8,355 research outputs found
Comparing and evaluating extended Lambek calculi
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was
innovative in many ways, notably as a precursor of linear logic. But it also
showed that we could treat our grammatical framework as a logic (as opposed to
a logical theory). However, though it was successful in giving at least a basic
treatment of many linguistic phenomena, it was also clear that a slightly more
expressive logical calculus was needed for many other cases. Therefore, many
extensions and variants of the Lambek calculus have been proposed, since the
eighties and up until the present day. As a result, there is now a large class
of calculi, each with its own empirical successes and theoretical results, but
also each with its own logical primitives. This raises the question: how do we
compare and evaluate these different logical formalisms? To answer this
question, I present two unifying frameworks for these extended Lambek calculi.
Both are proof net calculi with graph contraction criteria. The first calculus
is a very general system: you specify the structure of your sequents and it
gives you the connectives and contractions which correspond to it. The calculus
can be extended with structural rules, which translate directly into graph
rewrite rules. The second calculus is first-order (multiplicative
intuitionistic) linear logic, which turns out to have several other,
independently proposed extensions of the Lambek calculus as fragments. I will
illustrate the use of each calculus in building bridges between analyses
proposed in different frameworks, in highlighting differences and in helping to
identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona,
Spain. 201
Consensus in multi-agent systems with second-order dynamics and non-periodic sampled-data exchange
In this paper consensus in second-order multi-agent systems with a
non-periodic sampled-data exchange among agents is investigated. The sampling
is random with bounded inter-sampling intervals. It is assumed that each agent
has exact knowledge of its own state at all times. The considered local
interaction rule is PD-type. The characterization of the convergence properties
exploits a Lyapunov-Krasovskii functional method, sufficient conditions for
stability of the consensus protocol to a time-invariant value are derived.
Numerical simulations are presented to corroborate the theoretical results.Comment: The 19th IEEE International Conference on Emerging Technologies and
Factory Automation (ETFA'2014), Barcelona (Spain
T_c for dilute Bose gases: beyond leading order in 1/N
Baym, Blaizot, and Zinn-Justin have recently used the large N approximation
to calculate the effect of interactions on the transition temperature of dilute
Bose gases. We extend their calculation to next-to-leading-order in 1/N and
find a relatively small correction of -26% to the leading-order result. This
suggests that the large N approximation works surprisingly well in this
application.Comment: 21 pages, 7+1 figures; an embarassing factor of 2 has been corrected
in the evaluation of one diagram, changing the previous +18% result for the
NLO correction to -26
Two loop renormalization of the magnetic coupling and non-perturbative sector in hot QCD
The goal of this paper is two-fold. The first aim is to present a detailed
version of the computation of the two-loop renormalization of the magnetic
coupling in hot QCD. The second is to compare with lattice simulations the
string tension of a spatial Wilson loop using the result of our two-loop
computationComment: 32 page
Thermodynamic graph-rewriting
We develop a new thermodynamic approach to stochastic graph-rewriting. The
ingredients are a finite set of reversible graph-rewriting rules called
generating rules, a finite set of connected graphs P called energy patterns and
an energy cost function. The idea is that the generators define the qualitative
dynamics, by showing which transformations are possible, while the energy
patterns and cost function specify the long-term probability of any
reachable graph. Given the generators and energy patterns, we construct a
finite set of rules which (i) has the same qualitative transition system as the
generators; and (ii) when equipped with suitable rates, defines a
continuous-time Markov chain of which is the unique fixed point. The
construction relies on the use of site graphs and a technique of `growth
policy' for quantitative rule refinement which is of independent interest. This
division of labour between the qualitative and long-term quantitative aspects
of the dynamics leads to intuitive and concise descriptions for realistic
models (see the examples in S4 and S5). It also guarantees thermodynamical
consistency (AKA detailed balance), otherwise known to be undecidable, which is
important for some applications. Finally, it leads to parsimonious
parameterizations of models, again an important point in some applications
Renormalization of Matter Field Theories on the Lattice and the Flow Equation
We give a new proof of the renormalizability of a class of matter field
theories on a space-time lattice; in particular we consider and
massive Yukawa theories with Wilson fermions. We use the Polchinski approach to
renormalization, which is based on the Wilson flow equation; this approach is
substantially simpler than the BPHZ method, applied to the lattice by Reisz. We
discuss matter theories with staggered fermions. In particular we analyse a
simple kind of staggered fermions with minimal doubling, using which we prove
the renormalizability of a chiral sigma model with exact chiral symmetry on the
lattice.Comment: 32 pages, Late
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