http://popups.lib.uliege.be/1373-5411/index.php?id=67 Full text issues fr Mon, 13 May 2024 16:14:59 +0200 Mon, 13 May 2024 17:07:56 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=67 0 http://popups.lib.uliege.be/1373-5411/index.php?id=357 This paper deals with an introduction to computing anticipatory systems starting with Robert Rosen's definition of anticipatory systems. Firstly, the internalist and externalist aspects of anticipation will be explained at an intuitive point of view. Secondly, the concepts of incursion and hyperincursion are proposed to model anticipatory systems. Thirdly, a simple example of a computing anticipatory system will be simulated on computer from an incursive harmonic oscillator. This oscillator includes an anticipatory model of itself in view of computing its successives tates. Wed, 26 Jun 2024 11:38:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=357 http://popups.lib.uliege.be/1373-5411/index.php?id=363 A theory of organization of complexity was constructed in order to create a common semiotic lineage among the diverse symbol systems used by various disciplines (Chandler, t996, L997). The foundations of the theory are developed from observations on the nonlinear dynamics of organisms within ecoments -- ecoments being defined as the immediate surroundings of one hierarchical degree of an emergent system. Each system (sub-system, sub-sub-system ... ) is assigned four primitives attributes (closure, conformation, concatenation and cyclicity) which are subject to scaling and semiotic constraints. In principle, each of these four terms is enumerable for a local system. Degrees of organization (symbolized as Oo) are composed from lesser organized systems to higher organized systems in terms of the enumeration of the four primitives. The emergent organizations are enumerated: 1,2,3, ... The patterns of organization at any particular level, Oo, are composed from patterns at other levels. Thus, no particular science or philosophy is assigned a privileged role in the unfolding of the dynamics. Mathematically, the organized systems are composed under the scientific representations of categories as developed in Chandler, 1991, and Ehresmann and Vanbremeersch 1987, 1997. Categorical objects have the unique mathematical characteristic of creating a 'logical shell' for other classes of mathematical structures. (see S. Mac Lane, Mathematics, Form and Structure, 1986.) This 'logical shell' character of category theory is used here to construct hierarchical relationships between scientific observations and mathematical structures. This notation parallels natural history and allows the facile accounting of the molecular biological mechanisms within a living system. Implications of this theory of natural organization for the design of artifrcial hierarchical systems arc apparent. Wed, 26 Jun 2024 11:41:38 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=363 http://popups.lib.uliege.be/1373-5411/index.php?id=370 Working on the pre-attentive stage of perception by the human visual system (HVS), we propose both a modelling of chromatic perception (l) by means of 4 attactors associated to a mathematical symbolism induced by branching theory, and some structures for the shapes -or coloured shapes- processing. This research involved by the computer graphics and neurophysiology results about recognition of optical signal processing circuits have necessitated to reinvest the visual chain : object (emitter or re-emitter), light information vehicle, the colour receiver, the processors of the SVH. The local physico-mathematical formula set very developed about propagation, has brought solutions for monochromatic waves and for obstacle with smooth edge reveal neither various curvatures (2) nor a fortiori the texture of reemitting object U(3). A resort to a formula-set about interaction matter radiation, extended to a systemic approach,give an algorithmic stage to take account the spatial character (2) and (3). Taking account on one side this scalar conjecture about visual information, and on another side a retinal functional specialisation, we propose a modelling of C occluding edge detection of 3D-object. C except in isolated points by envelop method. The elaboration of a valuation table of morphemes associating the mathematical characteristics of curves with their pregnance treat the more cognitive stage of processing associating edge and colour. Some pictures illustrate the abilities of curves family to suggest 3D-shape. The chromaticity of delimited areas strengthen, or rather create, psycho-affective suggests associated to logos. Wed, 26 Jun 2024 12:17:09 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=370 http://popups.lib.uliege.be/1373-5411/index.php?id=381 La prophétie est un très ancien rêve de l'humanité : le désir de connaître l'avenir et, si possible, d'en changer le cours, est irrésistible depuis l'homme des cavernes et les chamans et est toujours présent parmi nous, depuis les cartomanciennes, les devins et les astrologues jusqu'aux planificateurs en économie et auteurs de science fiction. Il y a cependant de nombreuses limitations à l'anticipation et à l'action. Elles sont fondamentalement de deux espèces : - celles inhérentes à la nature profonde de l'évolution