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Ioannis Raptis

Publications and source records attributed to Ioannis Raptis.

At least 19 recordsLinked to original sources
arXiv2026

A-Relativity: A General Theory of Gravity from Structure Sheaf

The aim of this paper is to introduce and disseminate to a wider readership of mathematicians, mathematical physicists and philosophers of mathematics and physics alike the basic theoretical, both conceptual and technical, tenets of Mallios's Abstract Differential Geometry, as well as to present and to summarise the main results from its applications in the last quarter of a century towards formulating an entirely homological algebraic, purely gauge-theoretic, finitistic, quantal and manifestly background geometrical smooth spacetime manifold independent vacuum Einstein gravity. New, previously unpublished, constructions and results are included in the paper.

physics.gen-ph↗
arXiv2024

Observability of Linear Time-Invariant Systems with Relative Measurements: A Geometric Approach

This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables. We concentrate on linear time-invariant systems, in which the observation matrix serves as the algebraic representation of a graph object. This graph object encapsulates the availability of relative measurements. Utilizing algebraic graph theory and abstract linear algebra (geometric) tools, we establish a link between the structure of the graph of relative measurements and the system-theoretic observability subspace of linear systems. Special emphasis is given to multi-agent networked systems whose dynamics are governed by the linear consensus protocol. We demonstrate the importance of absolute information and its placement to the system's dynamics in achieving full-state estimation. Finally, the analysis shifts to the synthesis of a distributed observer with relative measurements for single integrator dynamics, exemplifying the relevance of the preceding analytical findings. We support our theoretical analysis with numerical simulations.

eess.SY↗
arXiv2024

A Heuristic Philosophical Discourse on Various Applications of Abstract Differential Geometry in Quantum Gravity Research

In the present paper, we outline and expound the fundamental and novel qualitative-cum-philosophical premises, principles, ideas, concepts, constructions and results that originate from our ongoing research project of applying the conceptual panoply and the technical machinery of Abstract Differential Geometry (ADG) to various persistently outstanding issues in Quantum Gravity (QG) research. At the end of the paper, we discuss the potential philosophical repercussions of two possible future research routes that the main stream of our applications of ADG to QG may bifurcate towards in view of three independent, but overlapping, research papers that are currently under development.

physics.hist-ph↗
arXiv2024

Multiplicatively Ordered and Directed Hybrid Jordan-Lie Superalgebra

A new algebra, hitherto not encountered in the usual Lie algebraic varieties or supervarieties, is introduced. The paper explores the rich and novel structure of the algebra, and it compares it on the one hand with the Jordan-Lie Superalgebras studied by Okubo and Kamiya, and on the other, with the four usual Euclidean division rings of the reals (R), the complexes (C), the quaternions (H) and the octonions (O), key algebraic properties of which the algebra is seen to combine, alter, extend and generalise. A potential physical application of the algebra is briefly alluded to at the end.

math-ph↗
arXiv2022

Leaderless Swarm Formation Control: From Global Specifications to Local Control Laws

This paper introduces a distributed leaderless swarm formation control framework to address the problem of collectively driving a swarm of robots to track a time-varying formation. The swarm's formation is captured by the trajectory of an abstract shape that circumscribes the convex hull of robots' positions and is independent of the number of robots and their ordering in the swarm. For each robot in the swarm, given global specifications in terms of the trajectory of the abstract shape parameters, the proposed framework synthesizes a control law that steers the swarm to track the desired formation using the information available at the robot's local neighbors. For this purpose, we generate a suitable local reference trajectory that the robot controller tracks by solving the input-output linearization problem. Here, we select the swarm output to be the parameters of the abstract shape. For this purpose, we design a dynamic average consensus estimator to estimate the abstract shape parameters. The abstract shape parameters are used as the swarm state feedback to generate a suitable robot trajectory. We demonstrate the effectiveness and robustness of the proposed control framework by providing the simulation of coordinated collective navigation of a group of car-like robots in the presence of robots and communication link failures.

cs.RO↗
arXiv2016

Dynamic Endpoint Object Conveyance Using a Large-Scale Actuator Network

Large-Scale Actuator Networks (LSAN) are a rapidly growing class of electromechanical systems. A prime application of LSANs in the industrial sector is distributed manipulation. LSAN's are typically implemented using: vibrating plates, air jets, and mobile multi-robot teams. This paper investigates a surface capable of morphing its shape using an array of linear actuators to impose two dimensional translational movement on a set of objects. The collective nature of the actuator network overcomes the limitations of the single Degree of Freedom (DOF) manipulators, and forms a complex topography to convey multiple objects to a reference location. A derivation of the kinematic constraints and limitations of an arbitrary multi-cell surface is provided. These limitations determine the allowable actuator alignments when configuring the surface. A fusion of simulation and practical results demonstrate the advantages of using this technology over static feeders.

cs.RO↗
arXiv2016

A Particle-Filtering Based Approach for Distributed Fault Diagnosis of Large-Scale Interconnected Nonlinear Systems

This paper deals with the problem of designing a distributed fault detection and isolation algorithm for nonlinear large-scale systems that are subjected to multiple fault modes. To solve this problem, a network of communicating detection nodes is deployed to monitor the monolithic process. Each node consists of an estimator with partial observation of the system's state. The local estimator executes a distributed variation of the particle filtering algorithm using the partial sensor measurements and the fault progression model of the process. During the implementation of the algorithm, each node communicates with its neighbors by sharing pre-processed information. The communication topology is defined using graph theoretic tools. The information fusion between the neighboring nodes is performed by means of a distributed average consensus algorithm to ensure the agreement over the value of the local likelihood functions. The proposed method enables online hypothesis testing without the need of a bank of estimators. Numerical simulations demonstrate the efficiency of the proposed approach.

