9,850 research outputs found
A feasible algorithm for typing in Elementary Affine Logic
We give a new type inference algorithm for typing lambda-terms in Elementary
Affine Logic (EAL), which is motivated by applications to complexity and
optimal reduction. Following previous references on this topic, the variant of
EAL type system we consider (denoted EAL*) is a variant without sharing and
without polymorphism. Our algorithm improves over the ones already known in
that it offers a better complexity bound: if a simple type derivation for the
term t is given our algorithm performs EAL* type inference in polynomial time.Comment: 20 page
Unification and Logarithmic Space
We present an algebraic characterization of the complexity classes Logspace
and NLogspace, using an algebra with a composition law based on unification.
This new bridge between unification and complexity classes is inspired from
proof theory and more specifically linear logic and Geometry of Interaction.
We show how unification can be used to build a model of computation by means
of specific subalgebras associated to finite permutations groups. We then prove
that whether an observation (the algebraic counterpart of a program) accepts a
word can be decided within logarithmic space. We also show that the
construction can naturally represent pointer machines, an intuitive way of
understanding logarithmic space computing
Classical Structures Based on Unitaries
Starting from the observation that distinct notions of copying have arisen in
different categorical fields (logic and computation, contrasted with quantum
mechanics) this paper addresses the question of when, or whether, they may
coincide. Provided all definitions are strict in the categorical sense, we show
that this can never be the case. However, allowing for the defining axioms to
be taken up to canonical isomorphism, a close connection between the classical
structures of categorical quantum mechanics, and the categorical property of
self-similarity familiar from logical and computational models becomes
apparent.
The required canonical isomorphisms are non-trivial, and mix both typed
(multi-object) and untyped (single-object) tensors and structural isomorphisms;
we give coherence results that justify this approach.
We then give a class of examples where distinct self-similar structures at an
object determine distinct matrix representations of arrows, in the same way as
classical structures determine matrix representations in Hilbert space. We also
give analogues of familiar notions from linear algebra in this setting such as
changes of basis, and diagonalisation.Comment: 24 pages,7 diagram
Polarization state of the optical near-field
The polarization state of the optical electromagnetic field lying several
nanometers above complex dielectric structures reveals the intricate
light-matter interaction that occurs in this near-field zone. This information
can only be extracted from an analysis of the polarization state of the
detected light in the near-field. These polarization states can be calculated
by different numerical methods well-suited to near--field optics. In this
paper, we apply two different techniques (Localized Green Function Method and
Differential Theory of Gratings) to separate each polarisation component
associated with both electric and magnetic optical near-fields produced by
nanometer sized objects. The analysis is carried out in two stages: in the
first stage, we use a simple dipolar model to achieve insight into the physical
origin of the near-field polarization state. In the second stage, we calculate
accurate numerical field maps, simulating experimental near-field light
detection, to supplement the data produced by analytical models. We conclude
this study by demonstrating the role played by the near-field polarization in
the formation of the local density of states.Comment: 9 pages, 11 figures, accepted for publication in Phys. Rev.
Damage-cluster distributions and size effect on strength in compressive failure
We investigate compressive failure of heterogeneous materials on the basis of
a continuous progressive damage model. The model explicitely accounts for
tensile and shear local damage and reproduces the main features of compressive
failure of brittle materials like rocks or ice. We show that the size
distribution of damage-clusters, as well as the evolution of an order
parameter, the size of the largest damage-cluster, argue for a critical
interpretation of fracture. The compressive failure strength follows a normal
distribution with a very small size effect on the mean strength, in good
agreement with experiments
Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution
We propose two strategies to improve the quality of tractography results
computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both
methods are based on the same PDE framework, defined in the coupled space of
positions and orientations, associated with a stochastic process describing the
enhancement of elongated structures while preserving crossing structures. In
the first method we use the enhancement PDE for contextual regularization of a
fiber orientation distribution (FOD) that is obtained on individual voxels from
high angular resolution diffusion imaging (HARDI) data via constrained
spherical deconvolution (CSD). Thereby we improve the FOD as input for
subsequent tractography. Secondly, we introduce the fiber to bundle coherence
(FBC), a measure for quantification of fiber alignment. The FBC is computed
from a tractography result using the same PDE framework and provides a
criterion for removing the spurious fibers. We validate the proposed
combination of CSD and enhancement on phantom data and on human data, acquired
with different scanning protocols. On the phantom data we find that PDE
enhancements improve both local metrics and global metrics of tractography
results, compared to CSD without enhancements. On the human data we show that
the enhancements allow for a better reconstruction of crossing fiber bundles
and they reduce the variability of the tractography output with respect to the
acquisition parameters. Finally, we show that both the enhancement of the FODs
and the use of the FBC measure on the tractography improve the stability with
respect to different stochastic realizations of probabilistic tractography.
