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In the prevailing model, Lgr5+ cells are the only intestinal stem cells (ISCs) that sustain homeostatic epithelial regeneration by upward migration of progeny through elusive upper crypt transit-amplifying (TA) intermediates. Here, we identify a proliferative upper crypt population marked by Fgfbp1, in the location of putative TA cells, that is transcriptionally distinct from Lgr5+ cells. Using a kinetic reporter for time-resolved fate mapping and Fgfbp1-CreERT2 lineage tracing, we establish that Fgfbp1+ cells are multi-potent and give rise to Lgr5+ cells, consistent with their ISC function. Fgfbp1+ cells also sustain epithelial regeneration following Lgr5+ cell depletion. We demonstrate that FGFBP1, produced by the upper crypt cells, is an essential factor for crypt proliferation and epithelial homeostasis. Our findings support a model in which tissue regeneration originates from upper crypt Fgfbp1+ cells that generate progeny propagating bi-directionally along the crypt-villus axis and serve as a source of Lgr5+ cells in the crypt base.
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Mucosa Intestinal , Receptores Acoplados a Proteínas G , Receptores Acoplados a Proteínas G/metabolismo , Animales , Ratones , Mucosa Intestinal/metabolismo , Mucosa Intestinal/citología , Células Madre/metabolismo , Células Madre/citología , Linaje de la Célula , Regeneración , Proliferación Celular , Células Epiteliales/metabolismo , Células Epiteliales/citología , Ratones Endogámicos C57BL , HomeostasisRESUMEN
Elucidating the cellular organization of the cerebral cortex is critical for understanding brain structure and function. Using large-scale single-nucleus RNA sequencing and spatial transcriptomic analysis of 143 macaque cortical regions, we obtained a comprehensive atlas of 264 transcriptome-defined cortical cell types and mapped their spatial distribution across the entire cortex. We characterized the cortical layer and region preferences of glutamatergic, GABAergic, and non-neuronal cell types, as well as regional differences in cell-type composition and neighborhood complexity. Notably, we discovered a relationship between the regional distribution of various cell types and the region's hierarchical level in the visual and somatosensory systems. Cross-species comparison of transcriptomic data from human, macaque, and mouse cortices further revealed primate-specific cell types that are enriched in layer 4, with their marker genes expressed in a region-dependent manner. Our data provide a cellular and molecular basis for understanding the evolution, development, aging, and pathogenesis of the primate brain.
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Corteza Cerebral , Macaca , Análisis de la Célula Individual , Transcriptoma , Animales , Humanos , Ratones , Corteza Cerebral/citología , Corteza Cerebral/metabolismo , Macaca/metabolismo , Transcriptoma/genéticaRESUMEN
Downward social mobility is a well-known mental risk factor for depression, but its neural mechanism remains elusive. Here, by forcing mice to lose against their subordinates in a non-violent social contest, we lower their social ranks stably and induce depressive-like behaviors. These rank-decline-associated depressive-like behaviors can be reversed by regaining social status. In vivo fiber photometry and single-unit electrophysiological recording show that forced loss, but not natural loss, generates negative reward prediction error (RPE). Through the lateral hypothalamus, the RPE strongly activates the brain's anti-reward center, the lateral habenula (LHb). LHb activation inhibits the medial prefrontal cortex (mPFC) that controls social competitiveness and reinforces retreats in contests. These results reveal the core neural mechanisms mutually promoting social status loss and depressive behaviors. The intertwined neuronal signaling controlling mPFC and LHb activities provides a mechanistic foundation for the crosstalk between social mobility and psychological disorder, unveiling a promising target for intervention.
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Habénula , Estatus Social , Ratones , Animales , Recompensa , Conducta Social , Habénula/fisiología , DepresiónRESUMEN
Harmonizing cell types across the single-cell community and assembling them into a common framework is central to building a standardized Human Cell Atlas. Here, we present CellHint, a predictive clustering tree-based tool to resolve cell-type differences in annotation resolution and technical biases across datasets. CellHint accurately quantifies cell-cell transcriptomic similarities and places cell types into a relationship graph that hierarchically defines shared and unique cell subtypes. Application to multiple immune datasets recapitulates expert-curated annotations. CellHint also reveals underexplored relationships between healthy and diseased lung cell states in eight diseases. Furthermore, we present a workflow for fast cross-dataset integration guided by harmonized cell types and cell hierarchy, which uncovers underappreciated cell types in adult human hippocampus. Finally, we apply CellHint to 12 tissues from 38 datasets, providing a deeply curated cross-tissue database with â¼3.7 million cells and various machine learning models for automatic cell annotation across human tissues.