naturelle de n'importe quelle situation - celles qui résultent de nos propres limitations comme observateurs, en relation avec nos capacités perceptives et d'apprentissage, et aussi comme constructeurs de modèles et acteurs. Ce travail présente un survol rapide de ces divers aspects. Prophecy is a very old dream of mankind: the desire to know the future and, if possible, to twist the course of future events is overwhelming since cavemen and shamans and is still very much with us, from fortune tellers, astrologers and soothsayers to economic planners and science fiction novelists. There are however many limits to anticipation, and subsequent action. They seem to be basically of two classes : - those inherent to the deep nature of natural evolution of all kinds of situations - those related to our own limitations as observing systems, i.e. as perceivers, learners, modellers and actors. This papers presents a short overview of these topics. Wed, 26 Jun 2024 12:31:42 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=381 http://popups.lib.uliege.be/1373-5411/index.php?id=389 The aim of this paper is to highlight some process control competitiveness deposits to improve process control engineering. Rationale scientific foundations should be a significant contribution to improve process control of the future. To anticipate control systems through control engineering, we focus our interest in the definition of process control requirements and the definition of perennial control and document requirements, whatever the implementation into oFthe-shelves I&C devices should be. Wed, 26 Jun 2024 13:47:09 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=389 http://popups.lib.uliege.be/1373-5411/index.php?id=392 Wed, 26 Jun 2024 14:45:21 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=392 http://popups.lib.uliege.be/1373-5411/index.php?id=394 The main challenge of systems science is to elaborate a general transdisciplinary langage pertinent not only to describe and interpret systems of different natures physical, chemical, biological, social, cognitive, but also to understand their dynamics over a wide time scale, from their emergence, to their evolution toward complexity and autonomy. In this paper we present the main features of a metamodel that has been proposed recently in this context. We then use this language to investigate the evolution of the anticipative behavior of natural systems through the different stages of self-organization, self-regulation, autopoiesis, self-reference and autonomy. We show that their anticipative behavior begins with the first modes of circular causality, reaches a sort of apex with the anticipation capability of cognitive systems (like human beings), and then becomes irrelevant and meaningless with strictly autonomous systems which are identical with both their physical structure and their virtual possibles. Wed, 26 Jun 2024 15:44:15 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=394 http://popups.lib.uliege.be/1373-5411/index.php?id=400 The distinction of external (exo) and internal (endo) perspectives is addressed with respect to the issues of observation and measurement in quantum theory. It is demonstrated how the exo/endo-terminology can be fruitfully applied to two equally important concepts of reality in the quantum world: local (common sense) reality and holistic (nonlocal) reality. Basic elements of the exo/endo-distinction are then used to interpret certain features concerning the issues of time, histories, and presence. Thu, 27 Jun 2024 10:09:35 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=400 http://popups.lib.uliege.be/1373-5411/index.php?id=402 This paper presents an integrated Bayesian solution to the problem of object location estimation, object recognition and sensor action planning under uncertainty. The emphasis is on finding the best next sensing action. The method uses elementary notions from Bayesian decision theory. The best action is found as the one that optimises the expected value of a utility function, which is the logarithm of the volume of the uncertainty ellipsoid around the estimate of a target position. An example shows that this method is capable of controlling the sensing actions of an ultrasonic sensor mounted on a robot, where the target is to accurately position a drill on a cylinder before drilling a hole. The presented algorithm is easy to apply and computationally tractable. Thu, 27 Jun 2024 10:22:18 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=402 http://popups.lib.uliege.be/1373-5411/index.php?id=412 In this paper, I expose a new idea based on a fundamental movement of doubling in the three-dimensional space. The resulting theory and equation allow us to understand the constitution of any micro or macroscopic system (atomic, molecular, solar, galactic,...) that is always an anticipatory system. An application to the solar system justifies the theory and explains the whys and wherefores of the speed of light. Thu, 27 Jun 2024 10:31:49 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=412 http://popups.lib.uliege.be/1373-5411/index.php?id=433 This paper presents a backstepping procedure for the design of discontinuous time invariant state feedback controllers for the stabilization of