25,098 research outputs found
Analysis of Software Patches Using Numerical Abstract Interpretation
International audienceWe present a static analysis for software patches. Given two syntactically close versions of a program, our analysis can infer a semantic difference, and prove that both programs compute the same outputs when run on the same inputs. Our method is based on abstract interpretation, and parametric in the choice of an abstract domain. We focus on numeric properties only. Our method is able to deal with unbounded executions of infinite-state programs, reading from infinite input streams. Yet, it is limited to comparing terminating executions, ignoring non terminating ones.We first present a novel concrete collecting semantics, expressing the behaviors of both programs at the same time. Then, we propose an abstraction of infinite input streams able to prove that programs that read from the same stream compute equal output values. We then show how to leverage classic numeric abstract domains, such as polyhedra or octagons, to build an effective static analysis. We also introduce a novel numeric domain to bound differences between the values of the variables in the two programs, which has linear cost, and the right amount of relationality to express useful properties of software patches.We implemented a prototype and experimented on a few small examples from the literature. Our prototype operates on a toy language, and assumes a joint syntactic representation of two versions of a program given, which distinguishes between common and distinctive parts
Similar self-organizing scale-invariant properties characterize early cancer invasion and long range species spread
Occupancy of new habitats through dispersion is a central process in nature.
In particular, long range dispersal is involved in the spread of species and
epidemics, although it has not been previously related with cancer invasion, a
process that involves spread to new tissues. We show that the early spread of
cancer cells is similar to the species individuals spread and that both
processes are represented by a common spatio-temporal signature, characterized
by a particular fractal geometry of the boundaries of patches generated, and a
power law-scaled, disrupted patch size distribution. We show that both
properties are a direct result of long-distance dispersal, and that they
reflect homologous ecological processes of population self-organization. Our
results are significant for processes involving long-range dispersal like
biological invasions, epidemics and cancer metastasis.Comment: 21 pages, 2 figure
Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity
A general framework for solving image inverse problems is introduced in this
paper. The approach is based on Gaussian mixture models, estimated via a
computationally efficient MAP-EM algorithm. A dual mathematical interpretation
of the proposed framework with structured sparse estimation is described, which
shows that the resulting piecewise linear estimate stabilizes the estimation
when compared to traditional sparse inverse problem techniques. This
interpretation also suggests an effective dictionary motivated initialization
for the MAP-EM algorithm. We demonstrate that in a number of image inverse
problems, including inpainting, zooming, and deblurring, the same algorithm
produces either equal, often significantly better, or very small margin worse
results than the best published ones, at a lower computational cost.Comment: 30 page
Brain Activity Mapping from MEG Data via a Hierarchical Bayesian Algorithm with Automatic Depth Weighting
A recently proposed iterated alternating sequential (IAS) MEG inverse solver algorithm, based on the coupling of a hierarchical Bayesian model with computationally efficient Krylov subspace linear solver, has been shown to perform well for both superficial and deep brain sources. However, a systematic study of its ability to correctly identify active brain regions is still missing. We propose novel statistical protocols to quantify the performance of MEG inverse solvers, focusing in particular on how their accuracy and precision at identifying active brain regions. We use these protocols for a systematic study of the performance of the IAS MEG inverse solver, comparing it with three standard inversion methods, wMNE, dSPM, and sLORETA. To avoid the bias of anecdotal tests towards a particular algorithm, the proposed protocols are Monte Carlo sampling based, generating an ensemble of activity patches in each brain region identified in a given atlas. The performance in correctly identifying the active areas is measured by how much, on average, the reconstructed activity is concentrated in the brain region of the simulated active patch. The analysis is based on Bayes factors, interpreting the estimated current activity as data for testing the hypothesis that the active brain region is correctly identified, versus the hypothesis of any erroneous attribution. The methodology allows the presence of a single or several simultaneous activity regions, without assuming that the number of active regions is known. The testing protocols suggest that the IAS solver performs well with both with cortical and subcortical activity estimation
How should spin-weighted spherical functions be defined?
Spin-weighted spherical functions provide a useful tool for analyzing
tensor-valued functions on the sphere. A tensor field can be decomposed into
complex-valued functions by taking contractions with tangent vectors on the
sphere and the normal to the sphere. These component functions are usually
presented as functions on the sphere itself, but this requires an implicit
choice of distinguished tangent vectors with which to contract. Thus, we may
more accurately say that spin-weighted spherical functions are functions of
both a point on the sphere and a choice of frame in the tangent space at that
point. The distinction becomes extremely important when transforming the
coordinates in which these functions are expressed, because the implicit choice
of frame will also transform. Here, it is proposed that spin-weighted spherical
functions should be treated as functions on the spin group. This approach more
cleanly reflects the geometry involved, and allows for a more elegant
description of the behavior of spin-weighted functions. In this form, the
spin-weighted spherical harmonics have simple expressions as elements of the
Wigner representations, and transformations under rotation are
simple. Two variants of the angular-momentum operator are defined directly in
terms of the spin group; one is the standard angular-momentum operator
, while the other is shown to be related to the spin-raising
operator . Computer code is also included, providing an explicit
implementation of the spin-weighted spherical harmonics in this form.Comment: Final version as publishe
- âŠ