Skip to main content

Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
Post a Comment

Basal Ganglia (BG)

Image
Dr. Rishabh Pathak

The Basal Ganglia (BG) is a group of interconnected subcortical nuclei in the brain that play a crucial role in motor control, cognition, emotion, and behavior modulation. Here is a detailed explanation of the Basal Ganglia:


1.   Anatomy: The Basal Ganglia is a complex network of nuclei located deep within the brain, including structures such as the striatum (comprising the caudate nucleus and putamen), globus pallidus (external and internal segments), subthalamic nucleus, and substantia nigra (pars compacta and pars reticulata). These nuclei are interconnected with the cerebral cortex, thalamus, and brainstem regions, forming circuits that regulate motor and non-motor functions.

2.     Function:

o  Motor Control: The Basal Ganglia are involved in the planning, initiation, execution, and modulation of voluntary movements. They contribute to motor coordination, movement scaling, action selection, and the suppression of unwanted movements. Dysfunction in the Basal Ganglia can lead to movement disorders such as Parkinson's disease, Huntington's disease, and dystonia.

o   Cognition: Beyond motor functions, the Basal Ganglia also play a role in cognitive processes such as decision-making, reward processing, learning, and memory. They are implicated in action selection, habit formation, and the integration of motor and cognitive functions.

o  Emotion and Behavior: The Basal Ganglia influence emotional responses, motivation, and social behavior. They are involved in regulating mood, reward-seeking behavior, impulsivity, and the processing of emotional stimuli. Dysfunction in the Basal Ganglia circuits can contribute to psychiatric disorders like depression, addiction, and obsessive-compulsive disorder.

3. Neurotransmitters: The Basal Ganglia circuits primarily utilize the neurotransmitters dopamine, gamma-aminobutyric acid (GABA), and glutamate to transmit signals between different nuclei. Dopaminergic projections from the substantia nigra and ventral tegmental area play a critical role in modulating Basal Ganglia function and are particularly affected in Parkinson's disease and other movement disorders.


4.    Pathophysiology:

o   Parkinson's Disease: Degeneration of dopaminergic neurons in the substantia nigra leads to dopamine deficiency in the Basal Ganglia, resulting in motor symptoms like tremors, rigidity, bradykinesia, and postural instability. Treatment strategies for Parkinson's disease often involve dopaminergic medications, deep brain stimulation, and physical therapy.

o    Huntington's Disease: In Huntington's disease, a genetic disorder, degeneration of the striatum and other Basal Ganglia nuclei leads to involuntary movements, cognitive decline, and psychiatric symptoms. The disease is characterized by chorea, dystonia, and progressive neurodegeneration.

5.  Clinical Implications: Understanding the role of the Basal Ganglia in motor control, cognition, and emotion is essential for diagnosing and treating neurological and psychiatric disorders. Imaging techniques, electrophysiological studies, and computational models are used to investigate Basal Ganglia function and dysfunction in health and disease.

In summary, the Basal Ganglia is a complex brain structure involved in a wide range of functions, including motor control, cognition, emotion, and behavior modulation. Dysregulation of Basal Ganglia circuits can lead to movement disorders, cognitive impairments, and psychiatric symptoms, highlighting the importance of studying these nuclei in both health and disease.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Ocular Artifacts

Dr. Rishabh Pathak
Ocular artifacts in EEG recordings are commonly caused by movements of the eyes, such as blinking, eye flutter, and eye movements associated with eye opening and closure. These artifacts can mimic epileptiform discharges and other EEG patterns, making them important to recognize and differentiate.  Nature of Ocular Artifacts : o    Ocular artifacts are primarily due to the movement of the electrical dipoles created by the eyes, particularly during activities like eye opening, closure, and directed gaze. o    The movement of these dipoles generates changing electrical fields that appear as EEG activity, with characteristics such as slow waves and spikes. o    Ocular artifacts are typically limited to the frontal region and do not extend into the central region of the brain. 2.      Differentiation from Epileptiform Discharges : o   Ocular artifacts can sometimes appear as bifrontal spike and slow wave complexes, resembling inter...
Post a Comment
Read more

Unrestricted Sampling

Dr. Rishabh Pathak
Unrestricted sampling, also known as simple random sampling, is a fundamental sampling technique where each element in the population has an equal and independent chance of being selected for the sample. In unrestricted sampling: 1.     Equal Probability of Selection : §   In simple random sampling, every element in the population has an equal probability of being chosen for the sample. This ensures that each unit is selected independently of other units, without any bias towards specific elements. 2.     Random Selection : §   The selection of sample elements is done randomly, without any systematic pattern or predetermined order. This randomness is essential to ensure that the sample is representative of the population and to minimize selection bias. 3.     Independence of Selection : §   Each selection is made independently of previous selections, meaning that the inclusion or exclusion of one element does not influence the ...
Post a Comment
Read more

Amphiarthrodial or Cartilaginous Joints

Dr. Rishabh Pathak
Amphiarthrodial joints, also known as cartilaginous joints, are joints where the adjacent bones are connected by cartilage. These joints allow for limited movement and provide both stability and flexibility to the skeletal system. Here is an overview of amphiarthrodial or cartilaginous joints: Amphiarthrodial or Cartilaginous Joints: 1.     Structure : o     Cartilage : §   Amphiarthrodial joints are characterized by the presence of cartilage between the articulating surfaces of the bones. §   The cartilage can be hyaline cartilage or fibrocartilage, depending on the specific joint and its function. o     Lack of Joint Cavity : §   Similar to fibrous joints, cartilaginous joints do not have a synovial cavity, and the bones are held together by the cartilaginous tissue. 2.     Types : o     Synchondroses : §   Synchondroses are cartilaginous joints where the connecting material is hyaline carti...
Post a Comment
Read more

Cell Maturation (Dendrite and Axon Growth)

Dr. Rishabh Pathak
Cell maturation, encompassing dendrite and axon growth, is a crucial stage of brain development where neurons undergo structural changes to establish connections and form functional neural circuits. Here is an overview of cell maturation in the context of dendrite and axon growth: 1.      Dendrite Growth : o     Definition : Dendrites are branched extensions of a neuron that receive signals from other neurons and transmit these signals to the cell body. o     Dendritic Arborization : During maturation, neurons extend and elaborate their dendritic arbors, increasing the surface area available for synaptic connections. o     Synaptic Integration : Dendritic growth is essential for forming synapses with other neurons, allowing for the integration of incoming signals and information processing. o     Activity-Dependent Plasticity : Dendritic growth can be influenced by neural activity and sensory experiences, sh...
Post a Comment
Read more

Distinguishing Features Ictal Epileptiform Patterns

Dr. Rishabh Pathak
The distinguishing features of ictal epileptiform patterns are critical for differentiating them from other EEG activities and for accurate seizure diagnosis. Here are the key distinguishing features outlined in the document: 1.      Stereotyped Nature : Ictal patterns are often stereotyped across seizures for the individual patient. This means that the same pattern tends to recur in different seizures, which aids in identification. 2.    Evolution of Activity : A hallmark of ictal patterns is their evolution, which can manifest as changes in frequency, amplitude, distribution, and waveform. This evolution is a key feature that helps differentiate ictal patterns from other types of EEG activity, such as normal rhythms or artifacts. 3.   Behavioral Changes : Ictal patterns are typically associated with stereotyped behavioral changes. While some seizures may not exhibit obvious movements, the presence of behavioral changes is a significant indicator of s...
Post a Comment
Read more