nonholonomic systems in chained form. To highlight its effectiveness, our procedure is applied to two nonholonomic physical systems, namely, a unicycle and a car-like mobile robots. It is worth noticing that this approach may be considered as new systematic way to design time-invariant discontinuous controllers for nonholonomic systems. Thu, 27 Jun 2024 10:51:09 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=433 http://popups.lib.uliege.be/1373-5411/index.php?id=461 According to Hans Primas many epistemological questions of the so-called measurement problem of quantum physics can be solved by the distinction of the exo- and endo-perspective of a physical system. Pascual Jordan - one of the founding fathers of quantum theory - formulated already in 1947 the idea that the subconscious level in psychology may be equivalent to - what is now called - the endo-level in quantum physics. The model of pragmatic information (MPI), which is a candidate for a non-classical model of psychology, predicts that the behavior of a non-classical system depends on the conditions of its observation. The exchanged pragmatic information (meaningful information) ties the "observer" (e.g. a person) and the "observed" (e.g. a machine) together and creates an "organizational closed system". It is assumed that this process produces non-local correlations between the observer and the observed. The "observer effect" can be regarded as a special phenomenon of psycho-physical systems. As a target to demonstrate this "observer effect", a quantum physical random event generator(REG) was used which was observed by human subjects who had the instruction to "influence mentally" the outcome of the observed REG. The "observers" are characterized by a set of psychological variables which were measured by questionnaires before the observation-experiment. The "observed" is characterized by a set of statistical variables describing the observed random process. An "observer effect" should show up in correlations between these two sets of variables. The results support the assumptions of the MPI that a human observer (or other selforganizing systems?) may select certain noise fluctuations from a seemingly separated system via non-local correlations if a feedback-loop generates "meaning" of the process to the observer. The process can be adequately described by the concept of"pragmatic information". It is shown that the concept of "pragmatic information" is a much better descriptor of the observation process than any other "Shannon-type" measure of information. The correlations between psychological and physical variables reflect the pragmatic information of the display and the instruction given to the subjects. The result of the experiment further show that external attribution of meaning is a necessary condition for the occurrence of the observer effect. It is argued that "observer effects" are no "signals" but "only" (non-local) correlations or "pseudo-signals" which do not allow to "identify" situations without resources from the environment- or to use a technical example - do not allow to built "faster-than-light-telegraphs". From this point of view, the distinction between the "internal" and the "external" pragmatic information of an observer experiment gives a criterion for the replication of the non-local correlations. The seemingly "internal" meaning exists only "post hoc" as correlation. It is a feature of the "organizational closure" of the system which is created by the external attribution of meaning to the system. If the "internal" pragmatic information about the system available to the experimenter from a previous experiment could be "used" to code a real extemal signal, the non-local correlations change or disappear, leading to a result completely different from the previous experiment. From this viewpoint the well-known replication problem of psychological experiments appears in a new light. Thu, 27 Jun 2024 11:12:17 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=461 http://popups.lib.uliege.be/1373-5411/index.php?id=498 In this paper, the author presents a conceptual model of a unified field theory that is based on group symmetry characteristics of matter -- i.e., on the 'charge' conserving and gaugeinvariant properties of elementary particles and fields. In such a model, it will be shown that emergence of order and structure in physical, chemical and biological systems inevitably arises through a series of bipolar symmetry breaking phase transitions in an expanding universe. The basic foundation of the proposed model is derived from recent developments in quantum field theory, e.g., super-symmetry group models, where the existence of higher quantum spin states and greater degrees of freedom in the space-time manifold is posulated. In the proposed unified field model, the origin of the physical universe is considered an 'ergodic' phenomenon, i.e., a probabistically rare, but temporally-finite event. The cosmic 'big bang' is thus seen as arising from a thennodynamically unstable state of primordial matter in an extremely low entropic state in a localized region of the background vacuum (governed by a scalar potential), that led to a hyper-inflationary expansion of the emergent physical universe, as recently described