Molecular flexibility of citrus pectins by combined sedimentation and viscosity analysis

The flexibility/rigidity of pectins plays an important part in their structure-function relationship and therefore on their commercial applications in the food and biomedical industries. Earlier studies based on sedimentation analysis in the ultracentrifuge have focused on molecular weight distributions and qualitative and semi-quantitative descriptions based on power law and Wales-van Holde treatments of conformation in terms of "extended" conformations [Harding, S. E., Berth, G., Ball, A., Mitchell, J.R., & Garcìa de la Torre, J. (1991). The molecular weight distribution and conformation of citrus pectins in solution studied by hydrodynamics. Carbohydrate Polymers, 168, 1-15; Morris, G. A., Foster, T. J., & Harding, S.E. (2000). The effect of degree of esterification on the hydrodynamic properties of citrus pectin. Food Hydrocolloids, 14, 227-235]. In the present study, four pectins of low degree of esterification 17-27% and one of high degree of esterification (70%) were characterised in aqueous solution (0.1 M NaCl) in terms of intrinsic viscosity [η], sedimentation coefficient (s°20,w) and weight average molar mass (Mw). Solution conformation/flexibility was estimated qualitatively using the conformation zoning method [Pavlov, G.M., Rowe, A.J., & Harding, S.E. (1997). Conformation zoning of large molecules using the analytical ultracentrifuge. Trends in Analytical Chemistry, 16, 401-405] and quantitatively (persistence length Lp) using the traditional Bohdanecky and Yamakawa-Fujii relations combined together by minimisation of a target function. Sedimentation conformation zoning showed an extended coil (Type C) conformation and persistence lengths all within the range Lp=10-13 nm (for a fixed mass per unit length)

Variable sets over an algebra of lifetimes: a contribution of lattice theory to the study of computational topology

A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines the structure of data through topology. The basic techniques have been extended in several different directions, permuting the encoding of topological features by so called barcodes or equivalently persistence diagrams. The set of points of all such diagrams determines a complete Heyting algebra that can explain aspects of the relations between persistent bars through the algebraic properties of its underlying lattice structure. In this paper, we investigate the topos of sheaves over such algebra, as well as discuss its construction and potential for a generalised simplicial homology over it. In particular we are interested in establishing a topos theoretic unifying theory for the various flavours of persistent homology that have emerged so far, providing a global perspective over the algebraic foundations of applied and computational topology.Comment: 20 pages, 12 figures, AAA88 Conference proceedings at Demonstratio Mathematica. The new version has restructured arguments, clearer intuition is provided, and several typos correcte

Persistent topology for natural data analysis - A survey

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and classification of cells, lesions, music pieces, gait, oil and gas reservoirs, cyclones, galaxies, bones, brain connections, languages, handwritten and gestured letters are shown

The Role of Motivational Persistence and Resilience Over the Well-being Changes Registered in Time

The present study investigates the interaction between personal characteristics that are considered nowadays strengths used to face difficult events or transition period. A number of 200 married or living together participants completed self-reports for common goals, motivational persistence, resilience and well-being. Results show that persistence and resilience do interact with each other at an individual level but also from a family concept perspective. Moreover, maintaining apositive outlook and family spirituality do have an impact over the intensity and direction of the relationship between long term purposes pursuing and recurrence of unattained purposes and changes in well-being registered in time. Resiliency as a personal characteristic and family resilience show good psychometric qualities for this study. Although some of the results are descriptive, in-depth analyses of direction and intensity of the relationships lead the finalconclusions to suggestions for further research and implications for psychological practice

A Stable Multi-Scale Kernel for Topological Machine Learning

Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes

Labelings for Decreasing Diagrams

This article is concerned with automating the decreasing diagrams technique of van Oostrom for establishing confluence of term rewrite systems. We study abstract criteria that allow to lexicographically combine labelings to show local diagrams decreasing. This approach has two immediate benefits. First, it allows to use labelings for linear rewrite systems also for left-linear ones, provided some mild conditions are satisfied. Second, it admits an incremental method for proving confluence which subsumes recent developments in automating decreasing diagrams. The techniques proposed in the article have been implemented and experimental results demonstrate how, e.g., the rule labeling benefits from our contributions