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

The Viscoelastic response of the tendons

Image
Dr. Rishabh Pathak

The viscoelastic response of tendons refers to their unique mechanical behavior characterized by a combination of viscous (time-dependent deformation) and elastic (time-independent deformation) properties. Tendons exhibit viscoelasticity due to the presence of collagen fibers and proteoglycans in their extracellular matrix, which contribute to their mechanical properties. Here is an explanation of the viscoelastic response of tendons:

Viscoelastic Response of Tendons:

1.    Elastic Behavior:

o    Elasticity:

§  Tendons exhibit elastic behavior, meaning they can deform under load and return to their original shape when the load is removed.

§  The elastic properties of tendons allow them to store and release energy during muscle contractions, contributing to the efficiency of movement.

2.    Viscous Behavior:

o    Viscosity:

§  Tendons also display viscous behavior, where deformation is time-dependent and involves energy dissipation.

§  The viscous component of tendon behavior is related to the flow of fluid within the tendon structure and the sliding of collagen fibers.

3.    Creep and Stress Relaxation:

o    Creep:

§  When a constant load is applied to a tendon over time, it gradually elongates due to creep, a viscoelastic phenomenon.

§  Creep behavior in tendons is influenced by factors such as collagen fiber orientation and the composition of the extracellular matrix.

o    Stress Relaxation:

§  Stress relaxation refers to the decrease in stress within a tendon when held at a constant length over time.

§  Tendons exhibit stress relaxation as the collagen fibers reorganize and adjust their alignment in response to sustained loading.

4.    Rate Dependency:

o    Strain Rate:

§  The mechanical properties of tendons can vary depending on the rate at which they are loaded.

§  Tendons may exhibit different stiffness and damping characteristics at different loading rates, reflecting their viscoelastic nature.

5.    Hysteresis:

o    Energy Dissipation:

§  Tendons exhibit hysteresis, where the energy input during loading is not fully recovered during unloading.

§  The hysteresis loop represents the energy dissipated as heat within the tendon structure due to viscous damping.

6.    Adaptation to Loading:

o    Mechanical Loading:

§  Tendons can adapt their viscoelastic properties in response to mechanical loading, such as exercise or training.

§  Regular loading can lead to changes in tendon stiffness, strength, and viscoelastic behavior to better withstand mechanical stresses.

Understanding the viscoelastic response of tendons is essential for biomechanical analyses, injury prevention strategies, and rehabilitation protocols. The complex interplay between the elastic and viscous components of tendon behavior influences their ability to transmit forces, absorb shock, and support joint movement effectively.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

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 of Electrode Artifacts

Dr. Rishabh Pathak
Electrode artifacts in EEG recordings can present with distinct features that differentiate them from genuine brain activity.  1.      Types of Electrode Artifacts : o Variety : Electrode artifacts encompass several types, including electrode pop, electrode contact, electrode/lead movement, perspiration artifacts, salt bridge artifacts, and movement artifacts. o Characteristics : Each type of electrode artifact exhibits specific waveform patterns and spatial distributions that aid in their identification and differentiation from true EEG signals. 2.    Electrode Pop : o Description : Electrode pop artifacts are characterized by paroxysmal, sharply contoured transients that interrupt the background EEG activity. o Localization : These artifacts typically involve only one electrode and lack a field indicating a gradual decrease in potential amplitude across the scalp. o Waveform : Electrode pop waveforms have a rapid rise and a slower fall compared to in...
Post a Comment
Read more

Elements Selection Techniques

Dr. Rishabh Pathak
Element selection techniques play a crucial role in determining how individual elements or units are chosen from the population to form a sample. Here are some common element selection techniques used in sampling: 1.     Unrestricted Sampling : §   In unrestricted sampling, each element in the population has an equal chance of being selected for the sample. This approach is commonly used in simple random sampling, where every element is selected independently of other elements. 2.     Restricted Sampling : §   Restricted sampling involves imposing certain restrictions or conditions on the selection of sample elements. This can include stratification, clustering, or other criteria that guide the selection process. Restricted sampling techniques include: §   Stratified Sampling: The population is divided into homogeneous subgroups (strata), and samples are selected from each stratum to ensure representation of different characteristics. § ...
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

Beta Activity compared to Muscles Artifacts

Dr. Rishabh Pathak
Beta activity in EEG recordings can sometimes be confused with muscle artifacts due to their overlapping frequency components. Frequency Components : o   Muscle artifacts often have frequency components of 25 Hz and greater, which can overlap with the frequency range of beta activity. o   Beta activity in EEG recordings typically falls within the beta frequency range of 13-30 Hz, with variations based on specific brain states and cognitive processes. 2.      Waveform Characteristics : o   Electromyographic (EMG) artifacts, which represent muscle activity, have distinct waveform characteristics that can help differentiate them from beta activity. o   EMG artifacts may exhibit a sharper contour with less rhythmicity, especially when the high-frequency filter is set at 70 Hz or higher, compared to the smoother contour and rhythmicity of beta activity. 3.      High-Frequency Filter Settings : o   Adjusting the high-frequency f...
Post a Comment
Read more