104 research outputs found
Automatic Average-case Analysis of Algorithms
International audienceMany probabilistic properties of elementary discrete combinatorial structures of interest for the average-case analysis of algorithms prove to be decidable. This paper presents a general framework in which such decision procedures can be developed. It is based on a combination of generating function techniques for counting, and complex analysis techniques for asymptotic estimations. We expose here the theory of exact analysis in terms of generating functions for four different domains: the iterative/recursive and unlabelled/labelled data type domains. We then present some major components of the associated asymptotic theory and exhibit a class of naturally arising functions that can be automatically analyzed. A fair fragment of this theory is also incorporated into a system called Lambda-Upsilon-Omega. In this way, using computer algebra, one can produce automatically non-trivial average-case analyses of algorithms operating over a variety of "decomposable" combinatorial structures. At a fundamental level, this paper is part of a global attempt at understanding why so many elementary combinatorial problems tend to have elementary asymptotic solutions. In several cases, it proves possible to relate entire classes of elementary combinatorial problems whose structure is well defined with classes of elementary "special" functions and classes of asymptotic forms relative to counting, probabilities, or average-case complexity
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
We employ computer algebra algorithms to prove a collection of identities
involving Bessel functions with half-integer orders and other special
functions. These identities appear in the famous Handbook of Mathematical
Functions, as well as in its successor, the DLMF, but their proofs were lost.
We use generating functions and symbolic summation techniques to produce new
proofs for them.Comment: Final version, some typos were corrected. 21 pages, uses svmult.cl
Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model
We first study the properties of the Fuchsian ordinary differential equations
for the three and four-particle contributions and
of the square lattice Ising model susceptibility. An analysis of some
mathematical properties of these Fuchsian differential equations is sketched.
For instance, we study the factorization properties of the corresponding linear
differential operators, and consider the singularities of the three and
four-particle contributions and , versus the
singularities of the associated Fuchsian ordinary differential equations, which
actually exhibit new ``Landau-like'' singularities. We sketch the analysis of
the corresponding differential Galois groups. In particular we provide a
simple, but efficient, method to calculate the so-called ``connection
matrices'' (between two neighboring singularities) and deduce the singular
behaviors of and . We provide a set of comments and
speculations on the Fuchsian ordinary differential equations associated with
the -particle contributions and address the problem of the
apparent discrepancy between such a holonomic approach and some scaling results
deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
Rigorous Polynomial Approximation using Taylor Models in Coq
International audienceOne of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assistant, with a special focus on genericity and efficiency for our implementation. We give an abstract interface for rigorous polynomial approximations, parameter- ized by the type of coefficients and the implementation of polynomials, and we instantiate this interface to the case of Taylor models with inter- val coefficients, while providing all the machinery for computing them. We compare the performances of our implementation in Coq with those of the Sollya tool, which contains an implementation of Taylor models written in C. This is a milestone in our long-term goal of providing fully formally proved and efficient Taylor models
Associations of food group and nutrient intake, diet quality, and meal sizes between adults and children in the same household: a cross-sectional analysis of U.S. households
Postreinforcement Pause Duration Varies Within a Session and With a Variable Response Requirement but Not as a Function of Prior Revolutions
The Effects of Playing with Thin Dolls on Body Image and Food Intake in Young Girls
This study experimentally tested the effects of playing with thin dolls on body image and food intake in 6- to 10-year-old Dutch girls (Nâ=â117). Girls were randomly assigned to play with a thin doll, an average-sized doll, or Legos in a no doll control condition. After 10Â min, they participated in a taste-test and completed questionnaires about body image. No differences were found between conditions for any of the body image variables. However, girls who played with the average-sized doll ate significantly more food than girls in other exposure conditions. Although no support was found for the assumption that playing with thin dolls influences body image, the dolls directly affected actual food intake in these young girls
Write, draw, show, and tell: a child-centred dual methodology to explore perceptions of out-of-school physical activity
Background
Research to increase childrenâs physical activity and inform intervention design has, to date, largely underrepresented childrenâs voices. Further, research has been limited to singular qualitative methods that overlook childrenâs varied linguistic ability and interaction preference. The aim of this study was to use a novel combination of qualitative techniques to explore childrenâs current views, experiences and perceptions of out-of-school physical activity as well as offering formative opinion about future intervention design.
Methods
Write, draw, show and tell (WDST) groups were conducted with 35 children aged 10â11 years from 7 primary schools. Data were analysed through a deductive and inductive process, firstly using the Youth Physical Activity Promotion Model as a thematic framework, and then inductively to enable emergent themes to be further explored. Pen profiles were constructed representing key emergent themes.
Results
The WDST combination of qualitative techniques generated complimentary interconnected data which both confirmed and uncovered new insights into factors relevant to childrenâs out-of-school physical activity. Physical activity was most frequently associated with organised sports. Fun, enjoyment, competence, and physical activity provision were all important predictors of childrenâs out-of-school physical activity. Paradoxically, parents served as both significant enablers (i.e. encouragement) and barriers (i.e. restricting participation) to physical activity participation. Some of these key findings would have otherwise remained hidden when compared to more traditional singular methods based approaches.
Conclusions
Parents are in a unique position to promote health promoting behaviours serving as role models, physical activity gatekeepers and choice architects. Given the strong socialising effect parents have on childrenâs physical activity, family-based physical activity intervention may offer a promising alternative compared to traditional school-based approaches. Parents' qualitative input is important to supplement childrenâs voices and inform future family-based intervention design. The WDST method developed here is an inclusive, interactive and child-centred methodology which facilitates the exploration of a wide range of topics and enhances data credibility
Unpacking the behavioural components and delivery features of early childhood obesity prevention interventions in the TOPCHILD Collaboration: a systematic review and intervention coding protocol.
INTRODUCTION: Little is known about how early (eg, commencing antenatally or in the first 12 months after birth) obesity prevention interventions seek to change behaviour and which components are or are not effective. This study aims to (1) characterise early obesity prevention interventions in terms of target behaviours, delivery features and behaviour change techniques (BCTs), (2) explore similarities and differences in BCTs used to target behaviours and (3) explore effectiveness of intervention components in preventing childhood obesity. METHODS AND ANALYSIS: Annual comprehensive systematic searches will be performed in Epub Ahead of Print/MEDLINE, Embase, Cochrane (CENTRAL), CINAHL, PsycINFO, as well as clinical trial registries. Eligible randomised controlled trials of behavioural interventions to prevent childhood obesity commencing antenatally or in the first year after birth will be invited to join the Transforming Obesity in CHILDren Collaboration. Standard ontologies will be used to code target behaviours, delivery features and BCTs in both published and unpublished intervention materials provided by trialists. Narrative syntheses will be performed to summarise intervention components and compare applied BCTs by types of target behaviours. Exploratory analyses will be undertaken to assess effectiveness of intervention components. ETHICS AND DISSEMINATION: The study has been approved by The University of Sydney Human Research Ethics Committee (project no. 2020/273) and Flinders University Social and Behavioural Research Ethics Committee (project no. HREC CIA2133-1). The study's findings will be disseminated through peer-reviewed publications, conference presentations and targeted communication with key stakeholders. PROSPERO REGISTRATION NUMBER: CRD42020177408
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