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Recent critiques of the semantic conception of scientific theories suggest that a theory is not best formulated as a collection of models satisfying some set of kinematical or dynamical conditions. Thus it has been argued that additional…
How much structural information is needed to distinguish living from non-living systems? Here, we show that the statistical properties of Delaunay tessellations suffice to differentiate prokaryotic and eukaroytic cell packings from a wide…
Although many solar systems have been discovered, only one example of life is known. Thus, terrestrial life represents merely one data point. Consequently, extrapolating from terrestrial life to life elsewhere in the galaxy and beyond is…
We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…
We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…
Earth system analysis is the study of the joint dynamics of biogeophysical, social and technological processes on our planet. To advance our understanding of possible future development pathways and identify management options for…
Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
What if physics is just the way we perceive geometry? That is, what if geometry and physics will one day become one and the same discipline? I believe that will mean we will at last really understand physics, without postulates other than…
Despite the important role of sidewalks in supporting mobility, accessibility, and public health, there is a lack of high-quality datasets and corresponding analyses on sidewalk existence and condition. Our work explores a twofold vision:…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…
The problem of mathematical modeling in geography is one of the most important strategies in order to establish the evolution and the prevision of geographical phenomena. Models must have a simplified structure, to reflect essential…
Cellular systems are observed everywhere in nature, from crystal domains in metals, soap froth and cucumber cells to the network of cosmological voids. Surprisingly, despite their disparate scale and origin all cellular systems follow…
The quest for life in the Universe is often affected by the free use of extrapolations of our phenomenological geocentric knowledge. We point out that the existence of a living organism, and a population of organisms, requires the existence…
We review some basic issues of the life-prescribed development of the Earth's system and the Earth's atmosphere and discourse the unity of Earth's type of life in physical and transcendental divisions. In physical division, we exemplify and…
Following Thurston's geometrisation picture in dimension three, we study geometric manifolds in a more general setting in arbitrary dimensions, with respect to the following problems: (i) The existence of maps of non-zero degree (domination…
In analogy with the Poisson algebra of the quadratic forms on the symplectic plane, and the notion of duality in the projective plane introduced by Arnold in \cite{Arn}, where the concurrence of the triangle altitudes is deduced from the…
In this paper we derive a statistical law of Life. It governs the probability of death, or complementary of survival, of the living organisms. We have deduced such a law coupling the widely used Weibull statistics, developed for describing…
Driven by access to large volumes of movement data, the study of human mobility has grown rapidly over the past decades. The field has shown that human mobility is scale-free, proposed models to generate scale-free moving distance…