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Perfilación de la Expresión Génica , Transcriptoma , Humanos , Bases de Datos Factuales , Análisis de la Célula IndividualRESUMEN
Radial cell columns are a hallmark feature of cortical architecture in many mammalian species. It has long been held, based on the lack of orientation columns, that such functional units are absent in rodent primary visual cortex (V1). These observations led to the view that rodent visual cortex has a fundamentally different network architecture than that of carnivores and primates. While columns may be lacking in rodent V1, we describe in this review that modular clusters of inputs to layer 1 and projection neurons in the layers below are prominent features of the mouse visual cortex. We propose that modules organize thalamocortical inputs, intracortical processing streams, and transthalamic communications that underlie distinct sensory and sensorimotor functions.
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Corteza Visual , Ratones , Animales , Retroalimentación , Corteza Visual/fisiología , Interneuronas , Sensación , Vías Visuales/fisiología , MamíferosRESUMEN
The neocortex is a complex neurobiological system with many interacting regions. How these regions work together to subserve flexible behavior and cognition has become increasingly amenable to rigorous research. Here, I review recent experimental and theoretical work on the modus operandi of a multiregional cortex. These studies revealed several general principles for the neocortical interareal connectivity, low-dimensional macroscopic gradients of biological properties across cortical areas, and a hierarchy of timescales for information processing. Theoretical work suggests testable predictions regarding differential excitation and inhibition along feedforward and feedback pathways in the cortical hierarchy. Furthermore, modeling of distributed working memory and simple decision-making has given rise to a novel mathematical concept, dubbed bifurcation in space, that potentially explains how different cortical areas, with a canonical circuit organization but gradients of biological heterogeneities, are able to subserve their respective (e.g., sensory coding versus executive control) functions in a modularly organized brain.
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Neocórtex , Cognición/fisiología , Función Ejecutiva , Memoria a Corto Plazo/fisiología , Neocórtex/fisiología , Red Nerviosa/fisiologíaRESUMEN
Networks involved in information processing often have their nodes arranged hierarchically, with the majority of connections occurring in adjacent levels. However, despite being an intuitively appealing concept, the hierarchical organization of large networks, such as those in the brain, is difficult to identify, especially in absence of additional information beyond that provided by the connectome. In this paper, we propose a framework to uncover the hierarchical structure of a given network, that identifies the nodes occupying each level as well as the sequential order of the levels. It involves optimizing a metric that we use to quantify the extent of hierarchy present in a network. Applying this measure to various brain networks, ranging from the nervous system of the nematode Caenorhabditis elegans to the human connectome, we unexpectedly find that they exhibit a common network architectural motif intertwining hierarchy and modularity. This suggests that brain networks may have evolved to simultaneously exploit the functional advantages of these two types of organizations, viz., relatively independent modules performing distributed processing in parallel and a hierarchical structure that allows sequential pooling of these multiple processing streams. An intriguing possibility is that this property we report may be common to information processing networks in general.
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Encéfalo , Caenorhabditis elegans , Conectoma , Red Nerviosa , Encéfalo/fisiología , Encéfalo/anatomía & histología , Animales , Conectoma/métodos , Humanos , Red Nerviosa/fisiología , Modelos NeurológicosRESUMEN
In acute immune responses to infection, memory T cells develop that can spawn recall responses. This process has not been observable directly in vivo. Here we highlight the utility of mathematical inference to derive quantitatively testable models of mammalian CD8+ T cell memory development from complex experimental data. Previous inference studies suggested that precursors of memory T cells arise early during the immune response. Recent work has both validated a crucial prediction of this T cell diversification model and refined the model. While multiple developmental routes to distinct memory subsets might exist, a branch point occurs early in proliferating T cell blasts, from which separate differentiation pathways emerge for slowly dividing precursors of re-expandable memory cells and rapidly dividing effectors.
