poet, and of the sheepskin-costume appropriate for much of what was surrounding him. I am no sheep, I am no dog, No Councillor, and no shellfish — I have remained a wolf, my heart And all my fangs are wolfish. In the morning mist a crucifix appears. Not surprisingly the mythic German Emperor presents himself as a man become imbecile through senility, who is above all proud of the fact that his banner has not yet been eaten by moths.
Germany in internal need? Pressing need of business for an available Emperor? Wake up, old man, and take your beard off the table! What does the most ancient hero mean by it? Emperors have worn out their usefulness, and seen in that light Monarchs are also superfluous. Stay up the mountain, Old Man! Sword or noose would do equally good service for the disposal of these superfluous toadies. From there he went on to a meeting with King Ernest Augustus of Hanover in that place, who, "accustomed to life in Great Britain " detains him for a deadly length of time.
Finally, in Section XX , he is at the limit of his journey: In Hamburg he goes in to visit his mother. She, equally, is in control of her responsibilities:. A solemn promise of the greatest secrecy must be made in Old Testament fashion, in which he places his hand under the thigh of the Goddess she blushes slightly — having been drinking rum!