by A. Linde. While the overall entropy of the physical universe increased againstt he initial localized 'singularity' of the background vacuum, other localized low entropy states, with relatively stable structure and order, evolved through a nested hierarchy of symmetry breaking transitions. In addition, the stability of matter is maintained by the formation of gaugeinvariant local symmetries -- i.e., through the 'partial' restoration of local symmetry fields in a globally symmetric field. It is postulated that through such symmetry breaking and restoring processes, the emergence of 'proto-galaxies'( containing dark matter) and the presently observable galaxies, stellar bodies and planetary objects have arisen. Similarly, it is proposed that chemical and biological evolution at the terrestrial level have proceeded through an analogous series of symmetry breaking and restoring processes, with increasing degrees of complexities and emergent order. In the paper, a number of novel concepts are discussed that are based on the principles of an axiomatic symmetry field theory. These include: . the concepts of resting mass or inertia, which are viewed as the measure of relative resistance encountered by locally asymmetric fields when they are spatially displaced with respect to a globally symmetric field. Such a dynamical concept of mass appears to be consistent with the conceptual foundations of Mach's principle, . the underlying nature of the characteristic wave velocities of each globally symmetric field. In the proposed model, for example, it is postulated that gravitational field waves travel at propagation velocities greatly in excess of electromagnetic field transmissions. Such a conclusion appears to extend, but not contradict the principles of special relativity, . the existence of dark matter particles and fields, that exert weakly-coupled, but extremely long-ranged field effects that are not gravitational in origin. In such a scenario, it is postulated that all regions of the universe are causally linked by a finite dark matter field force that appear to be almost instantaneous, . the possible existence of parallel or muhiple universes that grew out of a series of thermodynamically unstable and low entropic regions of the primordial vacuum state of a 'super-universe'. . the emergent order and structure of more complex chemical and biological systems, that are consistent with, but not reductible to the symmetry breaking and restoring processes of physical systems. Thu, 27 Jun 2024 12:09:43 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=498 http://popups.lib.uliege.be/1373-5411/index.php?id=500 In order to understand the complex behaviors in megaloscopic systems, it is necessary to analyse the detailed mechanisms of non-separability in nonlinear processes. The essential roles of nonlinearity are pursued in the local-global linkage from deterministic points of view carrying out with nonlinear dynamical models; onset of subliminal threshold, self-organization of soft interface, and scaling relation in barrier-free cascade. It is emphasized that the non-separability and fluctuations in soft interfaces are closely associated with emergent behaviors of megaloscopic systems and that the law of unbroken wholeness is described by a relation of relations. Thu, 27 Jun 2024 13:00:20 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=500 http://popups.lib.uliege.be/1373-5411/index.php?id=507 From a few interpretation about the behaviour and characteristics of a hands watch, we will show that this usual wide-spread object can constitute a very valuable didactical tool for the study and the illustration of the Fourier transformations and in going further the same way for the discover of the Wavelets methodology for the signals and shapes analysis. By means of this way of thinking we are trying to elaborate a highly synoptical procedure for exploring the deep stuctures of some transformations from Time domain into Frequency or Spectral domain. It will become possible to underline the linkages between every transitions of domains and the "Jacobien's Operators" and the "Z Operators". Thu, 27 Jun 2024 13:25:53 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=507 http://popups.lib.uliege.be/1373-5411/index.php?id=513 Thu, 27 Jun 2024 13:32:44 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=513 http://popups.lib.uliege.be/1373-5411/index.php?id=520 We begin with a brief review of the basic notions of classical computability theory and the Turing machine. The concept of decidability and computability, as well as the Church-Turing thesis are also introduced. The recently formalized foundations of quantum computability theory are surveyed next. Included are such topics as the universal quantum computer; the use of quantum parallelism in computation; and the Church-Turing principle. We highlight some avenues of research for new computational paradigms and suggest that underlying the new advances in both the theory and practical aspects (actual devices), is a new conceptual basis for interpreting the interactions that produce complex and partially understood processe. Thu, 27 Jun 2024 13:45:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=520 http://popups.lib.uliege.be/1373-5411/index.php?id=527 