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Linfocitos T CD8-positivos , Células T de Memoria , Humanos , Animales , Diferenciación Celular , Activación de Linfocitos , Memoria Inmunológica , Subgrupos de Linfocitos T , MamíferosRESUMEN
The neural circuit of the brain is organized as a hierarchy of functional units with wide-ranging connections that support information flow and functional connectivity. Studies using MRI indicate a moderate coupling between structural and functional connectivity at the system level. However, how do connections of different directions (feedforward and feedback) and regions with different excitatory and inhibitory (E/I) neurons shape the hemodynamic activity and functional connectivity over the hierarchy are unknown. Here, we used functional MRI to detect optogenetic-evoked and resting-state activities over a somatosensory pathway in the mouse brain in relation to axonal projection and E/I distribution. Using a highly sensitive ultrafast imaging, we identified extensive activation in regions up to the third order of axonal projections following optogenetic excitation of the ventral posteriomedial nucleus of the thalamus. The evoked response and functional connectivity correlated with feedforward projections more than feedback projections and weakened with the hierarchy. The hemodynamic response exhibited regional and hierarchical differences, with slower and more variable responses in high-order areas and bipolar response predominantly in the contralateral cortex. Electrophysiological recordings suggest that these reflect differences in neural activity rather than neurovascular coupling. Importantly, the positive and negative parts of the hemodynamic response correlated with E/I neuronal densities, respectively. Furthermore, resting-state functional connectivity was more associated with E/I distribution, whereas stimulus-evoked effective connectivity followed structural wiring. These findings indicate that the structure-function relationship is projection-, cell-type- and hierarchy-dependent. Hemodynamic transients could reflect E/I activity and the increased complexity of hierarchical processing.
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Conectoma , Acoplamiento Neurovascular , Ratones , Animales , Encéfalo/fisiología , Mapeo Encefálico/métodos , Hemodinámica , Acoplamiento Neurovascular/fisiología , Imagen por Resonancia Magnética , Vías Nerviosas/fisiología , Red Nerviosa/fisiología , Conectoma/métodosRESUMEN
Scientists have long conjectured that the neocortex learns patterns in sensory data to generate top-down predictions of upcoming stimuli. In line with this conjecture, different responses to pattern-matching vs pattern-violating visual stimuli have been observed in both spiking and somatic calcium imaging data. However, it remains unknown whether these pattern-violation signals are different between the distal apical dendrites, which are heavily targeted by top-down signals, and the somata, where bottom-up information is primarily integrated. Furthermore, it is unknown how responses to pattern-violating stimuli evolve over time as an animal gains more experience with them. Here, we address these unanswered questions by analyzing responses of individual somata and dendritic branches of layer 2/3 and layer 5 pyramidal neurons tracked over multiple days in primary visual cortex of awake, behaving female and male mice. We use sequences of Gabor patches with patterns in their orientations to create pattern-matching and pattern-violating stimuli, and two-photon calcium imaging to record neuronal responses. Many neurons in both layers show large differences between their responses to pattern-matching and pattern-violating stimuli. Interestingly, these responses evolve in opposite directions in the somata and distal apical dendrites, with somata becoming less sensitive to pattern-violating stimuli and distal apical dendrites more sensitive. These differences between the somata and distal apical dendrites may be important for hierarchical computation of sensory predictions and learning, since these two compartments tend to receive bottom-up and top-down information, respectively.
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Calcio , Neocórtex , Masculino , Femenino , Ratones , Animales , Calcio/fisiología , Neuronas/fisiología , Dendritas/fisiología , Células Piramidales/fisiología , Neocórtex/fisiologíaRESUMEN
Plants and ecosystems worldwide are exposed to a wide range of chemical, physical, and biological factors of global change, many of which act concurrently. As bringing order to the array of factors is required in order to generate an enhanced understanding of simultaneous impacts, classification schemes have been developed. One such classification scheme is dedicated to capturing the different targets of global change factors along the ecological hierarchy. We build on this pioneering work, and refine the conceptual framework in several ways, focusing on plants and terrestrial systems: (i) we more strictly define the target level of the hierarchy, such that every factor typically has just one target level, and not many; (ii) we include effects above the level of the community, that is, there are effects also at the ecosystem scale that cannot be reduced to any level below this; (iii) we introduce the level of the landscape to capture certain land use change effects while abandoning the level below the individual. We discuss how effects can propagate along the levels of the ecological hierarchy, upwards and downwards, presenting opportunities for explaining non-additivity of effects of multiple factors. We hope that this updated conceptual framework will help inform the next generation of plant-focused global change experiments, specifically aimed at non-additivity of effects at the confluence of many factors.
