Skip to main content

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

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...

Cancellous Bone

Cancellous bone, also known as trabecular or spongy bone, is the other main type of bone tissue found in the human skeleton alongside cortical bone. Cancellous bone has a porous and lattice-like structure, providing flexibility, shock absorption, and a site for hematopoiesis (blood cell formation). Here are key features and characteristics of cancellous bone:

1.    Structure:

o    Trabeculae: Cancellous bone is composed of a network of thin, bony trabeculae that form an interconnected lattice structure.

o    Bone Marrow: The spaces between trabeculae contain red bone marrow, which is involved in the production of blood cells (hematopoiesis).

o    Less Compact: Cancellous bone is less dense and compact than cortical bone, with a higher surface area-to-volume ratio.

2.    Composition:

o    Trabecular Bone: The trabeculae are made up of lamellae, osteocytes, and canaliculi similar to cortical bone but with a more open and porous arrangement.

o    Collagen and Mineralization: Cancellous bone contains collagen fibers and mineral components like hydroxyapatite, providing a balance of strength and flexibility.

3.    Function:

o    Shock Absorption: The porous structure of cancellous bone allows it to absorb impact forces and distribute loads, reducing the risk of fractures.

o    Hematopoiesis: Red bone marrow within cancellous bone is a primary site for the production of red blood cells, white blood cells, and platelets.

o    Metabolic Activity: Cancellous bone is metabolically active and responds to mechanical stimuli, hormonal signals, and changes in bone density.

4.    Location:

o    Ends of Long Bones: Cancellous bone is typically found at the ends (epiphyses) of long bones, where it provides cushioning and support at joints.

o    Vertebrae and Pelvis: It also forms the internal structure of vertebrae, pelvis, and other flat bones, contributing to their strength and flexibility.

5.    Vascularization:

o    Cancellous bone has a higher vascular supply compared to cortical bone, with blood vessels penetrating the trabecular network to deliver nutrients and remove waste products.

o    The vascular network supports the metabolic needs of bone cells and facilitates the exchange of gases and nutrients.

6.    Mechanical Properties:

o    Cancellous bone is more flexible and compliant than cortical bone, making it well-suited for adapting to dynamic loads and maintaining bone health.

o    Its porous structure allows for rapid bone turnover, remodeling, and adaptation in response to mechanical stress and hormonal influences.

Understanding the unique characteristics and functions of cancellous bone is essential for comprehending the biomechanics of bone tissue, the role of bone marrow in hematopoiesis, and the structural adaptations of the skeleton to mechanical demands and metabolic requirements.

 

Comments

Popular posts from this blog

Cell Maturation (Dendrite and Axon Growth)

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...

Distinguishing Features of Electrode Artifacts

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...

Beta Activity compared to Muscles Artifacts

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...

Elements Selection Techniques

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. § ...

Translocation, Retention and Potential Neurological Lesion in The Brain and Following Nanoparticle Exposure

Translocation, retention, and potential neurological lesions in the brain following nanoparticle exposure are important considerations in nanotoxicology and neurotoxicology research. Here are some key points regarding the impact of nanoparticle exposure on the brain: 1.       Translocation to the Brain : o Nanoparticles can enter the brain through various routes, including systemic circulation, olfactory nerve pathways, and disrupted blood-brain barrier (BBB) integrity. o Factors such as nanoparticle size, surface properties, shape, and surface modifications influence their ability to cross biological barriers and reach the brain parenchyma. 2.      Retention in the Brain : o Once nanoparticles translocate to the brain, they may exhibit different retention times depending on their physicochemical properties and interactions with brain cells. o Nanoparticles can accumulate in specific brain regions, such as the olfactory bulb, hippocampus, and...