11,160 research outputs found
Shift Radix Systems - A Survey
Let be an integer and . The {\em shift radix system} is defined by has the {\em finiteness
property} if each is eventually mapped to
under iterations of . In the present survey we summarize
results on these nearly linear mappings. We discuss how these mappings are
related to well-known numeration systems, to rotations with round-offs, and to
a conjecture on periodic expansions w.r.t.\ Salem numbers. Moreover, we review
the behavior of the orbits of points under iterations of with
special emphasis on ultimately periodic orbits and on the finiteness property.
We also describe a geometric theory related to shift radix systems.Comment: 45 pages, 16 figure
Rational self-affine tiles
An integral self-affine tile is the solution of a set equation , where
is an integer matrix and is a finite
subset of . In the recent decades, these objects and the induced
tilings have been studied systematically. We extend this theory to matrices
. We define rational self-affine tiles
as compact subsets of the open subring of the ad\'ele ring , where the factors of the
(finite) product are certain -adic completions of a number field
that is defined in terms of the characteristic polynomial of .
Employing methods from classical algebraic number theory, Fourier analysis in
number fields, and results on zero sets of transfer operators, we establish a
general tiling theorem for these tiles. We also associate a second kind of
tiles with a rational matrix. These tiles are defined as the intersection of a
(translation of a) rational self-affine tile with . Although these intersection
tiles have a complicated structure and are no longer self-affine, we are able
to prove a tiling theorem for these tiles as well. For particular choices of
digit sets, intersection tiles are instances of tiles defined in terms of shift
radix systems and canonical number systems. Therefore, we gain new results for
tilings associated with numeration systems
Scaling of nascent nodes in extended s-wave superconductors
We analyze the low-energy properties of superconductors near the onset of
accidental nodes, i.e. zeroes of the gap function not enforced by symmetry. The
existence of such nodes has been motivated by recent experiments suggesting a
transition between nodeless and nodal superconductivity in iron-based
compounds. We find that the low-temperature behavior of the penetration depth,
the specific heat, and the NMR spin-lattice relaxation rate are determined by
the scaling properties of a quantum critical point associated with the nascent
nodes. Although the power-law exponents are insensitive to weak short-range
electronic interactions, they can be significantly altered by the curvature of
the Fermi surface or by the three-dimensional character of the gap.
Consequently, the behavior of macroscopic quantities near the onset of nodes
can be used as a criterion to determine the nodal structure of the gap
function.Comment: minor changes; version accepted for publicatio
Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings
We study link-diluted Ising spin glass models on the hierarchical
lattice and on a three-dimensional lattice close to the percolation threshold.
We show that previously computed zero temperature fixed points are unstable
with respect to temperature perturbations and do not belong to any critical
line in the dilution-temperature plane. We discuss implications of the presence
of such spurious unstable fixed points on the use of optimization algorithms,
and we show how entropic effects should be taken into account to obtain the
right physical behavior and critical points.Comment: 4 pages, 4 figures. A major typo error in formula (8) has been
correcte
Self-affine Manifolds
This paper studies closed 3-manifolds which are the attractors of a system of
finitely many affine contractions that tile . Such attractors are
called self-affine tiles. Effective characterization and recognition theorems
for these 3-manifolds as well as theoretical generalizations of these results
to higher dimensions are established. The methods developed build a bridge
linking geometric topology with iterated function systems and their attractors.
A method to model self-affine tiles by simple iterative systems is developed
in order to study their topology. The model is functorial in the sense that
there is an easily computable map that induces isomorphisms between the natural
subdivisions of the attractor of the model and the self-affine tile. It has
many beneficial qualities including ease of computation allowing one to
determine topological properties of the attractor of the model such as
connectedness and whether it is a manifold. The induced map between the
attractor of the model and the self-affine tile is a quotient map and can be
checked in certain cases to be monotone or cell-like. Deep theorems from
geometric topology are applied to characterize and develop algorithms to
recognize when a self-affine tile is a topological or generalized manifold in
all dimensions. These new tools are used to check that several self-affine
tiles in the literature are 3-balls. An example of a wild 3-dimensional
self-affine tile is given whose boundary is a topological 2-sphere but which is
not itself a 3-ball. The paper describes how any 3-dimensional handlebody can
be given the structure of a self-affine 3-manifold. It is conjectured that
every self-affine tile which is a manifold is a handlebody.Comment: 40 pages, 13 figures, 2 table
Merging Automobile Insurance Regulatory Bodies: The Case of Atlantic Canada
The recent automobile liability insurance crisis in Atlantic Canada has prompted the four provincial legislations (Newfoundland and Labrador, New Brunswick, Nova Scotia and Prince Edward Island) to setup a task force to redesign, if necessary, the personal automobile insurance system. After reviewing some of the most interesting new regulatory changes, our paper proposes a new area of discussion: The merger of the four provincial insurance regulatory bodies to combat insurance fraud. We base our paper on the principle that recent premium increases are mainly due to an increase in insurance fraud. We show that merging the regulatory bodies may reduce insurance fraud if the merger allows savings on the average audit cost and on the development of better fraud detection technology. Finally, we suggest a fraud reducing insurance taxation scheme to finance insurance fraud investigations. La récente crise dans le Canada Atlantique au sujet de l'assurance de la responsabilité civile des automobilistes a contraint les gouvernements des quatre provinces (Terre-Neuve et Labrador, Nouveau-Brunswick, Nouvelle-Écosse et l'Île-du-Prince-Édouard) à mettre en place une commission pour étudier la possibilité de réorganiser, si nécessaire, leur système d'assurance automobile. Après avoir analysé les plus intéressantes modifications à la réglementation mises en place dans ces provinces, notre étude offre un nouveau terrain de discussion, soit la fusion des quatre réglementations provinciales afin de combattre la fraude à l'assurance. Notre étude se base sur le principe que les récentes augmentations dans les primes sont attribuables à une augmentation de la fraude à l'assurance dans ces provinces. En fusionnant les réglementations des quatre provinces, nous montrons que la fraude à l'assurance peut diminuer si la fusion permet d'épargner une partie du coût de vérification encouru par les assureurs lors de réclamations douteuses. Également, nous montrons qu'une telle fusion peut permettre de développer une meilleure technologie de vérification des réclamations. Nous terminons le papier en suggérant un système de taxation particulier qui non seulement peut financer les investissements nécessaires pour combattre la fraude, mais peut également réduire la fraude directement.insurance fraud, asymmetric information, insurance taxation, public policy, fraude à l'assurance, information asymétrique, taxation à l'assurance, politique publique
Merging automobile regulatory bodies: The case of Atlantic Canada
The recent automobile liability insurance crisis in Atlantic Canada has prompted the four provincial legislations (Newfoundland and Labrador, New Brunswick, Nova Scotia and Prince Edward Island) to setup a task force to redesign, if necessary, the personal automobile insurance system. After reviewing some of the most interesting new regulatory changes, our paper proposes a new area of discussion: The merger of the four provincial insurance regulatory bodies to combat insurance fraud. We base our paper on the principle that recent premium increases are mainly due to an increase in insurance fraud. We show that merging the regulatory bodies may reduce insurance fraud if the merger allows savings on the average audit cost and on the development of better fraud detection technology. Finally, we suggest a fraud reducing insurance taxation scheme to finance insurance fraud investigations. --Insurance Fraud,Asymmetric Information,Insurance Taxation,Public Policy
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