2,088 research outputs found
Generalizations of the Recursion Theorem
We consider two generalizations of the recursion theorem, namely Visser's ADN
theorem and Arslanov's completeness criterion, and we prove a joint
generalization of these theorems
Effective Genericity and Differentiability
We prove that a real x is 1-generic if and only if every differentiable
computable function has continuous derivative at x. This provides a counterpart
to recent results connecting effective notions of randomness with
differentiability. We also consider multiply differentiable computable
functions and polynomial time computable functions.Comment: Revision: added sections 6-8; minor correction
Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations
In this paper we perform the parameter-dependent center manifold reduction
near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf
bifurcations in delay differential equations (DDEs). This allows us to
initialize the continuation of codimension one equilibria and cycle
bifurcations emanating from these codimension two bifurcation points. The
normal form coefficients are derived in the functional analytic perturbation
framework for dual semigroups (sun-star calculus) using a normalization
technique based on the Fredholm alternative. The obtained expressions give
explicit formulas which have been implemented in the freely available numerical
software package DDE-BifTool. While our theoretical results are proven to apply
more generally, the software implementation and examples focus on DDEs with
finitely many discrete delays. Together with the continuation capabilities of
DDE-BifTool, this provides a powerful tool to study the dynamics near
equilibria of such DDEs. The effectiveness is demonstrated on various models
Flow-based reputation with uncertainty: Evidence-Based Subjective Logic
The concept of reputation is widely used as a measure of trustworthiness
based on ratings from members in a community. The adoption of reputation
systems, however, relies on their ability to capture the actual trustworthiness
of a target. Several reputation models for aggregating trust information have
been proposed in the literature. The choice of model has an impact on the
reliability of the aggregated trust information as well as on the procedure
used to compute reputations. Two prominent models are flow-based reputation
(e.g., EigenTrust, PageRank) and Subjective Logic based reputation. Flow-based
models provide an automated method to aggregate trust information, but they are
not able to express the level of uncertainty in the information. In contrast,
Subjective Logic extends probabilistic models with an explicit notion of
uncertainty, but the calculation of reputation depends on the structure of the
trust network and often requires information to be discarded. These are severe
drawbacks.
In this work, we observe that the `opinion discounting' operation in
Subjective Logic has a number of basic problems. We resolve these problems by
providing a new discounting operator that describes the flow of evidence from
one party to another. The adoption of our discounting rule results in a
consistent Subjective Logic algebra that is entirely based on the handling of
evidence. We show that the new algebra enables the construction of an automated
reputation assessment procedure for arbitrary trust networks, where the
calculation no longer depends on the structure of the network, and does not
need to throw away any information. Thus, we obtain the best of both worlds:
flow-based reputation and consistent handling of uncertainties
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