eess.SY↗
arXiv2006

Spacetime topology from the tomographic histories approach I: Non-relativistic Case

The tomographic histories approach is presented. As an inverse problem, we recover in an operational way the effective topology of the extended configuration space of a system. This means that from a series of experiments we get a set of points corresponding to events. The difference between effective and actual topology is drawn. We deduce the topology of the extended configuration space of a non-relativistic system, using certain concepts from the consistent histories approach to Quantum Mechanics, such as the notion of a record. A few remarks about the case of a relativistic system, preparing the ground for a forthcoming paper sequel to this, are made in the end.

gr-qc↗
arXiv2006

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of `poetic language'

gr-qc↗
arXiv2006

`Third' Quantization of Vacuum Einstein Gravity and Free Yang-Mills Theories

Based on the algebraico-categorical (:sheaf-theoretic and sheaf cohomological) conceptual and technical machinery of Abstract Differential Geometry, a new, genuinely background spacetime manifold independent, field quantization scenario for vacuum Einstein gravity and free Yang-Mills theories is introduced. The scheme is coined `third quantization' and, although it formally appears to follow a canonical route, it is fully covariant, because it is an expressly functorial `procedure'. Various current and future Quantum Gravity research issues are discussed under the light of 3rd-quantization. A postscript gives a brief account of this author's personal encounters with Rafael Sorkin and his work.

gr-qc↗
arXiv2005

`Iconoclastic', Categorical Quantum Gravity

This is a two-part, `2-in-1' paper. In Part I, the introductory talk at `Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international theoretical physics conference is presented in paper form (without references). In Part II, the more technical talk, originally titled ``Abstract Differential Geometric Excursion to Classical and Quantum Gravity'', is presented in paper form (with citations). The two parts are closely entwined, as Part I makes general motivating remarks for Part II.

gr-qc↗
arXiv2005

Finitary-Algebraic `Resolution' of the Inner Schwarzschild Singularity

A `resolution' of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed via Sorkin's finitary (:locally finite) poset substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence algebras and the finitary spacetime sheaves thereof. It is shown that the Einstein equations hold not only at the finitary poset level of `discrete events', but also at a suitable `classical continuum limit' of the said finitary sheaves and the associated differential triads that they define ADG-theoretically. We infer that the law of gravity does not break down in any (differential geometric) sense in the vicinity of the locus of the point-mass as the usual manifold based analysis of spacetime singularities in General Relativity has hitherto maintained. Various possible implications that such a total evasion of smooth gravitational singularities, as well as some anticipations of the wider significance that the general ADG-framework, may have for certain current `hot' issues in both classical and quantum gravity research are briefly discussed at the end.

gr-qc↗
arXiv2005

Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity

Previous work on applications of Abstract Differential Geometry (ADG) to discrete Lorentzian quantum gravity is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantum causal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein field equations were seen to hold, into a topos structure. This topos is seen to be a finitary instance of both an elementary and a Grothendieck topos, generalizing in a differential geometric setting, as befits ADG, Sorkin's finitary substitutes of continuous spacetime topologies. The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research.

gr-qc↗
arXiv2005

Smooth Singularities Exposed: Chimeras of the Differential Spacetime Manifold

The smooth gravitational singularities of the differential spacetime manifold based General Relativity (GR) are viewed from the perspective of the background manifold independent and, in extenso, Calculus-free Abstract Differential Geometry (ADG). In particular, the inner Schwarzschild singularity is being `resolved' ADG-theoretically in two different ways. A plethora of important mathematical, physical and philosophical issues in current classical and quantum gravity research are addressed and tackled.

gr-qc↗
arXiv2002

A Combinatory-Algebraic Perspective on Multipartiteness, Entanglement and Quantum Localization

We claim that both multipartiteness and localization of subsystems of compound quantum systems are of an essentially relative nature crucially depending on the set of operationalistically available states. In a more general setting, to capture the relativity and variability of our structures with respect to the observation means, sheaves of algebras may need be introduced. We provide the general formalism based on algebras which exhibits the relativity of multipartiteness and localization.

quant-ph↗
arXiv2002

Finitary, Causal and Quantal Vacuum Einstein Gravity

We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole construction is `fully covariant', `inherently quantum' (both expressions are analytically explained in the paper) and genuinely smooth background spacetime independent.

gr-qc↗
arXiv2002

Quantum Space-Time as a Quantum Causal Set

A recently proposed algebraic representation of the causal set model of the small-scale structure of space-time of Sorkin et al. is briefly reviewed and expanded. The algebraic model suggested, called quantum causal set, is physically interpreted as a locally finite, causal and quantal version of the kinematical structure of general relativity: the 4-dimensional Lorentzian space-time manifold and its continuous local orthochronous Lorentz symmetries. We discuss various possible dynamical scenarios for quantum causal sets mainly by using sheaf-theoretic ideas, and we entertain the possibility of constructing an inherently finite and genuinely smooth space-time background free quantum theory of gravity. At the end, based on the quantum causal set paradigm, we anticipate and roughly sketch out a potential future development of a noncommutative topology, sheaf and topos theory suitable for quantum space-time structure and its dynamics.

gr-qc↗