Thu, 27 Jun 2024 13:58:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=527 http://popups.lib.uliege.be/1373-5411/index.php?id=534 Testable theoretical predictions in the form of mathematically specified templates for morphology and dynamics can be made using quantum holography. This has already been shown to be the case for DNA and will be shown to be the case for the simplest cells - the Prokaryote. Thu, 27 Jun 2024 14:16:00 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=534 http://popups.lib.uliege.be/1373-5411/index.php?id=541 An externalist discourse on evolutionary process proceeding through selective retention of slightly modified heritable traits requires a generator of variations to be subjected to natural selection. This externalist classification takes the generation of variations to be totally independent of the subsequents elective processes. Prior variations are functionally symmetric in keeping the cause and the effect of the variations mutually interchangeable, otherwise they would be temporally asymmetric and evolutionary by themselves. The operation of natural selection that makes those symmetric variations temporally asymmetric in the effect is upon the accumulation of the preceding variations of similar nature. Natural selection viewed from the externalist perspective refers to a functional characteristic pertaining to the accumulated variations. Natural selection as a consequence of the accumulated variations is grounded upon the very accumulation process. Further elucidation of the accumulation process can be made by switching to the internalist stance. What is unique to the internalist stance is to make both the operations of generating variations and natural selection inseparable. Variations are genrated in the process of identifying the variations already made. The generation is in and of itself selective since the variations that could occur at whatever internal observers depend upon how the preceding variations could come to be observed and identified by the observers in the absence of the global perspective. The variations thus perceived can be embodied in the form of suppliers and consumers of resources of evolutionary significance. The internal observers functioning as either suppliers or consumers are both generative and selective. Natural selection can be seen as a consequence of the interplay among the internal observers aiming at necessary resources. The internalist stance grounds itself upon observation and measurement proceeding internally on material basis. Variations resulting in natural selection are a demonstration of the internalist stance par excellence. Evolution is a mode of natural dynamics, in which many participants interact with each other. In particular, any dynamics can identify itself by explicating how it addresses itself to the following two questions. (l) How does each participant come to detect others? (2) How does each move with and act upon others ? The Galilean-Newtonian mechanics concentrates on the second question on movement dynamics by dismissing the significance of the first question on detection dynamics only except for mentioning its role of identifiing the initial conditions. Thermodynamics, on the other hand, emphasizes the role of detection dynamics as demonstrated in its second law stating that if the process of detection proceeds only locally as it should, movement dynamics would necessarily exhibit an irreversible enhancement of randomization. We note that any detection dynamics proceeding internally is local in the sense that complete identification of evolving systems in a globally simultaneous manner is not attainable. Detection dynamics of necessarily local character comes to imply that there is an inevitable time-delay between detecting others in the neighborhood and acting upon them accordingly. The time-delay between detection and action perceived by each participant, or in the eyes of the participants, serves as a causative factor of evolutionary dynamics of any type. Most indicative of the time-delay between detection and action is heterotrophic activity, in the latter of which an arbitrary participant in an evolutionary process has the capacity of taking in necessary material resources as responding to detecting what its neighborhood looks like. Although it leaves behind only material flow continuity, heterotrophic activity as the capacity of wanting material resources for the sake of the continuity in the record is an agency connecting between detection and movement dynamics. Thu, 27 Jun 2024 14:39:02 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=541 http://popups.lib.uliege.be/1373-5411/index.php?id=548 Cognitive and other neural processes emerge from the interactions between neurons. Major advances have been made in studying networks in which the interactions occur instantaneously by means of graded synapses (Guckenheirner and Rowat 1997). In other networks, the interaction between neurons involves time-delayed signals (action potentials or spikes) that activate synapses on other neurons discontinuously in a pulse-like manner. These interactions can also be treated as being graded if, when appropriate, the infomration transmitted between neurons can be measured as the average number of spikes