On the asymptotic magnitude of subsets of Euclidean space

Magnitude is a canonical invariant of finite metric spaces which has its origins in category theory; it is analogous to cardinality of finite sets. Here, by approximating certain compact subsets of Euclidean space with finite subsets, the magnitudes of line segments, circles and Cantor sets are defined and calculated. It is observed that asymptotically these satisfy the inclusion-exclusion principle, relating them to intrinsic volumes of polyconvex sets.Comment: 23 pages. Version 2: updated to reflect more recent work, in particular, the approximation method is now known to calculate (rather than merely define) the magnitude; also minor alterations such as references adde

Antithrombin Budapest 3 An antithrombin variant with reduced heparin affinity resulting from the substitution L99F

AbstractThe molecular basis and functional properties of a variant antithrombin (AT) protein. AT Budapest 3, were studied. A single base substitution was identified in codon 99, CTC→TTC, altering the normal leucine to phenylalanine. The proband presented with a history of venous thrombotic disease and was found to be homozygous for the mutation. The variant protein demonstrated reduced heparin affinity and reduced antiproteinase activity in the presence of either unfractionated heparin or the AT-binding heparin pentasaccharide, when compared to normal AT. A small change in the isoelectric point was also identified. The substituted amino acid residue of AT Budapest 3 is located near to the proposed AT heparin binding site, and it is suggested that reduced heparin affinity of the variant protein may result from substitution-induced distortion of positive charge geometry in the binding site and/or changes in its position relative to the rest of the inhibitor molecule

Electronic structure and superconductivity of Europium

We have calculated the electronic structure of Eu for the bcc, hcp, and fcc crystal structures for volumes near equilibrium up to a calculated 90 GPa pressure using the augmented-plane wave method in the local-density approximation. The frozen-core approximation was used with a semi-empirical shift of the f-states energies in the radial Schr$\ddot{o}$dinger equation to move the occupied 4f valence states below the $\Gamma_1$ energy and into the core. This shift of the highly localized f-states yields the correct europium phase ordering with lattice parameters and bulk moduli in good agreement with experimental data. The calculated superconductivity properties under pressure for the $\it bcc$ and $\it hcp$ structures are also found to agree with and follow a $T_c$ trend similar to recent measurement by Debessai et al.$^1$Comment: 8 page

Non-commutative desingularization of determinantal varieties, I

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.Comment: 52 pages, 3 figures, all comments welcom

Neutral top-pion and lepton flavor violating processes

In the context of topcolor-assisted techicolor(TC2) models, we study the contributions of the neutral top-pion $\pi^{0}_{t}$ to the lepton flavor violating(LFV) processes $l_{i}\to l_{j}\gamma$ and $l_{i}\to l_{j}l_{k}l_{l}$. We find that the present experimental bound on $\mu\to e\gamma$ gives severe constraints on the free parameters of $TC2$ models. Taking into account these constraints, we consider the processes $l_{i}\to l_{j}l_{k}l_{l}$ generated by top-pion exchange at the tree-level and the one loop level, and obtain $Br(\mu\to 3e)\simeq 2.87\times 10^{-14}$, $1.1\times 10^{-15}\leq Br(\tau\to 3e)\simeq Br(\tau\to 2e\mu)\leq 4.4 \times 10^{-15}$, $3.1\times 10^{-15} \leq Br(\tau\to 2\mu e)\simeq Br(\tau\to 3\mu)\leq 1.5 \times 10^{-14}$ in most of the parameter space.Comment: latex files,16 pages, 6 figures. Submitted to Phys. Rev.

Autoantibodies against EPCR are found in antiphospholipid syndrome and are a risk factor for fetal death

The antiphospholipid syndrome (APS) is associated with thrombosis and fetal death but the pathologic mechanisms are poorly understood. Since endothelial protein C receptor (EPCR) plays a role in the anticoagulant system and in placental development, we hypothesized that anti-EPCR autoantibodies may be involved in clinical manifestations of APS and in fetal loss. The levels of immunoglobulin M (IgM) and IgG anti-EPCR autoantibodies were analyzed by enzyme-linked immunosorbent assay (ELISA) in 43 patients with APS and 43 controls. Anti-EPCR levels were higher in APS patients than in controls. Interestingly, one of the IgM anti-EPCR autoantibodies inhibited the generation of activated protein C on endothelium. Since markedly high anti-EPCR levels were found in women with fetal death, 87 patients with a first episode of unexplained fetal death were subsequently analyzed and their anti-EPCR levels were compared with 87 matched controls. We found that anti-EPCR autoantibodies constitute an independent risk factor for a first fetal death episode: the adjusted odds ratios (ORs) for anti-EPCR autoantibodies above the 95th percentile were 23.0 (95% confidence interval [CI], 2.0-266.3) for IgM and 6.8 (95% CI, 1.2-38.4) for IgG. Anti-EPCR autoantibodies can be detected in APS patients and are independent risk factors for fetal death

The institutional shaping of management: in the tracks of English individualism

Globalisation raises important questions about the shaping of economic action by cultural factors. This article explores the formation of what is seen by some as a prime influence on the formation of British management: individualism. Drawing on a range of historical sources, it argues for a comparative approach. In this case, the primary comparison drawn is between England and Scotland. The contention is that there is a systemic approach to authority in Scotland that can be contrasted to a personal approach in England. An examination of the careers of a number of Scottish pioneers of management suggests the roots of this systemic approach in practices of church governance. Ultimately this systemic approach was to take a secondary role to the personal approach engendered by institutions like the universities of Oxford and Cambridge, but it found more success in the different institutional context of the USA. The complexities of dealing with historical evidence are stressed, as is the value of taking a comparative approach. In this case this indicates a need to take religious practice as seriously as religious belief as a source of transferable practice. The article suggests that management should not be seen as a simple response to economic imperatives, but as shaped by the social and cultural context from which it emerges

Associated production of neutral toppion with a pair of heavy quarks in γγ\gamma\gamma collisions

We have studied a neutral toppion production process $\gamma\gamma\to f\bar{f}\Pi_{t}^{0}(f=t,b)$ in the topcolor-assisted technicolor(TC2) model. We find that the cross section of $\gamma\gamma\to t\bar{t}\Pi_{t}^{0}$ is much larger than that of $\gamma\gamma\to b\bar{b}\Pi_{t}^{0}$. On the other hand, the cross section can be obviously enhanced with the increasing of c.m.energy. With $\sqrt{s}=1600$ GeV, the cross section of $t\bar{t}\Pi_t^0$ production can reach the level of a few fb. The results show that $\gamma\gamma\to t\bar{t}\Pi^0_t \to t\bar{t}(t\bar{c})$ is the most ideal channel to detect neutral toppion due to the clean SM background. With such sufficient signals and clean background, neutral toppion could be detected at TESLA with high c.m.energy.Comment: 11 pages, 5 figure