Co-morbidity burden in Parkinson’s disease : Comparison with controls and its influence on prognosis

Financial support This study was funded by Parkinson’s UK, the Scottish Chief Scientist Office, NHS Grampian endowments, the BMA Doris Hillier award, RS Macdonald Trust, the BUPA Foundation, and SPRING. The funders had no involvement in the study. Acknowledgements We acknowledge funding for the PINE study from Parkinson’s UK (G-0502, G-0914, G-1302), the Scottish Chief Scientist Office(CAF/12/05), the BMA Doris Hillier award, RS Macdonald Trust, the BUPA Foundation, NHS Grampian endowments and SPRING. We thank the patients and controls for their participation and the research staff who collected data and supported the study database.Peer reviewedPostprintPostprintPublisher PD

Titration of Monolayers

The early work on the effect of pH on ionizable materials at aqueous interfaces and the consequent development of the concept of an effective pH in the interface region, which differs from tnat in aqueous bulk phase, are outlined. Properties as a function of pH of monolayers of a variety of surfactant types, viz., weak and nonelectrolytes (fatty acids, amines, amine oxides, alcohols, ethers), intermediate strength electrolytes (alkyl phosphates), strong electrolytes (alkyl sulfates and alkane sulfonates, both as spread a:nd adsorbed monolayers) and two zwitterionic materials, are presented in some detail. Use is made of the approaches of Schulman and Hughes and of Davies for analysis of the results which are shown generally to be consistent with a shift towards weakness of the monolayer electrolyte because of the charge developed during its ionization; exceptions are the zwitterionic materials. Points of interest are (a) the need to invoke acid-soap formation to explain the surface potential- pH data of close-packed fatty acid monolayers; (b) a prevalent tendency for most of the anionic or nonionic monolayers to form oxonium ions at \u27ery low pH; (c) the relatively expanded nature of the uncharged form of monolayers of the highly dipolar amine oxide compared to its ionized form; (d) definite indications of »weakness« in both spread and adsorbed films of long chain sulfates and alkane sulfonates. A brief section on the influence of pH on polyelectrolyte monolayers is included

Specific Counterion Effects in Surface and Colloid Chemistry. Ionized Monolayers

Data are presented on the effect of various monovalent cations on the rr,-A and 8V-A characteristics of charged insoluble monolayers. The following interaction sequences were established: R-coo-, Li > Na > K > tetramethylammonium > tetraethylammonium; R-S04-, Cs = Rb> K > Na> Li; R-N (CHah+. SCN > >I> N03 >Br> Cl> F; R-NH(CH3)2+ and R-NHs+, Br> Cl. The results thus parallel data on ion sequence effects reported in other branches of colloid and physical chemistry. They are discussed in the light of various hypotheses advanced to explain these effects. The monolayer rr,-A curves were compared with those predicted from theoretically derived equations of state: agreement was generally poor

Specific Counterion Effects in Surface and Colloid Chemistry. Ionized Monolayers

Data are presented on the effect of various monovalent cations on the rr,-A and 8V-A characteristics of charged insoluble monolayers. The following interaction sequences were established: R-coo-, Li > Na > K > tetramethylammonium > tetraethylammonium; R-S04-, Cs = Rb> K > Na> Li; R-N (CHah+. SCN > >I> N03 >Br> Cl> F; R-NH(CH3)2+ and R-NHs+, Br> Cl. The results thus parallel data on ion sequence effects reported in other branches of colloid and physical chemistry. They are discussed in the light of various hypotheses advanced to explain these effects. The monolayer rr,-A curves were compared with those predicted from theoretically derived equations of state: agreement was generally poor

Adsorption of Surfactants on Mineral Solids

Factors influendng 1he adsorption of ionic surfactants on solids are outlined. Emphasis is placed on the role of electrostatic forces and of lateral association within adsorbed layers. MechanLsms leading to charge gene.ration on solids are descdbed, and the dependence of adsorption on charge effects i\u27s mustrated by reference to published data on a number of different solid surfactan:t systems. It is shown how the electrostatic factor can be strongly modified · by the presence of inorganic salts. The importance of chain-chain interactions is illustrated by the influence of chains length and composition on adsorption, and also by the pH dependence of the adsorption of long chain, weak electrolytes. This leads to a discussion of the possible role of highly surface active long chain complexes. Lastly, the influence of polymers on the adsorption of surfactants is discussed

Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

Charges, Monopoles and Duality Relations

A charge-monopole theory is derived from simple and self-evident postulates. Charges and monopoles take an analogous theoretical structure. It is proved that charges interact with free waves emitted from monopoles but not with the corresponding velocity fields. Analogous relations hold for monopole equations of motion. The system's equations of motion can be derived from a regular Lagrangian function.Comment: 17 pages + 3 figures