8,183 research outputs found
Decidability of the interval temporal logic ABBar over the natural numbers
In this paper, we focus our attention on the interval temporal logic of the
Allen's relations "meets", "begins", and "begun by" (ABBar for short),
interpreted over natural numbers. We first introduce the logic and we show that
it is expressive enough to model distinctive interval properties,such as
accomplishment conditions, to capture basic modalities of point-based temporal
logic, such as the until operator, and to encode relevant metric constraints.
Then, we prove that the satisfiability problem for ABBar over natural numbers
is decidable by providing a small model theorem based on an original
contraction method. Finally, we prove the EXPSPACE-completeness of the proble
Begin, After, and Later: a Maximal Decidable Interval Temporal Logic
Interval temporal logics (ITLs) are logics for reasoning about temporal
statements expressed over intervals, i.e., periods of time. The most famous ITL
studied so far is Halpern and Shoham's HS, which is the logic of the thirteen
Allen's interval relations. Unfortunately, HS and most of its fragments have an
undecidable satisfiability problem. This discouraged the research in this area
until recently, when a number non-trivial decidable ITLs have been discovered.
This paper is a contribution towards the complete classification of all
different fragments of HS. We consider different combinations of the interval
relations Begins, After, Later and their inverses Abar, Bbar, and Lbar. We know
from previous works that the combination ABBbarAbar is decidable only when
finite domains are considered (and undecidable elsewhere), and that ABBbar is
decidable over the natural numbers. We extend these results by showing that
decidability of ABBar can be further extended to capture the language
ABBbarLbar, which lays in between ABBar and ABBbarAbar, and that turns out to
be maximal w.r.t decidability over strongly discrete linear orders (e.g. finite
orders, the naturals, the integers). We also prove that the proposed decision
procedure is optimal with respect to the complexity class
Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality
We consider a family of vector fields defined in some bounded domain of R^p,
and we assume that they satisfy Hormander's rank condition of some step r, and
that their coefficients have r-1 continuous derivatives. We extend to this
nonsmooth context some results which are well-known for smooth Hormander's
vector fields, namely: some basic properties of the distance induced by the
vector fields, the doubling condition, Chow's connectivity theorem, and, under
the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's
inequality. By known results, these facts also imply a Sobolev embedding. All
these tools allow to draw some consequences about second order differential
operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous
version) changed. Some references adde
Analytic determination of dynamical and mosaic length scales in a Kac glass model
We consider a disordered spin model with multi-spin interactions undergoing a
glass transition. We introduce a dynamic and a static length scales and compute
them in the Kac limit (long--but--finite range interactions). They diverge at
the dynamic and static phase transition with exponents (respectively) -1/4 and
-1. The two length scales are approximately equal well above the mode coupling
transition. Their discrepancy increases rapidly as this transition is
approached. We argue that this signals a crossover from mode coupling to
activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on
Glassy phases in Random Heteropolymers with correlated sequences
We develop a new analytic approach for the study of lattice heteropolymers,
and apply it to copolymers with correlated Markovian sequences. According to
our analysis, heteropolymers present three different dense phases depending
upon the temperature, the nature of the monomer interactions, and the sequence
correlations: (i) a liquid phase, (ii) a ``soft glass'' phase, and (iii) a
``frozen glass'' phase. The presence of the new intermediate ``soft glass''
phase is predicted for instance in the case of polyampholytes with sequences
that favor the alternation of monomers.
Our approach is based on the cavity method, a refined Bethe Peierls
approximation adapted to frustrated systems. It amounts to a mean field
treatment in which the nearest neighbor correlations, which are crucial in the
dense phases of heteropolymers, are handled exactly. This approach is powerful
and versatile, it can be improved systematically and generalized to other
polymeric systems
Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields
We consider a family of vector fields and we assume a horizontal regularity
on their derivatives. We discuss the notion of commutator showing that
different definitions agree. We apply our results to the proof of a ball-box
theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate
articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520
Factor PD-Clustering
Factorial clustering methods have been developed in recent years thanks to
the improving of computational power. These methods perform a linear
transformation of data and a clustering on transformed data optimizing a common
criterion. Factorial PD-clustering is based on Probabilistic Distance
clustering (PD-clustering). PD-clustering is an iterative, distribution free,
probabilistic, clustering method. Factor PD-clustering make a linear
transformation of original variables into a reduced number of orthogonal ones
using a common criterion with PD-Clustering. It is demonstrated that Tucker 3
decomposition allows to obtain this transformation. Factor PD-clustering makes
alternatively a Tucker 3 decomposition and a PD-clustering on transformed data
until convergence. This method could significantly improve the algorithm
performance and allows to work with large dataset, to improve the stability and
the robustness of the method
Entropic long range order in a 3D spin glass model
We uncover a new kind of entropic long range order in finite dimensional spin
glasses. We study the link-diluted version of the Edwards-Anderson spin glass
model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction
algorithms, we prove that there exists a region of the phase diagram (at zero
temperature and link density low enough), where spins are long range
correlated, even if the ground states energy stiffness is null. In other words,
in this region twisting the boundary conditions cost no energy, but spins are
long range correlated by means of pure entropic effects.Comment: 15 pages, 6 figures. v3: added a phase diagram for ferromagnetically
biased coupling
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