Skip to main content

Unveiling Hidden Neural Codes: SIMPL – A Scalable and Fast Approach for Optimizing Latent Variables and Tuning Curves in Neural Population Data

Dr. Rishabh Pathak
This research paper presents SIMPL (Scalable Iterative Maximization of Population-coded Latents), a novel, computationally efficient algorithm designed to refine the estimation of latent variables and tuning curves from neural population activity. Latent variables in neural data represent essential low-dimensional quantities encoding behavioral or cognitive states, which neuroscientists seek to identify to understand brain computations better. Background and Motivation Traditional approaches commonly assume the observed behavioral variable as the latent neural code. However, this assumption can lead to inaccuracies because neural activity sometimes encodes internal cognitive states differing subtly from observable behavior (e.g., anticipation, mental simulation). Existing latent variable models face challenges such as high computational cost, poor scalability to large datasets, limited expressiveness of tuning models, or difficulties interpreting complex neural network-based functio...
Post a Comment

Sensitive of surface morphology with respect to Stiffness Ratio

Image
Dr. Rishabh Pathak

The sensitivity of surface morphology with respect to the stiffness ratio between the cortex and subcortex is a crucial factor in understanding the mechanisms of cortical folding and brain development. Here are some key points regarding the sensitivity of surface morphology to the stiffness ratio:


1.  Influence on Folding Patterns: The stiffness ratio between the cortex and subcortex plays a significant role in shaping the folding patterns of the cerebral cortex. Variations in the stiffness ratio can lead to changes in the depth, frequency, and complexity of cortical folds, impacting the overall surface morphology of the brain.


2.  Stress Distribution: Differences in stiffness between the cortex and subcortex affect the distribution of mechanical stresses within the brain tissue. A mismatch in stiffness can result in uneven stress distribution, leading to alterations in cortical folding patterns and surface morphology.


3.     Surface Deformations: Changes in the stiffness ratio can influence the extent of surface deformations and the formation of cortical folds. A higher stiffness ratio may promote smoother brain surfaces with shallower folds, while a lower stiffness ratio can lead to more pronounced folding patterns.


4.     Mechanical Stability: The stiffness ratio contributes to the mechanical stability of the brain tissue and its ability to resist deformations. An optimal balance in stiffness between the cortex and subcortex is essential for maintaining structural integrity and preventing excessive folding or stretching of the cortical surface.


5.     Computational Modeling: Computational models can simulate the sensitivity of surface morphology to variations in the stiffness ratio by adjusting this parameter and observing the resulting changes in cortical folding patterns. These models provide insights into how the stiffness ratio influences the mechanical behavior and morphological features of the brain.


6.     Clinical Relevance: Abnormalities in the stiffness ratio between cortical layers have been associated with neurodevelopmental disorders and brain pathologies. Understanding the impact of the stiffness ratio on surface morphology can provide valuable insights into the underlying mechanisms of these conditions.


7. Biomechanical Interactions: The stiffness ratio is part of the complex biomechanical interactions that govern cortical folding and brain development. It interacts with other factors such as cortical thickness, growth rates, and genetic influences to shape the structural and functional properties of the cerebral cortex.


By investigating the sensitivity of surface morphology to the stiffness ratio, researchers can gain a deeper understanding of the mechanical principles underlying cortical folding and brain morphogenesis. This knowledge is essential for elucidating the intricate processes that govern brain development and for exploring the implications of mechanical factors in neurodevelopmental disorders and brain health.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Relation of Model Complexity to Dataset Size

Dr. Rishabh Pathak
Core Concept The relationship between model complexity and dataset size is fundamental in supervised learning, affecting how well a model can learn and generalize. Model complexity refers to the capacity or flexibility of the model to fit a wide variety of functions. Dataset size refers to the number and diversity of training samples available for learning. Key Points 1. Larger Datasets Allow for More Complex Models When your dataset contains more varied data points , you can afford to use more complex models without overfitting. More data points mean more information and variety, enabling the model to learn detailed patterns without fitting noise. Quote from the book: "Relation of Model Complexity to Dataset Size. It’s important to note that model complexity is intimately tied to the variation of inputs contained in your training dataset: the larger variety of data points your dataset contains, the more complex a model you can use without overfitting....
Post a Comment
Read more

Linear Models

Dr. Rishabh Pathak
1. What are Linear Models? Linear models are a class of models that make predictions using a linear function of the input features. The prediction is computed as a weighted sum of the input features plus a bias term. They have been extensively studied over more than a century and remain widely used due to their simplicity, interpretability, and effectiveness in many scenarios. 2. Mathematical Formulation For regression , the general form of a linear model's prediction is: y^ ​ = w0 ​ x0 ​ + w1 ​ x1 ​ + … + wp ​ xp ​ + b where; y^ ​ is the predicted output, xi ​ is the i-th input feature, wi ​ is the learned weight coefficient for feature xi ​ , b is the intercept (bias term), p is the number of features. In vector form: y^ ​ = wTx + b where w = ( w0 ​ , w1 ​ , ... , wp ​ ) and x = ( x0 ​ , x1 ​ , ... , xp ​ ) . 3. Interpretation and Intuition The prediction is a linear combination of features — each feature contributes prop...
Post a Comment
Read more

Predicting Probabilities

Dr. Rishabh Pathak
1. What is Predicting Probabilities? The predict_proba method estimates the probability that a given input belongs to each class. It returns values in the range [0, 1] , representing the model's confidence as probabilities. The sum of predicted probabilities across all classes for a sample is always 1 (i.e., they form a valid probability distribution). 2. Output Shape of predict_proba For binary classification , the shape of the output is (n_samples, 2) : Column 0: Probability of the sample belonging to the negative class. Column 1: Probability of the sample belonging to the positive class. For multiclass classification , the shape is (n_samples, n_classes) , with each column corresponding to the probability of the sample belonging to that class. 3. Interpretation of predict_proba Output The probability reflects how confidently the model believes a data point belongs to each class. For example, in ...
Post a Comment
Read more

Uncertainty Estimates from Classifiers

Dr. Rishabh Pathak
1. Overview of Uncertainty Estimates Many classifiers do more than just output a predicted class label; they also provide a measure of confidence or uncertainty in their predictions. These uncertainty estimates help understand how sure the model is about its decision , which is crucial in real-world applications where different types of errors have different consequences (e.g., medical diagnosis). 2. Why Uncertainty Matters Predictions are often thresholded to produce class labels, but this process discards the underlying probability or decision value. Knowing how confident a classifier is can: Improve decision-making by allowing deferral in uncertain cases. Aid in calibrating models. Help in evaluating the risk associated with predictions. Example: In medical testing, a false negative (missing a disease) can be worse than a false positive (extra test). 3. Methods to Obtain Uncertainty from Classifiers 3.1 ...
Post a Comment
Read more

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 ...
Post a Comment
Read more