Papers by Roman R Zapatrin
International Journal of Theoretical Physics, Sep 28, 2006
International Conference on Logic Programming, Aug 23, 1994
International Journal of Theoretical Physics, Sep 22, 2006
The tomographic histories approach is presented. As an inverse problem, we recover in an operatio... more 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.
arXiv (Cornell University), Jun 16, 2005
The tomographic histories approach is presented. As an inverse problem, we recover in an operatio... more 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.
arXiv (Cornell University), Nov 15, 2006
arXiv (Cornell University), Nov 13, 2002
We claim that both multipartiteness and localization of subsystems of compound quantum systems ar... more 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.
arXiv (Cornell University), Jun 16, 2005
The tomographic histories approach is presented. As an inverse problem, we recover in an operatio... more 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.
WSEAS TRANSACTIONS ON SYSTEMS, 2020
Topos formalism for quantum mechanics is interpreted in a broader, information retrieval, perspec... more Topos formalism for quantum mechanics is interpreted in a broader, information retrieval, perspective. Contexts, its basic components, are treated as sources of information. Their interplay, called daseinisation, defined in purely logical terms, is reformulated in terms of two relations: exclusion and preclusion of queries. Then, broadening these options, daseinisation becomes a characteristic of proximity of contexts; to quantify it numerically, Shannon entropy is used.
Studies in Computational Intelligence, 2020
I show how space-like structures emerge within the topos-based approach to quantum mechanics. Wit... more I show how space-like structures emerge within the topos-based approach to quantum mechanics. With a physical system, or, more generally, with an operationalistic setup a context category is associated being in fact an ordered collection of contexts. Each context, in turn, is associated with certain configuration space. The minimax context principle is put forward. Its basic idea is that among various configuration spaces the 'physical space' is the configuration space of a structureless point particle. In order to implement it, two order relations on contexts are introduced being analogs of inner and outer daseinisation of projectors. The proposed minimax context principle captures two characteristic features of physical space: maximal with respect to refining the accuracy, and minimal by getting rid of extra degrees of freedom. A Foreword The main goal of this paper is to explore new options, which are provided by topos approach to quantum mechanics. This approach was initially aimed to bring objectivity to quantum mechanics. Its further development made it more general, applicable to a broad class of operationalistic theories, and it was named "Topos foundation for theories of physics" [1, 2, 3], denoted in the sequel by TFTP. In this essay I try to show that within TFTP we can describe how physical space is created as a result of measurements. Why 'created' rather than 'explored'? In brief, the reason is exactly the same as the reason why the value of the spin of a polarized particle emerges as a result of experiment; I illustrate it by a toy model of 'topologimeter'. Begin with a conventional paradigm: we are living in a physical spacetime M. The first step outwards is to state that the spacetime is something pre-existing and
International Journal of Theoretical Physics, 1995
The emphasis is made on the juxtaposition of (quantum theorem) proving versus quantum (theorem pr... more The emphasis is made on the juxtaposition of (quantum theorem) proving versus quantum (theorem proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input) principle is introduced to enhance the resolution of predicate satisfiability problem provided the processor is in a position to perform operations with continuous input. A realization of Zittereingang machine by a quantum system is suggested.
International Journal of Quantum Information, 2007
Given a mixed quantum state ρ of a qudit, we consider any observable M as a kind of "thermom... more Given a mixed quantum state ρ of a qudit, we consider any observable M as a kind of "thermometer" in the following sense. Given a source which emits pure states with certain distributions, we select distributions such that the appropriate average value of the observable M is equal to the average Tr M ρ of M in the state ρ. Among those distributions we find the most typical, namely, having the highest differential entropy. We call this distribution the conditional Gibbs ensemble as it turns out to be a Gibbs distribution characterized by a temperature-like parameter β. The expressions establishing the liaisons between the density operator ρ and its temperature parameter β are provided. Within this approach, the uniform mixed state has the highest "temperature," which tends to zero as the state in question approaches a pure state.
Classical and Quantum Gravity, 2001
A mathematical formalism for treating spacetime topology as a quantum observable is provided. We ... more A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.
arXiv: General Relativity and Quantum Cosmology, 2018
Dual structures on causal sets called timelets are introduced, being discrete analogs of global t... more Dual structures on causal sets called timelets are introduced, being discrete analogs of global time coordinates. Geometrical and algebraic features of the set of timelets on a causal set are studied.
Computational Intelligence. Theory and Applications, 2001
... In particular, we show that the standard quantum adder is perfectly suited to realize Kaufman... more ... In particular, we show that the standard quantum adder is perfectly suited to realize Kaufmann-like addition of fuzzy numbers encoded in the form of suitably prepared superpositions of input qubits and that it does it in a single run. ...
International Journal of Theoretical Physics, 2004
... Page 2. 1424 D'Hooghe, Pykacz, and Zapatrin In Section 2 we recall the main concepts and... more ... Page 2. 1424 D'Hooghe, Pykacz, and Zapatrin In Section 2 we recall the main concepts and ideas of quantum computation treated as a physical process and give examples of quantum gates used to con-struct a quantum adder. ... 2). 2.4. The Full Quantum Adder ...
International Journal of Theoretical Physics, 2004
We introduce superposition-based quantum networks composed of (i) the classical perceptron model ... more We introduce superposition-based quantum networks composed of (i) the classical perceptron model of multilayered, feedforward neural networks and (ii) the algebraic model of evolving reticular quantum structures as described in quantum gravity. The main feature of this model is moving from particular neural topologies to a quantum metastructure which embodies many differing topological patterns. Using quantum parallelism, training is possible on superpositions of different network topologies. As a result, not only classical transition functions, but also topology becomes a subject of training. The main feature of our model is that particular neural networks, with different topologies, are quantum states. We consider high-dimensional dissipative quantum structures as candidates for implementation of the model.
International Journal of Theoretical Physics, 2005
We claim that both multipartiteness and localization of subsystems of compound quantum systems ar... more 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.
Beyond Peaceful Coexistence, Apr 4, 2016
The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realitie... more The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realities. To what extent are these 'realities' real? Which 'physics' should be applied to quantitatively describe them? In this essay I dwell on few examples. The first is Adaptive neural networks, which are not networks and not neural, but still provide service similar to classical ANNs in extended fashion. The second is the emergence of objects looking like Einsteinian spacetime, which describe the behavior of an Internet surfer like geodesic motion. The third is the demonstration of nonclassical and even stronger-thanquantum probabilities in Information Retrieval, their use. Immense operable datasets provide new operationalistic environments, which become to greater and greater extent "realities". In this essay, I consider the overall Information Retrieval process as an objective physical process, representing it according to Melucci metaphor in terms of physical-like experiments. Various semantic environments are treated as analogs of various realities. The readers' attention is drawn to topos approach to physical theories, which provides a natural conceptual and technical framework to cope with the new emerging realities.
International Journal of Theoretical Physics, 1993
We want to show in this paper that it is possible to construct macroscopical entities that entail... more We want to show in this paper that it is possible to construct macroscopical entities that entail a quantum logical structure. We do this by means of the introduction of a simple macroscopical entity and study its structure in terms of lattices and graphs, and show that the lattice is non-Boolean.
A liaison between quantum logics and non-commutative differential geometry is outlined: a class o... more A liaison between quantum logics and non-commutative differential geometry is outlined: a class of quantum logics are proved to possess the structure of discrete differential manifolds. We show that the set of proper elements of an arbitrary atomic Greechie logic is naturally endowed by Koszul’s differential calculus.
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Papers by Roman R Zapatrin