9,373 research outputs found
Wild Ramification and the Cotangent Bundle
We define the characteristic cycle of a locally constant \'etale sheaf on a
smooth variety in positive characteristic ramified along boundary as a cycle in
the cotangent bundle of the variety, at least on a neighborhood of the generic
point of the divisor on the boundary. The crucial ingredient in the definition
is an additive structure on the boundary induced by the groupoid structure of
multiple self products.
We prove a compatibility with pull-back and local acyclicity in
non-characteristic situations. We also give a relation with the characteristic
cohomology class under a certain condition and a concrete example where the
intersection with the 0-section computes the Euler-Poincar\'e characteristic.Comment: 56 pages. In v2, the local acyclicity is proved in Proposition 3.14.
In v3, errors in Examples 2.18.2 and 3.18 are corrected. In v4, the
assumption in Proposition 3.14 on local acyclicity is weakened. In v5,
Conjectures on the integrality of the characteristic cycle and on the total
dimension of nearby cycles are formulated. In v6, some corrections are made
and explanations are adde
On the modelling of highly elastic flows of amorphous thermoplastics
Two approaches to the kinematic structuring of constitutive models for highly elastic flows of polymer melts have been examined systematically, assuming either: (1) additivity of elastic and viscous velocity gradients or (2) multiplicability of elastic and viscous deformation gradients. A series of constitutive models were compared, with differing kinematic structure but the same linear responses in elastic and viscous limits. They were solved numerically and their predictions compared, and they were also compared to those of the Giesekus model. Several variants, previously proposed as separate models, are shown to be equivalent and qualitatively in agreement with experiment, and therefore a sound basis for construction of models. But the assignment of viscous spin is critical: if it is assumed equal to the total spin with approach (1), or equal to zero with approach (2), then unphysical viscoelastic behaviour is predicted. © 2008 Elsevier Ltd. All rights reserved
Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery
In this work we address the problem of recovering sparse solutions to non
linear inverse problems. We look at two variants of the basic problem, the
synthesis prior problem when the solution is sparse and the analysis prior
problem where the solution is cosparse in some linear basis. For the first
problem, we propose non linear variants of the Orthogonal Matching Pursuit
(OMP) and CoSamp algorithms; for the second problem we propose a non linear
variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the
success rates of our algorithms on exponential and logarithmic functions. We
model speckle denoising as a non linear sparse recovery problem and apply our
technique to solve it. Results show that our method outperforms state of the
art methods in ultrasound speckle denoising
Logarithmic extensions of minimal models: characters and modular transformations
We study logarithmic conformal field models that extend the (p,q) Virasoro
minimal models. For coprime positive integers and , the model is defined
as the kernel of the two minimal-model screening operators. We identify the
field content, construct the W-algebra W(p,q) that is the model symmetry (the
maximal local algebra in the kernel), describe its irreducible modules, and
find their characters. We then derive the SL(2,Z) representation on the space
of torus amplitudes and study its properties. From the action of the
screenings, we also identify the quantum group that is Kazhdan--Lusztig-dual to
the logarithmic model.Comment: 43pp., AMSLaTeX++. V3: Some explanatory comments added, notational
inaccuracies corrected, references adde
LASSO ISOtone for High Dimensional Additive Isotonic Regression
Additive isotonic regression attempts to determine the relationship between a
multi-dimensional observation variable and a response, under the constraint
that the estimate is the additive sum of univariate component effects that are
monotonically increasing. In this article, we present a new method for such
regression called LASSO Isotone (LISO). LISO adapts ideas from sparse linear
modelling to additive isotonic regression. Thus, it is viable in many
situations with high dimensional predictor variables, where selection of
significant versus insignificant variables are required. We suggest an
algorithm involving a modification of the backfitting algorithm CPAV. We give a
numerical convergence result, and finally examine some of its properties
through simulations. We also suggest some possible extensions that improve
performance, and allow calculation to be carried out when the direction of the
monotonicity is unknown
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