24,418 research outputs found
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
From Simple to Complex and Ultra-complex Systems:\ud A Paradigm Shift Towards Non-Abelian Systems Dynamics
Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation
Topos Quantum Logic and Mixed States
The topos approach to the formulation of physical theories includes a new
form of quantum logic. We present this topos quantum logic, including some new
results, and compare it to standard quantum logic, all with an eye to
conceptual issues. In particular, we show that topos quantum logic is
distributive, multi-valued, contextual and intuitionistic. It incorporates
superposition without being based on linear structures, has a built-in form of
coarse-graining which automatically avoids interpretational problems usually
associated with the conjunction of propositions about incompatible physical
quantities, and provides a material implication that is lacking from standard
quantum logic. Importantly, topos quantum logic comes with a clear geometrical
underpinning. The representation of pure states and truth-value assignments are
discussed. It is briefly shown how mixed states fit into this approach.Comment: 25 pages; to appear in Electronic Notes in Theoretical Computer
Science (6th Workshop on Quantum Physics and Logic, QPL VI, Oxford, 8.--9.
April 2009), eds. B. Coecke, P. Panangaden, P. Selinger (2010
The Tate conjecture for K3 surfaces in odd characteristic
We show that the classical Kuga-Satake construction gives rise, away from
characteristic 2, to an open immersion from the moduli of primitively polarized
K3 surfaces (of any fixed degree) to a certain regular integral model for a
Shimura variety of orthogonal type. This allows us to attach to every polarized
K3 surface in odd characteristic an abelian variety such that divisors on the
surface can be identified with certain endomorphisms of the attached abelian
variety. In turn, this reduces the Tate conjecture for K3 surfaces over
finitely generated fields of odd characteristic to a version of the Tate
conjecture for certain endomorphisms on the attached Kuga-Satake abelian
variety, which we prove. As a by-product of our methods, we also show that the
moduli stack of primitively polarized K3 surfaces of degree 2d is
quasi-projective and, when d is not divisible by p^2, is geometrically
irreducible in characteristic p. We indicate how the same method applies to
prove the Tate conjecture for co-dimension 2 cycles on cubic fourfolds
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