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Within a mathematical model, the process of interaction of the metabolic processes such as glycolysis and gluconeogenesis is studied. As a result of the running of two opposite processes in a cell, the conditions for their interaction and…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
The things surrounding us vary dramatically, which implies that there are far more small things than large ones, e.g., far more small cities than large ones in the world. This dramatic variation is often referred to as fractal or scaling.…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
A painting consists of objects which are arranged in specific ways. The art of painting is drawing the objects, which can be considered as known trends, in an expressive manner. Detrended methods are suitable for characterizing the artistic…
Causality is pivotal to our understanding of the world, presenting itself in different forms: information-theoretic and relativistic, the former linked to the flow of information, the latter to the structure of space-time. Leveraging a…
In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…
As immersive analytics continues to grow as a discipline, so too should its underlying methodological support. Taxonomies play an important role for information visualization and human computer interaction. They provide an organization of…
We introduce the concept of {\it self-referential order} which provides a way to quantify structural organization in non crystalline materials. The key idea consists in the observation that, in a disordered system, where there is no ideal,…
We investigate complex synchronization patterns such as cluster synchronization and partial amplitude death in networks of coupled Stuart-Landau oscillators with fractal connectivities. The study of fractal or self-similar topology is…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
Metaphors of Computation and Information tended to detract attention from the intrinsic modes of neural system functions, uncontaminated by the observer's role for collection and interpretation of experimental data. Recognizing the…
Traditionally, cognition has been considered a uniquely human capability involving perception, memory, learning, reasoning, and problem-solving. However, recent research shows that cognition is a fundamental ability shared by all living…
Current methods for textual analysis rely on data annotated within predefined ontologies, often embedding human bias within black-box models. Despite achieving near-perfect performance, these approaches exploit unstructured, linear pattern…
Complex networks have certain properties that distinguish them from their respective uniform or regular counterparts. One of these properties is the variation of topological properties along different hierarchical levels. In this work, we…
Categorical orthodoxy has it that collections of ordinary mathematical structures such as groups, rings, or spaces, form categories (such as the category of groups); collections of 1-dimensional categorical structures, such as categories,…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
Developing and organizing new knowledge is a core activity for scholars. Recently, ontologies have been introduced as an approach for organizing knowledge. However, most ontologies do not readily support the development and organization of…
In this paper, we present a new cosmological model using fractal manifold. We prove that a space defined by this kind of manifold is an expanding space. This model provides us with consistent arguments pertaining to the relationship between…
We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the…