12,048 research outputs found
A template-based approach for the generation of abstractable and reducible models of featured networks
We investigate the relationship between symmetry reduction and inductive reasoning when applied to model checking networks of featured components. Popular reduction techniques for combatting state space explosion in model checking, like abstraction and symmetry reduction, can only be applied effectively when the natural symmetry of a system is not destroyed during specification. We introduce a property which ensures this is preserved, open symmetry. We describe a template-based approach for the construction of open symmetric Promela specifications of featured systems. For certain systems (safely featured parameterised systems) our generated specifications are suitable for conversion to abstract specifications representing any size of network. This enables feature interaction analysis to be carried out, via model checking and induction, for systems of any number of featured components. In addition, we show how, for any balanced network of components, by using a graphical representation of the features and the process communication structure, a group of permutations of the underlying state space of the generated specification can be determined easily. Due to the open symmetry of our Promela specifications, this group of permutations can be used directly for symmetry reduced model checking.
The main contributions of this paper are an automatic method for developing open symmetric specifications which can be used for generic feature interaction analysis, and the novel application of symmetry detection and reduction in the context of model checking featured networks.
We apply our techniques to a well known example of a featured network â an email system
Euler number of Instanton Moduli space and Seiberg-Witten invariants
We show that a partition function of topological twisted N=4 Yang-Mills
theory is given by Seiberg-Witten invariants on a Riemannian four manifolds
under the condition that the sum of Euler number and signature of the four
manifolds vanish. The partition function is the sum of Euler number of
instanton moduli space when it is possible to apply the vanishing theorem. And
we get a relation of Euler number labeled by the instanton number with
Seiberg-Witten invariants, too. All calculation in this paper is done without
assuming duality.Comment: LaTeX, 34 page
Introduction - History, Politics, Law
It would be difficult to find a major figure in the history of European political thought who would not have attempted to say something about how authority emerges, or is justified and critiqued, in the world beyond the single polity. Quite frequently, that effort would have involved some idea about a legal order, or at least a set of rules or regularities applicable in that world. Thomas Hobbes was neither the first nor the last major thinker who believed that the âinternationalâ realm was characterised by the independence of states existing âin the state and posture of gladiatorsâ, thus apparently denying that legal rules or practices or legal thinking could have much relevance therein. Yet others believed, as Immanuel Kant did, that without a constitutional vocabulary not much that was meaningful could be said about the human pursuit of freedom, and that silence about the latter would not only constitute a moral failure but an intellectual and perhaps political mistake. For a long time, the idiom of natural law claimed to offer a universally valid frame for thinking about the nature of the political, as well as providing authority for lawyersâ speculations about the rules and principles governing the conduct of individuals and corporate bodies wherever they might move. The name of the relevant discipline at German universities from the late seventeenth century onwards â ius naturae et gentium, the law of nature and of nations â revealed the full scope of its ambition. That discipline may have died away (although that is a debatable proposition) but any political thinking worth its salt will today (perhaps especially in the twenty-first century) aim to say something about how authority emerges, is maintained or critiqued not only within but also outside the single state. The world of ânationsâ or even âhumanityâ is established as an important theme of political and legal speculation
Exotic Smoothness and Physics
The essential role played by differentiable structures in physics is reviewed
in light of recent mathematical discoveries that topologically trivial
space-time models, especially the simplest one, , possess a rich
multiplicity of such structures, no two of which are diffeomorphic to each
other and thus to the standard one. This means that physics has available to it
a new panoply of structures available for space-time models. These can be
thought of as source of new global, but not properly topological, features.
This paper reviews some background differential topology together with a
discussion of the role which a differentiable structure necessarily plays in
the statement of any physical theory, recalling that diffeomorphisms are at the
heart of the principle of general relativity. Some of the history of the
discovery of exotic, i.e., non-standard, differentiable structures is reviewed.
