492,273 research outputs found
A QBF-based Formalization of Abstract Argumentation Semantics
Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).Peer reviewedPostprin
Reliable Modeling of Ideal Generic Memristors via State-Space Transformation
The paper refers to problems of modeling and computer simulation of generic memristors caused by the so-called window functions, namely the stick effect, nonconvergence, and finding fundamentally incorrect solutions. A profoundly different modeling approach is proposed, which is mathematically equivalent to window-based modeling. However, due to its numerical stability, it definitely smoothes the above problems away
Finite Groebner bases in infinite dimensional polynomial rings and applications
We introduce the theory of monoidal Groebner bases, a concept which
generalizes the familiar notion in a polynomial ring and allows for a
description of Groebner bases of ideals that are stable under the action of a
monoid. The main motivation for developing this theory is to prove finiteness
theorems in commutative algebra and its applications. A major result of this
type is that ideals in infinitely many indeterminates stable under the action
of the symmetric group are finitely generated up to symmetry. We use this
machinery to give new proofs of some classical finiteness theorems in algebraic
statistics as well as a proof of the independent set conjecture of Hosten and
the second author.Comment: 24 pages, adds references to work of Cohen, adds more details in
Section
Symmetry Algebras of Large-N Matrix Models for Open Strings
We have discovered that the gauge invariant observables of matrix models
invariant under U() form a Lie algebra, in the planar large-N limit. These
models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We
study here the gauge invariant states corresponding to open strings (`mesons').
We find that the algebra is an extension of a remarkable new Lie algebra by a product of more well-known algebras such as
and the Cuntz algebra. appears to be a generalization of
the Lie algebra of vector fields on the circle to non-commutative geometry. We
also use a representation of our Lie algebra to establish an isomorphism
between certain matrix models (those that preserve `gluon number') and open
quantum spin chains. Using known results on quantum spin chains, we are able to
identify some exactly solvable matrix models. Finally, the Hamiltonian of a
dimensionally reduced QCD model is expressed explicitly as an element of our
Lie algebra.Comment: 44 pages, 8 eps figures, 3 tables, LaTeX2.09; this is the published
versio
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