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EcosistemaRESUMEN
Traditional general circulation models, or GCMs-that is, three-dimensional dynamical models with unresolved terms represented in equations with tunable parameters-have been a mainstay of climate research for several decades, and some of the pioneering studies have recently been recognized by a Nobel prize in Physics. Yet, there is considerable debate around their continuing role in the future. Frequently mentioned as limitations of GCMs are the structural error and uncertainty across models with different representations of unresolved scales and the fact that the models are tuned to reproduce certain aspects of the observed Earth. We consider these shortcomings in the context of a future generation of models that may address these issues through substantially higher resolution and detail, or through the use of machine learning techniques to match them better to observations, theory, and process models. It is our contention that calibration, far from being a weakness of models, is an essential element in the simulation of complex systems, and contributes to our understanding of their inner workings. Models can be calibrated to reveal both fine-scale detail and the global response to external perturbations. New methods enable us to articulate and improve the connections between the different levels of abstract representation of climate processes, and our understanding resides in an entire hierarchy of models where GCMs will continue to play a central role for the foreseeable future.
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Cambio Climático , Clima , Predicción , Simulación por Computador , FísicaRESUMEN
When listening to spoken narratives, we must integrate information over multiple, concurrent timescales, building up from words to sentences to paragraphs to a coherent narrative. Recent evidence suggests that the brain relies on a chain of hierarchically organized areas with increasing temporal receptive windows to process naturalistic narratives. We hypothesized that the structure of this cortical processing hierarchy should result in an observable sequence of response lags between networks comprising the hierarchy during narrative comprehension. This study uses functional MRI to estimate the response lags between functional networks during narrative comprehension. We use intersubject cross-correlation analysis to capture network connectivity driven by the shared stimulus. We found a fixed temporal sequence of response lags-on the scale of several seconds-starting in early auditory areas, followed by language areas, the attention network, and lastly the default mode network. This gradient is consistent across eight distinct stories but absent in data acquired during rest or using a scrambled story stimulus, supporting our hypothesis that narrative construction gives rise to internetwork lags. Finally, we build a simple computational model for the neural dynamics underlying the construction of nested narrative features. Our simulations illustrate how the gradual accumulation of information within the boundaries of nested linguistic events, accompanied by increased activity at each level of the processing hierarchy, can give rise to the observed lag gradient.
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Mapeo Encefálico , Percepción del Habla , Percepción del Habla/fisiología , Comprensión/fisiología , Encéfalo/diagnóstico por imagen , Encéfalo/fisiología , Imagen por Resonancia MagnéticaRESUMEN
How infants experience the world is fundamental to understanding their cognition and development. A key principle of adult experience is that, despite receiving continuous sensory input, we perceive this input as discrete events. Here we investigate such event segmentation in infants and how it differs from adults. Research on event cognition in infants often uses simplified tasks in which (adult) experimenters help solve the segmentation problem for infants by defining event boundaries or presenting discrete actions/vignettes. This presupposes which events are experienced by infants and leaves open questions about the principles governing infant segmentation. We take a different, data-driven approach by studying infant event segmentation of continuous input. We collected whole-brain functional MRI (fMRI) data from awake infants (and adults, for comparison) watching a cartoon and used a hidden Markov model to identify event states in the brain. We quantified the existence, timescale, and organization of multiple-event representations across brain regions. The adult brain exhibited a known hierarchical gradient of event timescales, from shorter events in early visual regions to longer events in later visual and associative regions. In contrast, the infant brain represented only longer events, even in early visual regions, with no timescale hierarchy. The boundaries defining these infant events only partially overlapped with boundaries defined from adult brain activity and behavioral judgments. These findings suggest that events are organized differently in infants, with longer timescales and more stable neural patterns, even in sensory regions. This may indicate greater temporal integration and reduced temporal precision during dynamic, naturalistic perception.
