Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this map is a bijection and maps perturbed geodesics into perturbed Yang-Mills connections with the same Morse index.Comment: 58 pages, 3 figure

Analysis of Crash Patterns at Signalised Intersections

The paper reviews the crash patterns evident at signalised intersections in Victoria, and shows that such crashes are of four main types - right through, rear end, adjacent approaches, and pedestrian crashes. Crash patterns are then analysed in detail, focussing on the differences in site and operational characteristics between sites with a high, normal and low accident frequency over the 5 years (1987-1991) based upon an analysis of accident data and entering traffic volumes. The study indicated that the majority of the variation in accidents was not explained by traffic volumes, but by other factors. While no single factor was identified which would lead to a dramatic improvement in safety at signalised intersections, a range of measures were identified which would likely contribute to improved safety if applied at specific sites where relevant

Stability of Affine G-varieties and Irreducibility in Reductive Groups

Let $G$ be a reductive affine algebraic group, and let $X$ be an affine algebraic $G$-variety. We establish a (poly)stability criterion for points $x\in X$ in terms of intrinsically defined closed subgroups $H_{x}$ of $G$, and relate it with the numerical criterion of Mumford, and with Richardson and Bate-Martin-R\"ohrle criteria, in the case $X=G^{N}$. Our criterion builds on a close analogue of a theorem of Mundet and Schmitt on polystability and allows the generalization to the algebraic group setting of results of Johnson-Millson and Sikora about complex representation varieties of finitely presented groups. By well established results, it also provides a restatement of the non-abelian Hodge theorem in terms of stability notions.Comment: 29 pages. To appear in Int. J. Math. Note: this version 4 is identical with version 2 (version 3 is empty

Cohomological Hall algebras and character varieties

In this paper we investigate the relationship between twisted and untwisted character varieties via a specific instance of the Cohomological Hall algebra for moduli of objects in 3-Calabi-Yau categories introduced by Kontsevich and Soibelman. In terms of Donaldson--Thomas theory, this relationship is completely understood via the calculations of Hausel and Villegas of the E polynomials of twisted character varieties and untwisted character stacks. We present a conjectural lift of this relationship to the cohomological Hall algebra setting.Comment: Slight improvements picked up while editing for publication. To appear in IJM special volume for proceedings of VBAC 201

Recommendations for a core outcome set for measuring standing balance in adult populations: a consensus-based approach

Standing balance is imperative for mobility and avoiding falls. Use of an excessive number of standing balance measures has limited the synthesis of balance intervention data and hampered consistent clinical practice.To develop recommendations for a core outcome set (COS) of standing balance measures for research and practice among adults.A combination of scoping reviews, literature appraisal, anonymous voting and face-to-face meetings with fourteen invited experts from a range of disciplines with international recognition in balance measurement and falls prevention. Consensus was sought over three rounds using pre-established criteria.The scoping review identified 56 existing standing balance measures validated in adult populations with evidence of use in the past five years, and these were considered for inclusion in the COS.Fifteen measures were excluded after the first round of scoring and a further 36 after round two. Five measures were considered in round three. Two measures reached consensus for recommendation, and the expert panel recommended that at a minimum, either the Berg Balance Scale or Mini Balance Evaluation Systems Test be used when measuring standing balance in adult populations.Inclusion of two measures in the COS may increase the feasibility of potential uptake, but poses challenges for data synthesis. Adoption of the standing balance COS does not constitute a comprehensive balance assessment for any population, and users should include additional validated measures as appropriate.The absence of a gold standard for measuring standing balance has contributed to the proliferation of outcome measures. These recommendations represent an important first step towards greater standardization in the assessment and measurement of this critical skill and will inform clinical research and practice internationally

Behavior of high dose O+-implanted Si/Ge/Si structures

The synthesis of a buried oxide layer in multilayer Si/Ge/Si structures by the implantation of high doses of 200 keV O+ ions is studied by Rutherford backscattering analysis. The presence of Ge is found to have a minimal effect upon the mass transport of excess oxygen and interstitial silicon. Infrared transmission spectroscopy and x-ray photoelectron spectroscopy confirm that the oxygen atoms bond preferentially to silicon forming silicon dioxide and SiOx, where x<2, with no evidence for Ge—O bonding

A two-domain elevator mechanism for sodium/proton antiport

Sodium/proton (Na+/H+) antiporters, located at the plasma membrane in every cell, are vital for cell homeostasis1. In humans, their dysfunction has been linked to diseases, such as hypertension, heart failure and epilepsy, and they are well-established drug targets2. The best understood model system for Na+/H+ antiport is NhaA from Escherichia coli1, 3, for which both electron microscopy and crystal structures are available4, 5, 6. NhaA is made up of two distinct domains: a core domain and a dimerization domain. In the NhaA crystal structure a cavity is located between the two domains, providing access to the ion-binding site from the inward-facing surface of the protein1, 4. Like many Na+/H+ antiporters, the activity of NhaA is regulated by pH, only becoming active above pH 6.5, at which point a conformational change is thought to occur7. The only reported NhaA crystal structure so far is of the low pH inactivated form4. Here we describe the active-state structure of a Na+/H+ antiporter, NapA from Thermus thermophilus, at 3 Å resolution, solved from crystals grown at pH 7.8. In the NapA structure, the core and dimerization domains are in different positions to those seen in NhaA, and a negatively charged cavity has now opened to the outside. The extracellular cavity allows access to a strictly conserved aspartate residue thought to coordinate ion binding1, 8, 9 directly, a role supported here by molecular dynamics simulations. To alternate access to this ion-binding site, however, requires a surprisingly large rotation of the core domain, some 20° against the dimerization interface. We conclude that despite their fast transport rates of up to 1,500 ions per second3, Na+/H+ antiporters operate by a two-domain rocking bundle model, revealing themes relevant to secondary-active transporters in general

Carbohydrate Recognition by an Architecturally Complex α-N-Acetylglucosaminidase from Clostridium perfringens

CpGH89 is a large multimodular enzyme produced by the human and animal pathogen Clostridium perfringens. The catalytic activity of this exo-α-d-N-acetylglucosaminidase is directed towards a rare carbohydrate motif, N-acetyl-β-d-glucosamine-α-1,4-d-galactose, which is displayed on the class III mucins deep within the gastric mucosa. In addition to the family 89 glycoside hydrolase catalytic module this enzyme has six modules that share sequence similarity to the family 32 carbohydrate-binding modules (CBM32s), suggesting the enzyme has considerable capacity to adhere to carbohydrates. Here we suggest that two of the modules, CBM32-1 and CBM32-6, are not functional as carbohydrate-binding modules (CBMs) and demonstrate that three of the CBMs, CBM32-3, CBM32-4, and CBM32-5, are indeed capable of binding carbohydrates. CBM32-3 and CBM32-4 have a novel binding specificity for N-acetyl-β-d-glucosamine-α-1,4-d-galactose, which thus complements the specificity of the catalytic module. The X-ray crystal structure of CBM32-4 in complex with this disaccharide reveals a mode of recognition that is based primarily on accommodation of the unique bent shape of this sugar. In contrast, as revealed by a series of X-ray crystal structures and quantitative binding studies, CBM32-5 displays the structural and functional features of galactose binding that is commonly associated with CBM family 32. The functional CBM32s that CpGH89 contains suggest the possibility for multivalent binding events and the partitioning of this enzyme to highly specific regions within the gastrointestinal tract