The homotopy invariance of the string topology loop product and string bracket

Let M be a closed, oriented, n -manifold, and LM its free loop space. Chas and Sullivan defined a commutative algebra structure in the homology of LM, and a Lie algebra structure in its equivariant homology. These structures are known as the string topology loop product and string bracket, respectively. In this paper we prove that these structures are homotopy invariants in the following sense. Let f : M_1 \to M_2 be a homotopy equivalence of closed, oriented n -manifolds. Then the induced equivalence, Lf : LM_1 \to LM_2 induces a ring isomorphism in homology, and an isomorphism of Lie algebras in equivariant homology. The analogous statement also holds true for any generalized homology theory h_* that supports an orientation of the M_i 's.Comment: 21 pages, 2 figures final version published in Journal of Topolog

Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents

This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature. We develop the quantitative theory of this quantization and interpret it in terms of topological invariants. By implementing the celebrated Kirchhoff theorem we derive a general and explicit formula for the average generated current that plays a role of an efficient tool for treating the current quantization effects.Comment: 22 pages, 7 figure

A Common-Path Heterodyne Interferometer for Surface Profiling in Microelectronic Fabrication

We describe the design of a common-path heterodyne laser interferometer for the surface profiling of micron-sized photopatterned features during the microelectronic fabrication process. The common-path design of the interferometer’s reference and measurement arms effectively removes any path length difference in the measurement which can be attributed to the movement of the target surface. It is shown that repeated surface profiling during the ion milling process allows the difference in etch rates between the photoresist layer and the exposed portions of the underlying substrate layer to be monitored online. A prototype apparatus has been assembled and results demonstrating the usefulness of the device are reported. The surface profiles of both a photopatterned nickel–iron trench and an unmasked aluminum trench are measured and compared to those obtained using a stylus-based scanning profiler and an atomic force microscope

Campylobacter bacteremia in London: A 44-year single-center study.

PURPOSE: Campylobacter species are a well-recognized but rare cause of bloodstream infection. METHODS: Here we reviewed 41 cases of Campylobacter bloodstream infection occurring at a single center in London over 44years, comprising 0.2% of all recorded episodes during this time period. RESULTS: Patients had a mean age of 46years and, contrasting with previous reports, nearly 50% of our patients did not have significant comorbidities. Ciprofloxacin resistance increased over the study period with 35% of isolates overall being resistant compared with only 3% exhibiting macrolide resistance. Despite a minority of patients receiving appropriate empirical antibiotic therapy, overall mortality was only 7%. CONCLUSION: Campylobacter bacteremia remains a rare but significant cause of morbidity with a low associated mortality. Underlying immunosuppressive conditions are common but by no means universal. In our setting, macrolides would be favored as empirical agents to treat suspected Campylobacter enteritis, including cases with associated bacteremia

Ab initio theory and modeling of water

Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice I{\it h} at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner

Vertical integration and firm boundaries : the evidence

Since Ronald H. Coase's (1937) seminal paper, a rich set of theories has been developed that deal with firm boundaries in vertical or input–output structures. In the last twenty-five years, empirical evidence that can shed light on those theories also has been accumulating. We review the findings of empirical studies that have addressed two main interrelated questions: First, what types of transactions are best brought within the firm and, second, what are the consequences of vertical integration decisions for economic outcomes such as prices, quantities, investment, and profits. Throughout, we highlight areas of potential cross-fertilization and promising areas for future work