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Encéfalo , Imagen por Resonancia Magnética , Adulto , Encéfalo/diagnóstico por imagen , Cognición , Humanos , LactanteRESUMEN
With teams growing in all areas of scientific and scholarly research, we explore the relationship between team structure and the character of knowledge they produce. Drawing on 89,575 self-reports of team member research activity underlying scientific publications, we show how individual activities cohere into broad roles of 1) leadership through the direction and presentation of research and 2) support through data collection, analysis, and discussion. The hidden hierarchy of a scientific team is characterized by its lead (or L) ratio of members playing leadership roles to total team size. The L ratio is validated through correlation with imputed contributions to the specific paper and to science as a whole, which we use to effectively extrapolate the L ratio for 16,397,750 papers where roles are not explicit. We find that, relative to flat, egalitarian teams, tall, hierarchical teams produce less novelty and more often develop existing ideas, increase productivity for those on top and decrease it for those beneath, and increase short-term citations but decrease long-term influence. These effects hold within person-the same person on the same-sized team produces science much more likely to disruptively innovate if they work on a flat, high-L-ratio team. These results suggest the critical role flat teams play for sustainable scientific advance and the training and advancement of scientists.
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Creatividad , Procesos de Grupo , Liderazgo , Ciencia , Humanos , Ciencia/tendenciasRESUMEN
Do sensory cortices process more than one sensory modality? To answer these questions, scientists have generated a wide variety of studies at distinct space-time scales in different animal models, and often shown contradictory conclusions. Some conclude that this process occurs in early sensory cortices, but others that this occurs in areas central to sensory cortices. Here, we sought to determine whether sensory neurons process and encode physical stimulus properties of different modalities (tactile and acoustic). For this, we designed a bimodal detection task where the senses of touch and hearing compete from trial to trial. Two Rhesus monkeys performed this novel task, while neural activity was recorded in areas 3b and 1 of the primary somatosensory cortex (S1). We analyzed neurons' coding properties and variability, organizing them by their receptive field's position relative to the stimulation zone. Our results indicate that neurons of areas 3b and 1 are unimodal, encoding only the tactile modality in both the firing rate and variability. Moreover, we found that neurons in area 3b carried more information about the periodic stimulus structure than those in area 1, possessed lower response and coding latencies, and had a lower intrinsic time scale. In sum, these differences reveal a hidden processing-based hierarchy. Finally, using a powerful nonlinear dimensionality reduction algorithm, we show that the activity from areas 3b and 1 can be separated, establishing a clear division in the functionality of these two subareas of S1.
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Corteza Somatosensorial , Percepción del Tacto , Animales , Corteza Somatosensorial/fisiología , Percepción del Tacto/fisiología , Tacto , Lóbulo Parietal , Células Receptoras SensorialesRESUMEN
Deep learning (DL) has had unprecedented success and is now entering scientific computing with full force. However, current DL methods typically suffer from instability, even when universal approximation properties guarantee the existence of stable neural networks (NNs). We address this paradox by demonstrating basic well-conditioned problems in scientific computing where one can prove the existence of NNs with great approximation qualities; however, there does not exist any algorithm, even randomized, that can train (or compute) such a NN. For any positive integers K>2 and L, there are cases where simultaneously 1) no randomized training algorithm can compute a NN correct to K digits with probability greater than 1/2; 2) there exists a deterministic training algorithm that computes a NN with K 1 correct digits, but any such (even randomized) algorithm needs arbitrarily many training data; and 3) there exists a deterministic training algorithm that computes a NN with K 2 correct digits using no more than L training samples. These results imply a classification theory describing conditions under which (stable) NNs with a given accuracy can be computed by an algorithm. We begin this theory by establishing sufficient conditions for the existence of algorithms that compute stable NNs in inverse problems. We introduce fast iterative restarted networks (FIRENETs), which we both prove and numerically verify are stable. Moreover, we prove that only O(|logâ(ϵ)|) layers are needed for an ϵ-accurate solution to the inverse problem.
