Related papers: On the Philosophy of Higher Structures
This is primarily an expository piece and the first sentence of the introduction pretty much sums it up: This article is aimed at people who already know what mixed Hodge structures are and what they are good for, but who are not sure how…
Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…
Multi-scale structures are prevalent in both natural and artificial systems, as they can handle increasing complexity. Several terms are employed almost interchangeably across various application domains to refer to the multi-scale concept…
This paper presents the methodology for the system requirements and architecture w.r.t. their decomposition and refinement. It also introduces ideas of refinement layers and of refinement-based verification.
This paper explores the issues around the construction of large-scale complex systems which are built as 'systems of systems' and suggests that there are fundamental reasons, derived from the inherent complexity in these systems, why our…
In this article we survey some of the recent developments in the structure theory of set addition.
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
Current paper introduces a Hypergraph Graph model of data storage which can be represented as a hybrid data structure based on Hypergraph and Graph. The pro-posed data structure is claimed to realize complex combinatorial structures. The…
I give an overview of the motivations for and theory/phenomenology of supersymmetry.
In this article we have studied the structure of hypothetical two-dimensional polytropic stars. Considering some academic interest, we have developed a formalism to investigate some of the gross properties of such stellar objects. However,…
A given subset $A$ of natural numbers is said to be complete if every element of $\N$ is the sum of distinct terms taken from $A$. This topic is strongly connected to the knapsack problem which is known to be NP complete. The main goal of…
The aim of this paper is to introduce the idea of Logic with Verbs and to show its mathematical structure.
Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in…
This paper explores the hard problem of consciousness from a different perspective. Instead of drawing distinctions between the physical and the mental, an exploration of a more foundational relationship is examined: the relationship…
Higher-order interactions provide a nuanced understanding of the relational structure of complex systems beyond traditional pairwise interactions. However, higher-order network analyses also incur more cumbersome interpretations and greater…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…
The persistent challenge of formulating ontic structuralism in a rigorous manner, which prioritizes structures over the entities they contain, calls for a transformation of traditional logical frameworks. I argue that Univalent Foundations…
The purpose of this paper is (i) to expound the specification of a universe, according to those parts of mathematical physics which have been experimentally and observationally verified in our own universe; and (ii) to expound the possible…