309 research outputs found
About Folding-Unfolding Cuts and Cuts Modulo
We show in this note that cut elimination in deduction modulo subsumes cut elimination in deduction with the folding and unfolding rules
Normalization in Supernatural deduction and in Deduction modulo
Deduction modulo and Supernatural deduction are two extentions of predicate logic with computation rules. Whereas the application of computation rules in deduction modulo is transparent, these rules are used to build non-logical deduction rules in Supernatural deduction. In both cases, adding computation rules may jeopardize proof normalization, but various conditions have been given in both cases, so that normalization is preserved. We prove in this paper that normalization in Supernatural deduction and in Deduction modulo are equivalent, i.e. the set of computation rules for which one system strongly normalizes is the same as the set of computation rules for which the other is
Deduction modulo theory
This paper is a survey on Deduction modulo theor
The Stratified Foundations as a theory modulo
The Stratified Foundations are a restriction of naive set theory where the
comprehension scheme is restricted to stratifiable propositions. It is known
that this theory is consistent and that proofs strongly normalize in this
theory. Deduction modulo is a formulation of first-order logic with a general
notion of cut. It is known that proofs normalize in a theory modulo if it has
some kind of many-valued model called a pre-model. We show in this paper that
the Stratified Foundations can be presented in deduction modulo and that the
method used in the original normalization proof can be adapted to construct a
pre-model for this theory
Tiling Billards on Triangle Tilings, and Interval Exchange Transformations
We consider the dynamics of light rays in triangle tilings where triangles
are transparent and adjacent triangles have equal but opposite indices of
refraction. We find that the behavior of a trajectory on a triangle tiling is
described by an orientation-reversing three-interval exchange transformation on
the circle, and that the behavior of all the trajectories on a given triangle
tiling is described by a polygon exchange transformation. We show that, for a
particular choice of triangle tiling, certain trajectories approach the Rauzy
fractal, under rescaling.Comment: 31 pages, 19 figures, 2 appendices. Comments welcome
Unstructured intermediate states in single protein force experiments
Recent single-molecule force measurements on single-domain proteins have
highlighted a three-state folding mechanism where a stabilized intermediate
state (I) is observed on the folding trajectory between the stretched state and
the native state. Here we investigate on-lattice protein-like heteropolymer
models that lead to a three-state mechanism and show that force experiments can
be useful to determine the structure of I. We have mostly found that I is
composed of a core stabilized by a high number of native contacts, plus an
unstructured extended chain. The lifetime of I is shown to be sensitive to
modifications of the protein that spoil the core. We then propose three types
of modifications--point mutations, cuts, and circular permutations--aiming at:
(1) confirming the presence of the core and (2) determining its location,
within one amino acid accuracy, along the polypeptide chain. We also propose
force jump protocols aiming to probe the on/off-pathway nature of I.Comment: 10 page
The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
Infrared divergences in scattering amplitudes arise when a loop momentum
becomes collinear with a massless external momentum . In gauge
theories, it is known that the L-loop logarithm of a planar amplitude has much
softer infrared singularities than the L-loop amplitude itself. We argue that
planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected
behavior as already at the level of the integrand. Moreover,
we conjecture that the four-point integrand can be uniquely determined, to any
loop-order, by imposing the correct soft-behavior of the logarithm together
with dual conformal invariance and dihedral symmetry. We use these simple
criteria to determine explicit formulae for the four-point integrand through
seven-loops, finding perfect agreement with previously known results through
five-loops. As an input to this calculation we enumerate all four-point dual
conformally invariant (DCI) integrands through seven-loops, an analysis which
is aided by several graph-theoretic theorems we prove about general DCI
integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive
non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica
files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7
corrected, Lemma 2 remove
On the convergence of reduction-based and model-based methods in proof theory
In the recent past, the reduction-based and the model-based methods to prove
cut elimination have converged, so that they now appear just as two sides of
the same coin. This paper details some of the steps of this transformation
- …