Some new results suggesting the spatial localization of such exotic structures
are described and speculations are made on the possible opportunities that such
structures present for the further development of physical theories.Comment: 13 pages, LaTe
Donaldson-Thomas invariants and wall-crossing formulas
Notes from the report at the Fields institute in Toronto. We introduce the
Donaldson-Thomas invariants and describe the wall-crossing formulas for
numerical Donaldson-Thomas invariants.Comment: 18 pages. To appear in the Fields Institute Monograph Serie
Noncommutative Deformation of Spinor Zero Mode and ADHM Construction
A method to construct noncommutative instantons as deformations from
commutative instantons was provided in arXiv:0805.3373. Using this
noncommutative deformed instanton, we investigate the spinor zero modes of the
Dirac operator in a noncommutative instanton background on noncommutative R^4,
and we modify the index of the Dirac operator on the noncommutative space
slightly and show that the number of the zero mode of the Dirac operator is
preserved under the noncommutative deformation. We prove the existence of the
Green's function associated with instantons on noncommutative R^4, as a smooth
deformation of the commutative case. The feature of the zero modes of the Dirac
operator and the Green's function derives noncommutative ADHM equations which
coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one
correspondence between the instantons on noncommutative R^4 and ADHM data. An
example of a noncommutative instanton and a spinor zero mode are also given.Comment: 34 pages, no figures, v3: an appendix and some definitions
added,typos correcte
Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds
We adapt the notions of stability of holomorphic vector bundles in the sense
of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector
bundles for canonically polarized framed manifolds, i.e. compact complex
manifolds X together with a smooth divisor D such that K_X \otimes [D] is
ample. It turns out that the degree of a torsion-free coherent sheaf on X with
respect to the polarization K_X \otimes [D] coincides with the degree with
respect to the complete K\"ahler-Einstein metric g_{X \setminus D} on X
\setminus D. For stable holomorphic vector bundles, we prove the existence of a
Hermitian-Einstein metric with respect to g_{X \setminus D} and also the
uniqueness in an adapted sense.Comment: 21 pages, International Journal of Mathematics (to appear
Higher Spin Gravitational Couplings and the Yang--Mills Detour Complex
Gravitational interactions of higher spin fields are generically plagued by
inconsistencies. We present a simple framework that couples higher spins to a
broad class of gravitational backgrounds (including Ricci flat and Einstein)
consistently at the classical level. The model is the simplest example of a
Yang--Mills detour complex, which recently has been applied in the mathematical
setting of conformal geometry. An analysis of asymptotic scattering states
about the trivial field theory vacuum in the simplest version of the theory
yields a rich spectrum marred by negative norm excitations. The result is a
theory of a physical massless graviton, scalar field, and massive vector along
with a degenerate pair of zero norm photon excitations. Coherent states of the
unstable sector of the model do have positive norms, but their evolution is no
longer unitary and their amplitudes grow with time. The model is of
considerable interest for braneworld scenarios and ghost condensation models,
and invariant theory.Comment: 19 pages LaTe
The ADHM Construction of Instantons on Noncommutative Spaces
We present an account of the ADHM construction of instantons on Euclidean
space-time from the point of view of noncommutative geometry. We
recall the main ingredients of the classical construction in a coordinate
algebra format, which we then deform using a cocycle twisting procedure to
obtain a method for constructing families of instantons on noncommutative
space-time, parameterised by solutions to an appropriate set of ADHM equations.
We illustrate the noncommutative construction in two special cases: the
Moyal-Groenewold plane and the Connes-Landi plane
.Comment: Latex, 40 page
N=2 Topological Yang-Mills Theory on Compact K\"{a}hler Surfaces
We study a topological Yang-Mills theory with fermionic symmetry. Our
formalism is a field theoretical interpretation of the Donaldson polynomial
invariants on compact K\"{a}hler surfaces. We also study an analogous theory on
compact oriented Riemann surfaces and briefly discuss a possible application of
the Witten's non-Abelian localization formula to the problems in the case of
compact K\"{a}hler surfaces.Comment: ESENAT-93-01 & YUMS-93-10, 34pages: [Final Version] to appear in
Comm. Math. Phy
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