Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Evolution of Edge States and Critical Phenomena in the Rashba Superconductor with Magnetization

We study Andreev bound states (ABS) and resulting charge transport of Rashba superconductor (RSC) where two-dimensional semiconductor (2DSM) heterostructures is sandwiched by spin-singlet s-wave superconductor and ferromagnet insulator. ABS becomes a chiral Majorana edge mode similar to that in spinless chiral p-wave pairing in topological phase (TP). We clarify that two types of quantum criticality about the topological change of ABS near a quantum critical point (QCP), whether ABS exists at QCP or not. In the former type, ABS has a energy gap and does not cross at zero energy in non-topological phase (NTP). These complex properties can be detected by tunneling conductance between normal metal / RSC junctions.Comment: 5 pages, 6 figure

Delocalization and scaling properties of low-dimensional quasiperiodic systems

In this paper, we explore the localization transition and the scaling properties of both quasi-one-dimensional and two-dimensional quasiperiodic systems, which are constituted from coupling several Aubry-Andr\'{e} (AA) chains along the transverse direction, in the presence of next-nearest-neighbor (NNN) hopping. The localization length, two-terminal conductance, and participation ratio are calculated within the tight-binding Hamiltonian. Our results reveal that a metal-insulator transition could be driven in these systems not only by changing the NNN hopping integral but also by the dimensionality effects. These results are general and hold by coupling distinct AA chains with various model parameters. Furthermore, we show from finite-size scaling that the transport properties of the two-dimensional quasiperiodic system can be described by a single parameter and the scaling function can reach the value 1, contrary to the scaling theory of localization of disordered systems. The underlying physical mechanism is discussed.Comment: 9 pages, 8 figure

Controlled Release of Vancomycin and Tigecycline from an Orthopaedic Implant Coating Prevents Staphylococcus aureus Infection in an Open Fracture Animal Model.

Introduction:Treatment of open fractures routinely involves multiple surgeries and delayed definitive fracture fixation because of concern for infection. If implants were made less susceptible to infection, a one-stage procedure with intramedullary nailing would be more feasible, which would reduce morbidity and improve outcomes. Methods:In this study, a novel open fracture mouse model was developed using Staphylococcus aureus (S. aureus) and single-stage intramedullary fixation. The model was used to evaluate whether implants coated with a novel "smart" polymer coating containing vancomycin or tigecycline would be colonized by bacteria in an open fracture model infected with S. aureus. In vivo bioluminescence, ex vivo CFUs, and X-ray images were evaluated over a 42-day postoperative period. Results:We found evidence of a markedly decreased bacterial burden with the local release of vancomycin and tigecycline from the PEG-PPS polymer compared to polymer alone. Vancomycin was released in a controlled fashion and maintained local drug concentrations above the minimum inhibition concentration for S. aureus for greater than 7 days postoperatively. Bacteria were reduced 139-fold from implants containing vancomycin and undetected from the bone and soft tissue. Tigecycline coatings led to a 5991-fold reduction in bacteria isolated from bone and soft tissue and 15-fold reduction on the implants compared to polymer alone. Antibiotic coatings also prevented osteomyelitis and implant loosening as observed on X-ray. Conclusion:Vancomycin and tigecycline can be encapsulated in a polymer coating and released over time to maintain therapeutic levels during the perioperative period. Our results suggest that antibiotic coatings can be used to prevent implant infection and osteomyelitis in the setting of open fracture. This novel open fracture mouse model can be used as a powerful in vivo preclinical tool to evaluate and optimize the treatment of open fractures before further studies in humans