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Inteligencia Artificial , Aprendizaje Profundo , Algoritmos , Redes Neurales de la ComputaciónRESUMEN
A cardinal feature of the neocortex is the progressive increase of the spatial receptive fields along the cortical hierarchy. Recently, theoretical and experimental findings have shown that the temporal response windows also gradually enlarge, so that early sensory neural circuits operate on short timescales whereas higher-association areas are capable of integrating information over a long period of time. While an increased receptive field is accounted for by spatial summation of inputs from neurons in an upstream area, the emergence of timescale hierarchy cannot be readily explained, especially given the dense interareal cortical connectivity known in the modern connectome. To uncover the required neurobiological properties, we carried out a rigorous analysis of an anatomically based large-scale cortex model of macaque monkeys. Using a perturbation method, we show that the segregation of disparate timescales is defined in terms of the localization of eigenvectors of the connectivity matrix, which depends on three circuit properties: 1) a macroscopic gradient of synaptic excitation, 2) distinct electrophysiological properties between excitatory and inhibitory neuronal populations, and 3) a detailed balance between long-range excitatory inputs and local inhibitory inputs for each area-to-area pathway. Our work thus provides a quantitative understanding of the mechanism underlying the emergence of timescale hierarchy in large-scale primate cortical networks.
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Conectoma , Modelos Neurológicos , Neocórtex/fisiología , Red Nerviosa/fisiología , Animales , MacacaRESUMEN
Humans constantly receive massive amounts of information, both perceived from the external environment and imagined from the internal world. To function properly, the brain needs to correctly identify the origin of information being processed. Recent work has suggested common neural substrates for perception and imagery. However, it has remained unclear how the brain differentiates between external and internal experiences with shared neural codes. Here we tested this question in human participants (male and female) by systematically investigating the neural processes underlying the generation and maintenance of visual information from voluntary imagery, veridical perception, and illusion. The inclusion of illusion allowed us to differentiate between objective and subjective internality: while illusion has an objectively internal origin and can be viewed as involuntary imagery, it is also subjectively perceived as having an external origin like perception. Combining fMRI, eye-tracking, multivariate decoding, and encoding approaches, we observed superior orientation representations in parietal cortex during imagery compared with perception, and conversely in early visual cortex. This imagery dominance gradually developed along a posterior-to-anterior cortical hierarchy from early visual to parietal cortex, emerged in the early epoch of imagery and sustained into the delay epoch, and persisted across varied imagined contents. Moreover, representational strength of illusion was more comparable to imagery in early visual cortex, but more comparable to perception in parietal cortex, suggesting content-specific representations in parietal cortex differentiate between subjectively internal and external experiences, as opposed to early visual cortex. These findings together support a domain-general engagement of parietal cortex in internally generated experience.SIGNIFICANCE STATEMENT How does the brain differentiate between imagined and perceived experiences? Combining fMRI, eye-tracking, multivariate decoding, and encoding approaches, the current study revealed enhanced stimulus-specific representations in visual imagery originating from parietal cortex, supporting the subjective experience of imagery. This neural principle was further validated by evidence from visual illusion, wherein illusion resembled perception and imagery at different levels of cortical hierarchy. Our findings provide direct evidence for the critical role of parietal cortex as a domain-general region for content-specific imagery, and offer new insights into the neural mechanisms underlying the differentiation between subjectively internal and external experiences.
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Ilusiones , Percepción Visual , Humanos , Masculino , Femenino , Imaginación , Lóbulo Parietal , Encéfalo , Mapeo Encefálico , Imagen por Resonancia MagnéticaRESUMEN
BACKGROUND: Clustering is a fundamental problem in statistics and has broad applications in various areas. Traditional clustering methods treat features equally and ignore the potential structure brought by the characteristic difference of features. Especially in cancer diagnosis and treatment, several types of biological features are collected and analyzed together. Treating these features equally fails to identify the heterogeneity of both data structure and cancer itself, which leads to incompleteness and inefficacy of current anti-cancer therapies. OBJECTIVES: In this paper, we propose a clustering framework based on hierarchical heterogeneous data with prior pairwise relationships. The proposed clustering method fully characterizes the difference of features and identifies potential hierarchical structure by rough and refined clusters. RESULTS: The refined clustering further divides the clusters obtained by the rough clustering into different subtypes. Thus it provides a deeper insight of cancer that can not be detected by existing clustering methods. The proposed method is also flexible with prior information, additional pairwise relationships of samples can be incorporated to help to improve clustering performance. Finally, well-grounded statistical consistency properties of our proposed method are rigorously established, including the accurate estimation of parameters and determination of clustering structures. CONCLUSIONS: Our proposed method achieves better clustering performance than other methods in simulation studies, and the clustering accuracy increases with prior information incorporated. Meaningful biological findings are obtained in the analysis of lung adenocarcinoma with clinical imaging data and omics data, showing that hierarchical structure produced by rough and refined clustering is necessary and reasonable.