59,627 research outputs found
A Taxonomy for Attack Patterns on Information Flows in Component-Based Operating Systems
We present a taxonomy and an algebra for attack patterns on component-based
operating systems. In a multilevel security scenario, where isolation of
partitions containing data at different security classifications is the primary
security goal and security breaches are mainly defined as undesired disclosure
or modification of classified data, strict control of information flows is the
ultimate goal. In order to prevent undesired information flows, we provide a
classification of information flow types in a component-based operating system
and, by this, possible patterns to attack the system. The systematic
consideration of informations flows reveals a specific type of operating system
covert channel, the covert physical channel, which connects two former isolated
partitions by emitting physical signals into the computer's environment and
receiving them at another interface.Comment: 9 page
Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
We express AKNS hierarchies, admitting reductions to matrix NLS and matrix
mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a
universal result in this framework quickly generates an infinite family of
exact solutions, including e.g. the matrix solitons in the focusing NLS case.
Exploiting a general Miura transformation, we recover the generalized
Heisenberg magnet hierarchy and establish a corresponding solution formula for
it. Simply by exchanging the roles of the two derivations of the bidifferential
graded algebra, we recover "negative flows", leading to an extension of the
respective hierarchy. In this way we also meet a matrix and vector version of
the short pulse equation and also the sine-Gordon equation. For these equations
corresponding solution formulas are also derived. In all these cases the
solutions are parametrized in terms of matrix data that have to satisfy a
certain Sylvester equation
Factorization and the Dressing Method for the Gel'fand-Dikii Hierarch
The isospectral flows of an order linear scalar differential
operator under the hypothesis that it possess a Baker-Akhiezer function
were originally investigated by Segal and Wilson from the point of view of
infinite dimensional Grassmanians, and the reduction of the KP hierarchy to the
Gel'fand-Dikii hierarchy. The associated first order systems and their formal
asymptotic solutions have a rich Lie algebraic structure which was investigated
by Drinfeld and Sokolov. We investigate the matrix Riemann-Hilbert
factorizations for these systems, and show that different factorizations lead
respectively to the potential, modified, and ordinary Gel'fand-Dikii flows. Lie
algebra decompositions (the Adler-Kostant-Symes method) are obtained for the
modified and potential flows. For the appropriate factorization for the
Gel'fand-Dikii flows is not a group factorization, as would be expected; yet a
modification of the dressing method still works.
A direct proof, based on a Fredholm determinant associated with the
factorization problem, is given that the potentials are meromorphic in and
in the time variables. Potentials with Baker-Akhiezer functions include the
multisoliton and rational solutions, as well as potentials in the scattering
class with compactly supported scattering data. The latter are dense in the
scattering class
Lax operator algebras and Hamiltonian integrable hierarchies
We consider the theory of Lax equations in complex simple and reductive
classical Lie algebras with the spectral parameter on a Riemann surface of
finite genus. Our approach is based on the new objects -- the Lax operator
algebras, and develops the approach of I.Krichever treating the \gl(n) case.
For every Lax operator considered as the mapping sending a point of the
cotangent bundle on the space of extended Tyrin data to an element of the
corresponding Lax operator algebra we construct the hierarchy of mutually
commuting flows given by Lax equations and prove that those are Hamiltonian
with respect to the Krichever-Phong symplectic structure. The corresponding
Hamiltonians give integrable finite-dimensional Hitchin-type systems. For
example we derive elliptic , , Calogero-Moser systems in frame
of our approach.Comment: 27 page
Asymptotic Identity in Min-Plus Algebra: A Report on CPNS
Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions
Hyper-K{\"a}hler Hierarchies and their twistor theory
A twistor construction of the hierarchy associated with the hyper-K\"ahler
equations on a metric (the anti-self-dual Einstein vacuum equations, ASDVE, in
four dimensions) is given. The recursion operator R is constructed and used to
build an infinite-dimensional symmetry algebra and in particular higher flows
for the hyper-K\"ahler equations. It is shown that R acts on the twistor data
by multiplication with a rational function. The structures are illustrated by
the example of the Sparling-Tod (Eguchi-Hansen) solution. An extended
space-time is constructed whose extra dimensions correspond to
higher flows of the hierarchy. It is shown that is a moduli space of
rational curves with normal bundle in twistor
space and is canonically equipped with a Lax distribution for ASDVE
hierarchies. The space is shown to be foliated by four dimensional
hyper-K{\"a}hler slices. The Lagrangian, Hamiltonian and bi-Hamiltonian
formulations of the ASDVE in the form of the heavenly equations are given. The
symplectic form on the moduli space of solutions to heavenly equations is
derived, and is shown to be compatible with the recursion operator.Comment: 23 pages, 1 figur
Modular Index Invariants of Mumford Curves
We continue an investigation initiated by Consani-Marcolli of the relation between the algebraic geometry of p-adic Mumford curves and the noncommutative geometry of graph C*-algebras associated to the action of the uniformizing p-adic Schottky group on the Bruhat-Tits tree. We reconstruct invariants of Mumford curves related to valuations of generators of the associated Schottky group, by developing a graphical theory for KMS weights on the associated graph C*-algebra, and using modular index theory for KMS weights. We give explicit examples of the construction of graph weights for low genus Mumford curves. We then show that the theta functions of Mumford curves, and the induced currents on the Bruhat-Tits tree, define functions that generalize the graph weights. We show that such inhomogeneous graph weights can be constructed from spectral flows, and that one can reconstruct theta functions from such graphical data
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