Suppose for n∈ ℕ, set A⊆ℝⁿ and function f∶A→ℝⁿ. If set A, using the Hausdorff outer measure, is measurable in the sense of Carathèodory; we want to find an extension of the expected value, w.r.t the Hausdorff measure, that's unique, finite and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. The issue is current extensions of the expected value are finite for all functions in only a shy subset of ℝᴬ. The reason this issue wasn't resolved is mathematicians have not thought of the problem, focusing on application rather than generalization. Despite the lack of potential use, we'll attempt to solve the problem by defining a choice function---this shall choose a unique set of equivalent sequences of sets (Fₖ***) , where the set-theoretic limit of Fₖ*** is the graph of f; the measure Hʰ is the ℎ-Hausdorff measure, such for each k∈ℕ, 0 < Hʰ(Fₖ***) < +∞; and (fₖ*) is a sequence of functions where {(x,fₖ*(x))∶x∈ dom(Fₖ***)}=Fₖ***. Thus, the extended expected value of or E**[f,Fₖ***] is: ∀(ε>0)∃(N∈ℕ)∀(k∈N)(k≥N⇒1/Hʰ(dom(Fₖ***))∫dom(Fₖ*** )fₖ* dHʰ - E**[f,Fₖ***]<ε ) which should be unique, finite, and "natural" (defined on §2.3 & §2.4) for all f in a prevalent subset of ℝᴬ. Note we guessed the choice function using computer programming but we don’t use mathematical proofs due to the lack of expertise in the subject matter. Despite this, the biggest use of this research is the extension of the expected value is finite for "almost all" functions: this is easier to use in application when finding the "average" of functions covering an infinite expanse of space.

In bilaterians organism, the signaling of pyramidal neurons (PyrNs) is linked to the relative (prevalent) molecular chirality and physiological, perceptual, cognitive, and psychological functions and dysfunctions, providing the coupling of the central nervous system downstream and upstream evolutionary and developmental processes. The most apparent and discriminating morphological specificity of PyrNs is the geometry of the cell body. However, the question "why/how PyrNs soma gains the shape of quasi-tetrahedral symmetry" has never been explicitly articulated. If the basic function of PyrNs is sensory space perception, supporting the orientation, and movement coordination, then the pyramidal shape of soma is the best evolutionary-selected geometry to perform sensory-motor coupling. In biology, the impact of chiral symmetry (handedness) is evident at all levels of biological organization, from the prevalent symmetry of biological molecules to the morphology and function of bilateral organisms. How the tetrahedral symmetry of biomolecules is linked to the morphology and functions of bilateral organisms remains a challenging question. Cell chirality represents an intermediate point connecting two poles of biochirality. In this holistic perspective, examining the PyrNs' morphology-circuitry-function link is crucial to understanding the complex interaction between genetic, epigenetic, and environmental factors in the evolution of the CNS. The predictive power of our hypothesis can be partially expressed by the statement that the most integral and reliable biomarker of the neurodegenerative (including aging) and mental (including all variants of psychiatric illness) disorders would be the detection of the hemispheric asymmetry of D-amino acids (D-AAs) level in pyramidal neurons (PyrNs).

It is essential to consider the factors that affect early childhood development because doing so can help identify potential risks and window of opportunity for intervention to improve outcomes for children. However, identifying risk and protective factors in early childhood requires careful consideration of several challenges and an integrated approach that recognises the complex and dynamic nature of development. The purpose of this study was to identify and describe the prevalent psychosocial risk and protective factors in the early childhood development phase, using an ecological perspective. The study employed a quantitative cross-sectional study using a random sampling technique. The final sample consisted of 505 caregivers of children aged 5 years old and younger. This study revealed that the most prevalent protective factors include child self-regulation, parent-child warmth, family management and collective efficacy but more importantly social support. While risk factors may exist this is mitigated by social support as it moderates and buffers against the effects of risk factors, as indicated by the various research studies cited.

The mechanism of brain information processing unfolds within spatial and temporal domains inherently linked to the concept of symmetry. Biological evolution, beginning with the prevalent molecular chirality, results in the handedness of cognitive and psychological functions (the phenomena known as biochirality). The key element in the chain of chirality transfer from the downstream to upstream processes is the pyramidal neuron (PyrN) morphology-function paradigm (archetype). The most apparent landmark of PyrN is the geometry of the cell soma. However, “why/how PyrN soma gains the shape of quasi-tetrahedral symmetry” has never been explicitly articulated. Resolving the above inquiry is only possible based on the broad-view assumption that encoding 3D-space requires specific 3D-geometry of the neuronal detector and corresponding network. Accordingly, our hypothesis states that if the primary function of PyrNs, at the organism level, is sensory space perception, then the pyramidal shape of soma is the best evolutionary-selected geometry to support sensory-motor coupling.