L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

Evidence for a Bulk Complex Order-Parameter in Y0.9Ca0.1Ba2Cu3O7-delta Thin Films

We have measured the penetration depth of overdoped Y0.9Ca0.1Ba2Cu3O7-delta (Ca-YBCO) thin films using two different methods. The change of the penetration depth as a function of temperature has been measured using the parallel plate resonator (PPR), while its absolute value was obtained from a quasi-optical transmission measurements. Both sets of measurements are compatible with an order parameter of the form: Delta*dx2-y2+i*delta*dxy, with Delta=14.5 +- 1.5 meV and delta=1.8 meV, indicating a finite gap at low temperature. Below 15 K the drop of the scattering rate of uncondensed carriers becomes steeper in contrast to a flattening observed for optimally doped YBCO films. This decrease supports our results on the penetration depth temperature dependence. The findings are in agreement with tunneling measurements on similar Ca-YBCO thin films.Comment: 11 pages, 4 figure

Supersymmetry, homology with twisted coefficients and n-dimensional knots

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp. bosonic\} states) and a set of operators (supersymmetric infinitesimal transformations) in an explicit way. Thus we obtain a set of the Witten indexes for $K$. Our Witten indexes are topological invariants for $n$-dimensional knots. Our Witten indexes are not zero in general. If $K$ is equivalent to the trivial knot, all of our Witten indexes are zero. Our Witten indexes restrict the Alexander polynomials of $n$-knots. If one of our Witten indexes for an $n$-knot $K$ is nonzero, then one of the Alexander polynomials of $K$ is nontrivial. Our Witten indexes are connected with homology with twisted coefficients. Roughly speaking, our Witten indexes have path integral representation by using a usual manner of supersymmetric theory.Comment: 10pages, no figure

A comparison of arbitration procedures for risk averse disputants

We propose an arbitration model framework that generalizes many previous quantitative models of final offer arbitration, conventional arbitration, and some proposed alternatives to them. Our model allows the two disputants to be risk averse and assumes that the issue(s) in dispute can be summarized by a single quantifiable value. We compare the performance of the different arbitration procedures by analyzing the gap between the disputants' equilibrium offers and the width of the contract zone that these offers imply. Our results suggest that final offer arbitration should give results superior to those of conventional arbitration.Natural Sciences & Engineering Research Council (NSERC) Discovery Gran

Atomic structure of dislocation kinks in silicon

We investigate the physics of the core reconstruction and associated structural excitations (reconstruction defects and kinks) of dislocations in silicon, using a linear-scaling density-matrix technique. The two predominant dislocations (the 90-degree and 30-degree partials) are examined, focusing for the 90-degree case on the single-period core reconstruction. In both cases, we observe strongly reconstructed bonds at the dislocation cores, as suggested in previous studies. As a consequence, relatively low formation energies and high migration barriers are generally associated with reconstructed (dangling-bond-free) kinks. Complexes formed of a kink plus a reconstruction defect are found to be strongly bound in the 30-degree partial, while the opposite is true in the case of 90-degree partial, where such complexes are found to be only marginally stable at zero temperature with very low dissociation barriers. For the 30-degree partial, our calculated formation energies and migration barriers of kinks are seen to compare favorably with experiment. Our results for the kink energies on the 90-degree partial are consistent with a recently proposed alternative double-period structure for the core of this dislocation.Comment: 12 pages, two-column style with 8 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#rn_di

Testing for Network and Spatial Autocorrelation

Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in continuous variables. In this paper we propose two contributions to the literature on tests for autocorrelation. First, we propose a new test for autocorrelation in categorical variables. While some methods currently exist for assessing spatial autocorrelation in categorical variables, the most popular method is unwieldy, somewhat ad hoc, and fails to provide grounds for a single omnibus test. Second, we discuss the importance of testing for autocorrelation in data sampled from the nodes of a network, motivated by social network applications. We demonstrate that our proposed statistic for categorical variables can both be used in the spatial and network setting

A Comparison of Formal and Informal Dispute Resolution in Medical Malpractice

In this study we examine the experience of a single large hospital with an informal pre-litigation "complaint" process that resolves some cases outside of the legal system. The empirical results are generally consistent with an information structure where patients are poorly informed about the quality of medical care and the hospital does not know whether particular patients are litigious or not. The complaint process seems to resolve many complaints in a less costly manner than filing lawsuits. Almost half of all complaints are resolved before a lawsuit is filed. The large majority of these are dropped, and they are cases that would likely have been dropped even if they had been initiated as lawsuits. Very few cases are settled with a cash payment to patients before a lawsuit is filed, suggesting that patients must file lawsuits in order to convince the hospital that they are litigious enough to justify a settlement. Cases initiated through the complaint process are not resolved (dropped, settled, tried to a verdict) significantly differently from cases initiated as lawsuits, controlling for observable case characteristics. When settlements of lawsuits occur, the amounts paid do not vary depending on how the case originated, but settlements of complaints are much higher for cases settled after a lawsuit is filed, We conclude that the complaint process is a cost-effective "front-end" for the litigation process that provides information to patients regarding the quality of their medical care and, hence, the likelihood of negligence.