Stretching single polysaccharide molecules using AFM: A potential method for the investigation of the intermolecular uronate distribution of alginate?

Illustrative examples of the way in which the molecular force-extension behaviour of polysaccharides is governed by the nature of the linkage between their constituent pyranose rings are presented for a series of standard homopolymers. These results agree with previously proposed general hypotheses regarding the possibility of generating force-induced conformational transitions, and with the predictions of a model in which the inter-conversion of pyranose conformers is assumed to be an equilibrium process on the timescale of the molecular stretching. Subsequently, we investigate the potential of the technique in the characterisation of co-polymeric polysaccharides in which the nature of the glycan linkages is different between the two distinct residue types. Specifically, we explore the possibility that the ratio of mannuronic acid (M) to guluronic acid (G) in alginate chains will be reflected in their single molecule stretching behaviour, owing to their contrasting equatorial and axial linkages. Furthermore, as the technique described interrogates the sample one polymer at a time we outline the promise of, and the obstacles to, obtaining a new level of characterisation using this methodology where differences observed in the single molecule stretching curves obtained from single alginate samples reflectsomething of the real intermolecular distribution of the M / G ratio

Legal Models and Business Realities of Enterprise Groups - Mismatch and Change

Although conducted world-wide through hundreds of subsidiaries and affiliates, modern large business is, in economic reality, typically a single economically integrated enterprise functioning with a common objective under the control of its parent company. Yet the prevailing legal models are, for the most part, oblivious to this. Mistakenly adopting outmoded concepts inherited from the misty past, these models focus on many separate subsidiary corporations that make up the business and necessarily overlook the larger whole. The result of this outdated view is a mismatch between business reality and legal form which has led so frequently to poor legal and regulatory decision-making and ineffectual public control. While there is change stirring today, overall the law’s response to this mismatch has been piecemeal and unsystematic. After reviewing how we got to this unhappy point, this paper will sketch out a new legal theory of enterprise analysis as the basis of modern corporation law to serve the needs of the Twenty-First Century. In some areas it will replace and in other areas it will supplement existing legal models. Enterprise analysis focuses on the implementation of the underlying policies and rules of the specific body of law at issue, such as securities, tax, or bankruptcy, to determine whether the objectives of that body of law are better served in the specific matter by looking to the whole enterprise or, alternatively, to the particular corporate subsidiary entities involved. While overt recognition of this enterprise analysis has been limited, the American legal system today is in fact applying it in numerous areas

Legal Models and Business Realities of Enterprise Groups - Mismatch and Change

Although conducted world-wide through hundreds of subsidiaries and affiliates, modern large business is, in economic reality, typically a single economically integrated enterprise functioning with a common objective under the control of its parent company. Yet the prevailing legal models are, for the most part, oblivious to this. Mistakenly adopting outmoded concepts inherited from the misty past, these models focus on many separate subsidiary corporations that make up the business and necessarily overlook the larger whole. The result of this outdated view is a mismatch between business reality and legal form which has led so frequently to poor legal and regulatory decision-making and ineffectual public control. While there is change stirring today, overall the law’s response to this mismatch has been piecemeal and unsystematic. After reviewing how we got to this unhappy point, this paper will sketch out a new legal theory of enterprise analysis as the basis of modern corporation law to serve the needs of the Twenty-First Century. In some areas it will replace and in other areas it will supplement existing legal models. Enterprise analysis focuses on the implementation of the underlying policies and rules of the specific body of law at issue, such as securities, tax, or bankruptcy, to determine whether the objectives of that body of law are better served in the specific matter by looking to the whole enterprise or, alternatively, to the particular corporate subsidiary entities involved. While overt recognition of this enterprise analysis has been limited, the American legal system today is in fact applying it in numerous areas

Coulomb gauge Gribov copies and the confining potential

We study the approach, initiated by Marinari et al., to the static inter-quark potential based on Polyakov lines of finite temporal extent, evaluated in Coulomb gauge. We show that, at small spatial separations, the potential can be understood as being between two separately gauge invariant colour charges. At larger separations Gribov copies obstruct the non-perturbative identification of individually gauge invariant colour states. We demonstrate, for the first time, how gauge invariance can be maintained quite generally by averaging over Gribov copies. This allows us to extend the analysis of the Polyakov lines and the corresponding, gauge invariant quark-antiquark state to all distance scales. Using large scale lattice simulations, we show that this interpolating state possesses a good overlap with the ground state in the quark-antiquark sector and yields the full static inter-quark potential at all distances. A visual representation of the Gribov copies on the lattice is also presented.Comment: 22 pages, 9 figures, v2: minor changes, references adde

The beta function of the multichannel Kondo model

The beta function of the multichannel Kondo model is calculated exactly in the limit of large spin N and channel number M=gamma*N, with constant gamma. There are no corrections in any finite order of 1/N. One zero is found at a finite coupling strength, showing directly the Non--Fermi liquid behavior of the model. This renormalization group flow allows to introduce a variational principle for the entropy, to obtain the low temperature thermodynamics. Such in particular the low temperature thermodynamics of the non--crossing approximation to the Kondo model becomes accessible.Comment: 4 page

Conformal Symmetries of Adiabatic Modes in Cosmology

We remark on the existence of non-linearly realized conformal symmetries for scalar adiabatic perturbations in cosmology. These conformal symmetries are present for any cosmological background, beyond any slow-roll or quasi-de Sitter approximation. The dilatation transformation shifts the curvature perturbation by a constant, and corresponds to the well-known symmetry under spatial rescaling. We argue that the scalar sector is also invariant under special conformal transformations, which shift the curvature perturbation by a term linear in the spatial coordinates. We discuss whether these conformal symmetries can be extended to include tensor perturbations. Tensor modes introduce their own set of non-linearly realized symmetries. We identify an infinite set of large gauge transformations which maintain the transverse, traceless gauge condition, while shifting the tensor mode non-trivially.Comment: 16 page