3,181 research outputs found
Compressed Quantitative MRI: Bloch Response Recovery through Iterated Projection
Inspired by the recently proposed Magnetic Resonance Fingerprinting
technique, we develop a principled compressed sensing framework for
quantitative MRI. The three key components are: a random pulse excitation
sequence following the MRF technique; a random EPI subsampling strategy and an
iterative projection algorithm that imposes consistency with the Bloch
equations. We show that, as long as the excitation sequence possesses an
appropriate form of persistent excitation, we are able to achieve accurate
recovery of the proton density, , and off-resonance maps
simultaneously from a limited number of samples.Comment: 5 pages 2 figure
A Relational Logic for Higher-Order Programs
Relational program verification is a variant of program verification where
one can reason about two programs and as a special case about two executions of
a single program on different inputs. Relational program verification can be
used for reasoning about a broad range of properties, including equivalence and
refinement, and specialized notions such as continuity, information flow
security or relative cost. In a higher-order setting, relational program
verification can be achieved using relational refinement type systems, a form
of refinement types where assertions have a relational interpretation.
Relational refinement type systems excel at relating structurally equivalent
terms but provide limited support for relating terms with very different
structures.
We present a logic, called Relational Higher Order Logic (RHOL), for proving
relational properties of a simply typed -calculus with inductive types
and recursive definitions. RHOL retains the type-directed flavour of relational
refinement type systems but achieves greater expressivity through rules which
simultaneously reason about the two terms as well as rules which only
contemplate one of the two terms. We show that RHOL has strong foundations, by
proving an equivalence with higher-order logic (HOL), and leverage this
equivalence to derive key meta-theoretical properties: subject reduction,
admissibility of a transitivity rule and set-theoretical soundness. Moreover,
we define sound embeddings for several existing relational type systems such as
relational refinement types and type systems for dependency analysis and
relative cost, and we verify examples that were out of reach of prior work.Comment: Submitted to ICFP 201
Proving uniformity and independence by self-composition and coupling
Proof by coupling is a classical proof technique for establishing
probabilistic properties of two probabilistic processes, like stochastic
dominance and rapid mixing of Markov chains. More recently, couplings have been
investigated as a useful abstraction for formal reasoning about relational
properties of probabilistic programs, in particular for modeling
reduction-based cryptographic proofs and for verifying differential privacy. In
this paper, we demonstrate that probabilistic couplings can be used for
verifying non-relational probabilistic properties. Specifically, we show that
the program logic pRHL---whose proofs are formal versions of proofs by
coupling---can be used for formalizing uniformity and probabilistic
independence. We formally verify our main examples using the EasyCrypt proof
assistant
On Variable Density Compressive Sampling
We advocate an optimization procedure for variable density sampling in the
context of compressed sensing. In this perspective, we introduce a minimization
problem for the coherence between the sparsity and sensing bases, whose
solution provides an optimized sampling profile. This minimization problem is
solved with the use of convex optimization algorithms. We also propose a
refinement of our technique when prior information is available on the signal
support in the sparsity basis. The effectiveness of the method is confirmed by
numerical experiments. Our results also provide a theoretical underpinning to
state-of-the-art variable density Fourier sampling procedures used in magnetic
resonance imaging
Towards Statistical Prioritization for Software Product Lines Testing
Software Product Lines (SPL) are inherently difficult to test due to the
combinatorial explosion of the number of products to consider. To reduce the
number of products to test, sampling techniques such as combinatorial
interaction testing have been proposed. They usually start from a feature model
and apply a coverage criterion (e.g. pairwise feature interaction or
dissimilarity) to generate tractable, fault-finding, lists of configurations to
be tested. Prioritization can also be used to sort/generate such lists,
optimizing coverage criteria or weights assigned to features. However, current
sampling/prioritization techniques barely take product behavior into account.
We explore how ideas of statistical testing, based on a usage model (a Markov
chain), can be used to extract configurations of interest according to the
likelihood of their executions. These executions are gathered in featured
transition systems, compact representation of SPL behavior. We discuss possible
scenarios and give a prioritization procedure illustrated on an example.Comment: Extended version published at VaMoS '14
(http://dx.doi.org/10.1145/2556624.2556635
Advanced Probabilistic Couplings for Differential Privacy
Differential privacy is a promising formal approach to data privacy, which
provides a quantitative bound on the privacy cost of an algorithm that operates
on sensitive information. Several tools have been developed for the formal
verification of differentially private algorithms, including program logics and
type systems. However, these tools do not capture fundamental techniques that
have emerged in recent years, and cannot be used for reasoning about
cutting-edge differentially private algorithms. Existing techniques fail to
handle three broad classes of algorithms: 1) algorithms where privacy depends
accuracy guarantees, 2) algorithms that are analyzed with the advanced
composition theorem, which shows slower growth in the privacy cost, 3)
algorithms that interactively accept adaptive inputs.
We address these limitations with a new formalism extending apRHL, a
relational program logic that has been used for proving differential privacy of
non-interactive algorithms, and incorporating aHL, a (non-relational) program
logic for accuracy properties. We illustrate our approach through a single
running example, which exemplifies the three classes of algorithms and explores
new variants of the Sparse Vector technique, a well-studied algorithm from the
privacy literature. We implement our logic in EasyCrypt, and formally verify
privacy. We also introduce a novel coupling technique called \emph{optimal
subset coupling} that may be of independent interest
Assessing the Structural and Psychometric Properties of a New Personality Measure for Use With Military Personnel in the French Armed Forces
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