Moduli stacks of algebraic structures and deformation theory

We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate diagram category form affine stacks in the sense of Toen-Vezzosi's homotopical algebraic geometry. This includes simplicial moduli spaces of algebraic structures over a given object (for instance a cochain complex). When these algebraic structures are parametrised by properads, the tangent complexes give the known cohomology theory for such structures and there is an associated obstruction theory for infinitesimal, higher order and formal deformations. The methods are general enough to be adapted for more general kinds of algebraic structures.Comment: several corrections, especially in sections 6 and 7. Final version, to appear in the J. Noncommut. Geo

Function spaces and classifying spaces of algebras over a prop

The goal of this paper is to prove that the classifying spaces of categories of algebras governed by a prop can be determined by using function spaces on the category of props. We first consider a function space of props to define the moduli space of algebra structures over this prop on an object of the base category. Then we mainly prove that this moduli space is the homotopy fiber of a forgetful map of classifying spaces, generalizing to the prop setting a theorem of Rezk. The crux of our proof lies in the construction of certain universal diagrams in categories of algebras over a prop. We introduce a general method to carry out such constructions in a functorial way.Comment: 28 pages, modifications mainly in section 2 (more details in some proofs and additional explanations), typo corrections. Final version, to appear in Algebr. Geom. Topo

The homotopy theory of bialgebras over pairs of operads

We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in two steps. In the first step, we equip coalgebras over an operad with a cofibrantly generated model category structure. In the second one we use the adjunction between bialgebras and coalgebras via the free algebra functor. This result allows us to do classical homotopical algebra in various categories such as associative bialgebras, Lie bialgebras or Poisson bialgebras in chain complexes.Comment: 27 pages, final version, to appear in the Journal of Pure and Applied Algebr

Regularized Wasserstein Means for Aligning Distributional Data

We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the variational transportation to distribute a sparse discrete measure into the target domain. The resulting sparse representation well captures the desired property of the domain while reducing the mapping cost. We demonstrate the scalability and robustness of our method with examples in domain adaptation, point set registration, and skeleton layout

Multilevel Fixed and Sequential Acceptance Sampling: The R Package MFSAS

Multilevel acceptance sampling for attributes is used to decide whether a lot from an incoming shipment or outgoing production is accepted or rejected when the product has multiple levels of product quality or multiple types of (mutually exclusive) possible defects. This paper describes a package which provides the tools to create, evaluate, plot, and display the acceptance sampling plans for such lots for both fixed and sequential sampling. The functions for calculating cumulative probabilities for several common multivariate distributions (which are needed in the package) are provided as well.

Automatic Lumbar Vertebrae Segmentation in Fluoroscopic Images via Optimised Concurrent Hough Transform

Low back pain is a very common problem in the industrialised countries and its associated cost is enormous. Diagnosis of the underlying causes can be extremely difficult. Many studies have focused on mechanical disorders of the spine. Digital videofluoroscopy (DVF) was widely used to obtain images for motion studies. This can provide motion sequences of the lumbar spine, but the images obtained often suffer due to noise, exacerbated by the very low radiation dosage. Thus determining vertebrae position within the image sequence presents a considerable challenge. In this paper, we show how our new approach can automatically detect the positions and borders of vertebrae concurrently, relieving many of the problems experienced in other approaches. First, we use phase congruency to relieve difficulty associated with threshold selection in edge detection of the illumination variant DVF images. Then, our new Hough transform approach is applied to determine the moving vertebrae, concurrently. We include optimisation via a genetic algorithm as without it the extraction of moving multiple vertebrae is computationally daunting. Our results show that this new approach can indeed provide extractions of position and rotation which appear to be of sufficient quality to aid therapy and diagnosis of spinal disorders

Lumbar Spine Location in Fluoroscopic Images by Evidence Gathering

Low back pain (LBP) is a very common problem and lumbar segmental instability is one of the causes. It is important to investigate lumbar spine movement in order to understand instability better and as an aid to diagnosis. Digital videofluoroscopy provides a method of quantifying the motion of individual vertebrae, but due to the relatively poor image quality, it is difficult and time consuming to locate landmarks manually, from which the kinematics can be calculated. Some semi-automatic approaches have already been developed but these are still time consuming and require some manual interaction. In this paper we apply the Hough transform (HT) to locate the lumbar spinal segments automatically. The HT is a powerful tool in computer vision and it has good performance in noise and partial occlusion. A recent arbitrary shape representation avoids problems inherent with tabular representations in the generalised HT (GHT) by describing shapes using a continuous formulation. The target shape is described by a set of Fourier descriptors, which vote in an accumulator space from which the object parameters of translation (including the x and y direction), rotation and scale can be determined. At present, this algorithm has been applied to the images of lumbar spine, and has been shown to provide satisfactory results. Further work will concentrate on reducing the computational time for real-time application, and on approaches to refine information at the apices, given initialisation by the new HT method