per unit time (Freeman , 1992) ; i.e., the amount of information carried by individual spikes is relatively low. We refer to both of these types of interactions as "graded". There is a large armamentarium of mathematical and dynamical systems tools for studying the computations that such neurons perform. There is also a complementary connection between these tools and biological experimentation. The subject of the present paper is on networks in which averaging can not be done. The generation of spikes in these neurons is significantly affected by the temporal order of spikes sent to them by other neurons. Two input spike trains, having the same average spikes per unit time but different temporal spacing between the spikes, produce different outputs in target neurons ; i.e., the amount of information carried by individual spikes is relatively high. We refer to these networks as "spike-activated". By comparison to graded networks, there is little formal or experimental work on the general principles underlying these networks. There are many nonlinear physiological processes in spike-activated networks that need to be considered. We have begun by focusing on a single nonlinearity analysis, the threshold tansition between spiking and nonspiking behavior, and use linear perturbation to examine it. The findings indicate that there may be an epistemological distinction between graded networks and spike-activated networks. This is reminiscent of the distinction between endophysics and exophysics whose resolutions requires an external observer having information about a system and its external universe (Rôssler, 1989). Interestingly, the philosophical roots of our approach and the study of dynamics more generally may be traceable to Jacob Bôhme (1575-1624), a mystic and contemporary of Descartes. Bôhme influenced many philosophers and scientists, and may have provided Isaac Newton the metaphorical insight into his laws of physics (Mpitsos, 1995 ; Yates, 1972,1979). Thu, 27 Jun 2024 14:54:44 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=548 http://popups.lib.uliege.be/1373-5411/index.php?id=559 Norbert Wiener and Claude Shannon argued that the signal (communication) and the perturbations can be described only in terms of probability's theory as elements of some determined ensembles. The theory of information analyses all events from the point of view of the probability of their happening. Events can be in different states and each state can appear with a certain probabilitv. The author has designate as structural-diachronic cell the minimal tri-objectual, tri-relational, quadri propertitional ensemble expressed mathematically as a set of three minimal sets. The BIT representing the elementary unit of measure of the information, wve will associate it as a measure of the structural-diachronic cell. The non-Shannon phenomenological analysis of the measure unit of the information, in a Aristotelic-Liebnitzian demonstrates that the bit has by excellence a relational character, respectirely a semantic architecture. Two examples are given in order to presenting the method, one for form recognition and the second for the problem of the urn with 8 balls of different colours. By an innovative approach of the concept of information, the conception of inferential engines to be used in the knowledge basis of an UNIVERSAL EXPERT SYSTEM. Fri, 28 Jun 2024 08:44:28 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=559 http://popups.lib.uliege.be/1373-5411/index.php?id=564 Coherent wavelets form a unified basis of the multichannel perfect reconstruction analysis-synthesis filter bank of high resolution radar imaging and clinical magnetic resonance imaging (MRI). The filter bank construction is performed by the Kepplerian temporospatial phase detection strategy which allows for the stroboscopic and synchronous cross sectional quadrature filtering of phase histories in local frequency encoding multichannels with respect to the rotating coordinate frame of reference. The Kepplerian strategy and the associated filter bank construction take place in symplectic affine planes which are immersed as coadjoint orbits of the Heisenberg two-step nilpotent Lie group G into the foliated three-dimensional real projective space P(R x Lie(G)). Due to the factorization of transvections into affine dilations of opposite ratio, the Heisenberg group G under its natural sub-Riemannian metric acts on the line bundle realizing the projective space P(R x Lie(G)). Its elliptic non-Euclidean geometry without absolute quadric, associated to the unitary dual G, governs the design of the coils inside the bore of the MRI scanner system. It determines the distributional reproducing kernel of the tracial read-out process of quantum holograms excited and coexisting in the MRI scanner system. Thus the pathway of this paper leads from Keppler's approach to projective geometry to the Heisenberg approach to the sub-Riemannian geometry of quantum physics, and finally to the enormously, appealing topic of ensemble quantum computing. Fri, 28 Jun 2024 09:00:50 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=564 http://popups.lib.uliege.be/1373-5411/index.php?id=304 Fri, 21 Jun 2024 11:22:50 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=304