Visualization of four-dimensional X-ray absorption fine structure data using a virtual reality system

X-ray spectromicroscopy is extensively utilized for nondestructive mapping of chemical states in materials. However, understanding and analyzing the geometric and topological aspects of such data pose challenges due to their representation in 4D space, encompassing (x, y, z) coordinates along with the energy (E) axis and often extending to 5D space with the inclusion of time (t) or reaction degree. In this study, we addressed this challenge by developing a new approach and introducing a device named `4D-XASView', specifically designed for visualizing X-ray absorption fine structures (XAFS) data in 4D (comprising 3D space and energy), through a multi-projection system, within the virtual reality (VR) environment. As a test case for the new system, X-ray spectromicroscopy measurements were conducted on a specimen prepared from serpentinized harzburgite sourced from the upper mantle section of the Oman ophiolite. Our 4D-XASView facilitates the visualization and analysis of the geometric and topological aspects of the data using VR goggles, enabling detailed exploration of microstructures via rotation and zooming functionalities. This capability allows us to extract XAFS spectral data by selecting specific positions and regions, thereby aiding in the identification of `trigger sites' (magnetite in serpentine), which are characteristic locations within materials that substantially influence the macroscopic propagation of reactions. Our methodology establishes a new platform for analyzing 4D or 5D XAFS data that has applicability potential in various other multidimensional datasets, including microstructures coupled with spectroscopy and diffraction data.

Plato’s Allegory of the ‘Cave’ and Hyperspaces: Sonic Representation of the ‘Cave’ as a Four-Dimensional Acoustic Space via an Interactive Art Application

Mathematician and philosopher Charles Howard Hinton posited a plausible correlation between higher-dimensional spaces, also referred to as ‘hyperspaces’, and the allegorical concept articulated by the Ancient Greek philosopher Plato in his work, Republic, known as the ‘Cave.’ In Plato’s allegory, individuals find themselves situated in an underground ‘Cave’, constrained by chains on their legs and neck, perceiving shadows and sound reflections from the ‘real’ world cast on the ‘Cave’ wall as their immediate reality. Hinton extended the interpretation of these ‘shadows’ through the induction method, asserting that, akin to a 3D object casting a 2D shadow, the ‘shadow’ of a 4D hyper-object would exhibit one dimension less, manifesting as a 3D object. Building upon this conceptual framework, the authors posit a correlation between the perceived acoustic space of the bounded individuals within the ‘Cave’ and the characteristics of a 4D acoustic space, a proposition substantiated mathematically by scientific inquiry. Furthermore, the authors introduce an interactive art application developed as a methodical approach to exploring the hypothetical 4D acoustic space within Plato’s ‘Cave’, as perceived by the bounded individuals and someone liberated from his constraints navigating through the ‘Cave.’

Perception of rigidity in three- and four-dimensional spaces

Our brain employs mechanisms to adapt to changing visual conditions. In addition to natural changes in our physiology and those in the environment, our brain is also capable of adapting to "unnatural" changes, such as inverted visual-inputs generated by inverting prisms. In this study, we examined the brain's capability to adapt to hyperspaces. We generated four spatial-dimensional stimuli in virtual reality and tested the ability to distinguish between rigid and non-rigid motion. We found that observers are able to differentiate rigid and non-rigid motion of hypercubes (4D) with a performance comparable to that obtained using cubes (3D). Moreover, observers' performance improved when they were provided with more immersive 3D experience but remained robust against increasing shape variations. At this juncture, we characterize our findings as "3 1/2 D perception" since, while we show the ability to extract and use 4D information, we do not have yet evidence of a complete phenomenal 4D experience.

Perception, Cognition, and Action in Hyperspaces: Implications on Brain Plasticity, Learning, and Cognition

We live in a three-dimensional (3D) spatial world; however, our retinas receive a pair of 2D projections of the 3D environment. By using multiple cues, such as disparity, motion parallax, perspective, our brains can construct 3D representations of the world from the 2D projections on our retinas. These 3D representations underlie our 3D perceptions of the world and are mapped into our motor systems to generate accurate sensorimotor behaviors. Three-dimensional perceptual and sensorimotor capabilities emerge during development: the physiology of the growing baby changes hence necessitating an ongoing re-adaptation of the mapping between 3D sensory representations and the motor coordinates. This adaptation continues in adulthood and is quite general to successfully deal with joint-space changes (longer arms due to growth), skull and eye size changes (and still being able of accurate eye movements), etc. A fundamental question is whether our brains are inherently limited to 3D representations of the environment because we are living in a 3D world, or alternatively, our brains may have the inherent capability and plasticity of representing arbitrary dimensions; however, 3D representations emerge from the fact that our development and learning take place in a 3D world. Here, we review research related to inherent capabilities and limitations of brain plasticity in terms of its spatial representations and discuss whether with appropriate training, humans can build perceptual and sensorimotor representations of spatial 4D environments, and how the presence or lack of ability of a solid and direct 4D representation can reveal underlying neural representations of space.

Assessing the Dynamics and Complexity of Disease Pathogenicity Using 4-Dimensional Immunological Data

Investigating disease pathogenesis and personalized prognostics are major biomedical needs. Because patients sharing the same diagnosis can experience different outcomes, such as survival or death, physicians need new personalized tools, including those that rapidly differentiate several inflammatory phases. To address these topics, a pattern recognition-based method (PRM) that follows an inverse problem approach was designed to assess, in <10 min, eight concepts: synergy, pleiotropy, complexity, dynamics, ambiguity, circularity, personalized outcomes, and explanatory prognostics (pathogenesis). By creating thousands of secondary combinations derived from blood leukocyte data, the PRM measures synergic, pleiotropic, complex and dynamic data interactions, which provide personalized prognostics while some undesirable features-such as false results and the ambiguity associated with data circularity-are prevented. Here, this method is compared to Principal Component Analysis (PCA) and evaluated with data collected from hantavirus-infected humans and birds that appeared to be healthy. When human data were examined, the PRM predicted 96.9 % of all surviving patients while PCA did not distinguish outcomes. Demonstrating applications in personalized prognosis, eight PRM data structures sufficed to identify all but one of the survivors. Dynamic data patterns also distinguished survivors from non-survivors, as well as one subset of non-survivors, which exhibited chronic inflammation. When the PRM explored avian data, it differentiated immune profiles consistent with no, early, or late inflammation. Yet, PCA did not recognize patterns in avian data. Findings support the notion that immune responses, while variable, are rather deterministic: a low number of complex and dynamic data combinations may be enough to, rapidly, unmask conditions that are neither directly observable nor reliably forecasted.