This is shown in a clinical application: the reconstruction of the optic
radiation for epilepsy surgery planning
Some Remarks on the Model Theory of Epistemic Plausibility Models
Classical logics of knowledge and belief are usually interpreted on Kripke
models, for which a mathematically well-developed model theory is available.
However, such models are inadequate to capture dynamic phenomena. Therefore,
epistemic plausibility models have been introduced. Because these are much
richer structures than Kripke models, they do not straightforwardly inherit the
model-theoretical results of modal logic. Therefore, while epistemic
plausibility structures are well-suited for modeling purposes, an extensive
investigation of their model theory has been lacking so far. The aim of the
present paper is to fill exactly this gap, by initiating a systematic
exploration of the model theory of epistemic plausibility models. Like in
'ordinary' modal logic, the focus will be on the notion of bisimulation. We
define various notions of bisimulations (parametrized by a language L) and show
that L-bisimilarity implies L-equivalence. We prove a Hennesy-Milner type
result, and also two undefinability results. However, our main point is a
negative one, viz. that bisimulations cannot straightforwardly be generalized
to epistemic plausibility models if conditional belief is taken into account.
We present two ways of coping with this issue: (i) adding a modality to the
language, and (ii) putting extra constraints on the models. Finally, we make
some remarks about the interaction between bisimulation and dynamic model
changes.Comment: 19 pages, 3 figure
A lambda calculus for quantum computation with classical control
The objective of this paper is to develop a functional programming language
for quantum computers. We develop a lambda calculus for the classical control
model, following the first author's work on quantum flow-charts. We define a
call-by-value operational semantics, and we give a type system using affine
intuitionistic linear logic. The main results of this paper are the safety
properties of the language and the development of a type inference algorithm.Comment: 15 pages, submitted to TLCA'05. Note: this is basically the work done
during the first author master, his thesis can be found on his webpage.
Modifications: almost everything reformulated; recursion removed since the
way it was stated didn't satisfy lemma 11; type inference algorithm added;
example of an implementation of quantum teleportation adde
Noncyclic geometric changes of quantum states
Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by
geometric properties of a quantum system, have been much under focus in the
physics community as generalizations of the Abelian Berry phase. Apart from
being a general phenomenon displayed in various subfields of quantum physics,
the use of holonomies has lately been suggested as a robust technique to obtain
quantum gates; the building blocks of quantum computers. Non-Abelian holonomies
are usually associated with cyclic changes of quantum systems, but here we
consider a generalization to noncyclic evolutions. We argue that this open-path
holonomy can be used to construct quantum gates. We also show that a structure
of partially defined holonomies emerges from the open-path holonomy. This
structure has no counterpart in the Abelian setting. We illustrate the general
ideas using an example that may be accessible to tests in various physical
systems.Comment: Extended version, new title, journal reference adde
Dynamics of active membranes with internal noise
We study the time-dependent height fluctuations of an active membrane
containing energy-dissipating pumps that drive the membrane out of equilibrium.
Unlike previous investigations based on models that neglect either curvature
couplings or random fluctuations in pump activities, our formulation explores
two new models that take both of these effects into account. In the first
model, the magnitude of the nonequilibrium forces generated by the pumps is
allowed to fluctuate temporally. In the second model, the pumps are allowed to
switch between "on" and "off" states. We compute the mean squared displacement
of a membrane point for both models, and show that they exhibit distinct
dynamical behaviors from previous models, and in particular, a superdiffusive
regime specifically arising from the shot noise.Comment: 7 pages, 4 figure
- …