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Uncertainty in Multiclass Classification

Dr. Rishabh Pathak
1. What is Uncertainty in Classification? Uncertainty refers to the model’s confidence or doubt in its predictions. Quantifying uncertainty is important to understand how reliable each prediction is. In multiclass classification , uncertainty estimates provide probabilities over multiple classes, reflecting how sure the model is about each possible class. 2. Methods to Estimate Uncertainty in Multiclass Classification Most multiclass classifiers provide methods such as: predict_proba: Returns a probability distribution across all classes. decision_function: Returns scores or margins for each class (sometimes called raw or uncalibrated confidence scores). The probability distribution from predict_proba captures the uncertainty by assigning a probability to each class. 3. Shape and Interpretation of predict_proba in Multiclass Output shape: (n_samples, n_classes) Each row corresponds to the probabilities of ...
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Increasing the Cortical Thickness Increases the Gyral Wavelength

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Dr. Rishabh Pathak

Increasing the cortical thickness has been shown to influence the gyral wavelength during brain development. Here is an explanation of how changes in cortical thickness can impact the gyral wavelength:


1.     Physics-Based Models: Physics-based models predict that the gyral wavelength, which refers to the distance between adjacent gyri on the brain's surface, increases with increasing cortical thickness. These models take into account the mechanical properties of the cortical tissue and how variations in thickness can affect the folding patterns observed in the cerebral cortex.


2.     Radial Organization: The cortical thickness is largely determined by the radial organization of the cortical plate during early stages of development. As the cortex expands and thickens due to differential growth processes, the spacing between gyri is influenced by the overall thickness of the cortical tissue. Changes in cortical thickness can modulate the surface morphogenesis of the brain, leading to alterations in the gyral wavelength.


3.     Surface Morphology: Studies have shown that decreasing the cortical thickness can result in an increased number of folds and a decrease in the gyral wavelength. Conversely, increasing the cortical thickness leads to changes in the folding patterns, affecting the complexity of the brain's surface. These variations in cortical thickness and folding dynamics contribute to the overall structural organization of the cerebral cortex.


4.     Geological Analogies: The concept of cortical folding and its relationship to cortical thickness draws parallels to geological folding processes. Just as geological structures exhibit folding patterns based on the thickness and composition of rock layers, the brain's folding patterns are influenced by the mechanical interactions within the cortical tissue. Understanding how changes in cortical thickness impact the gyral wavelength provides insights into the mechanisms underlying brain morphogenesis.


5.     Developmental Implications: The relationship between cortical thickness and gyral wavelength has implications for brain development and function. Variations in cortical thickness can affect the surface area of the cortex, neuronal connectivity, and the distribution of functional areas across the brain. By studying how changes in cortical thickness influence the folding patterns of the cerebral cortex, researchers can gain a better understanding of the structural adaptations that occur during neurodevelopment.


In conclusion, increasing the cortical thickness is associated with an increase in the gyral wavelength, reflecting the intricate relationship between cortical morphology and brain development. By exploring the effects of cortical thickness on folding patterns, researchers can uncover the underlying mechanisms that shape the convoluted structure of the human brain and its functional implications.

 

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