1,829 research outputs found
Renormalization of Crumpled Manifolds
We consider a model of D-dimensional tethered manifold interacting by
excluded volume in R^d with a single point. By use of intrinsic distance
geometry, we first provide a rigorous definition of the analytic continuation
of its perturbative expansion for arbitrary D, 0 < D < 2. We then construct
explicitly a renormalization operation, ensuring renormalizability to all
orders. This is the first example of mathematical construction and
renormalization for an interacting extended object with continuous internal
dimension, encompassing field theory.Comment: 10 pages (1 figure, included), harvmac, SPhT/92-15
A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics
A ``hybrid method'', dedicated to asymptotic coefficient extraction in
combinatorial generating functions, is presented, which combines Darboux's
method and singularity analysis theory. This hybrid method applies to functions
that remain of moderate growth near the unit circle and satisfy suitable
smoothness assumptions--this, even in the case when the unit circle is a
natural boundary. A prime application is to coefficients of several types of
infinite product generating functions, for which full asymptotic expansions
(involving periodic fluctuations at higher orders) can be derived. Examples
relative to permutations, trees, and polynomials over finite fields are treated
in this way.Comment: 31 page
Recommended from our members
Approximate comparison of distance automata
Distance automata are automata weighted over the semiring (N∪ {∞}, min,+) (the tropical semiring). Such automata compute functions from words to N
∪{∞} such as the number of occurrences of a given letter. It is known that testing f 0 and two functions f,g computed by distance automata, answers "yes" if f <= (1-ε ) g, "no" if f \not\leq g, and may answer "yes" or "no" in all other cases. This result highly refines previously known decidability results of the same type. The core argument behind this quasi-decision procedure is an algorithm which is able to provide an approximated finite presentation to the closure under products of sets of matrices over the tropical semiring. We also provide another theorem, of affine domination, which shows that previously known decision procedures for cost-automata have an improved precision when used over distance automata
Graphs Identified by Logics with Counting
We classify graphs and, more generally, finite relational structures that are
identified by C2, that is, two-variable first-order logic with counting. Using
this classification, we show that it can be decided in almost linear time
whether a structure is identified by C2. Our classification implies that for
every graph identified by this logic, all vertex-colored versions of it are
also identified. A similar statement is true for finite relational structures.
We provide constructions that solve the inversion problem for finite
structures in linear time. This problem has previously been shown to be
polynomial time solvable by Martin Otto. For graphs, we conclude that every
C2-equivalence class contains a graph whose orbits are exactly the classes of
the C2-partition of its vertex set and which has a single automorphism
witnessing this fact.
For general k, we show that such statements are not true by providing
examples of graphs of size linear in k which are identified by C3 but for which
the orbit partition is strictly finer than the Ck-partition. We also provide
identified graphs which have vertex-colored versions that are not identified by
Ck.Comment: 33 pages, 8 Figure
- …