1,276 research outputs found
Continuous Multiclass Labeling Approaches and Algorithms
We study convex relaxations of the image labeling problem on a continuous
domain with regularizers based on metric interaction potentials. The generic
framework ensures existence of minimizers and covers a wide range of
relaxations of the originally combinatorial problem. We focus on two specific
relaxations that differ in flexibility and simplicity -- one can be used to
tightly relax any metric interaction potential, while the other one only covers
Euclidean metrics but requires less computational effort. For solving the
nonsmooth discretized problem, we propose a globally convergent
Douglas-Rachford scheme, and show that a sequence of dual iterates can be
recovered in order to provide a posteriori optimality bounds. In a quantitative
comparison to two other first-order methods, the approach shows competitive
performance on synthetical and real-world images. By combining the method with
an improved binarization technique for nonstandard potentials, we were able to
routinely recover discrete solutions within 1%--5% of the global optimum for
the combinatorial image labeling problem
Some applications of logic to feasibility in higher types
In this paper we demonstrate that the class of basic feasible functionals has
recursion theoretic properties which naturally generalize the corresponding
properties of the class of feasible functions. We also improve the Kapron -
Cook result on mashine representation of basic feasible functionals. Our proofs
are based on essential applications of logic. We introduce a weak fragment of
second order arithmetic with second order variables ranging over functions from
N into N which suitably characterizes basic feasible functionals, and show that
it is a useful tool for investigating the properties of basic feasible
functionals. In particular, we provide an example how one can extract feasible
"programs" from mathematical proofs which use non-feasible functionals (like
second order polynomials)
Higher Loop Anomalies and their Consistency Conditions in Nonlocal Regularization
An algebraic program of computation and characterization of higher loop BRST
anomalies is presented. We propose a procedure for disentangling a genuine{\it
local} higher loop anomaly from the quantum dressings of lower loop anomalies.
For such higher loop anomalies we derive a local consistency condition, which
is the generalisation of the Wess-Zumino condition for the one-loop anomaly.
The development is presented in the framework of the field-antifield formalism,
making use of a nonlocal regularization method. The theoretical construction is
exemplified by explicitly computing the two-loop anomaly of chiral
gravity. We also give, for the first time, an explicit check of the local
two--loop consistency condition that is associated with this anomaly.Comment: 26 pages, LaTeX2e or LaTeX2.09, 1 figure (uses epsf
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
Theoretical backgrounds of durability analysis by normalized equivalent stress functionals
Generalized durability diagrams and their properties are considered for a material under a multiaxial loading given by an arbitrary function of time. Material strength and durability under such loading are described in terms of durability, safety factor and normalized equivalent stress. Relations between these functionals are analysed. We discuss some material properties including time and load stability, self-degradation (ageing), and monotonic damaging. Phenomenological strength conditions are presented in terms of the normalized equivalent stress. It is shown that the damage based durability analysis is reduced to a particular case of such strength conditions. Examples of the reduction are presented for some known durability models. The approach is applicable to the strength and durability description at creep and impact loading and their combination
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