Quantum chains with a Catalan tree pattern of conserved charges: the Δ=−1\Delta = -1 XXZ model and the isotropic octonionic chain

A class of quantum chains possessing a family of local conserved charges with a Catalan tree pattern is studied. Recently, we have identified such a structure in the integrable $SU(N)$-invariant chains. In the present work we find sufficient conditions for the existence of a family of charges with this structure in terms of the underlying algebra. Two additional systems with a Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ model with $\Delta=-1$. The other is a new octonionic isotropic chain, generalizing the Heisenberg model. This system provides an interesting example of an infinite family of noncommuting local conserved quantities.Comment: 20 pages in plain TeX; uses macro harvma

Structure of the conservation laws in integrable spin chains with short range interactions

We present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. With the use of the boost operator, we establish the general form of the XYZ conserved charges in terms of simple polynomials in spin variables and derive recursion relations for the relative coefficients of these polynomials. For two submodels of the XYZ chain - namely the XXX and XY cases, all the charges can be calculated in closed form. For the XXX case, a simple description of conserved charges is found in terms of a Catalan tree. This construction is generalized for the su(M) invariant integrable chain. We also indicate that a quantum recursive (ladder) operator can be traced back to the presence of a hamiltonian mastersymmetry of degree one in the classical continuous version of the model. We show that in the quantum continuous limits of the XYZ model, the ladder property of the boost operator disappears. For the Hubbard model we demonstrate the non-existence of a ladder operator. Nevertheless, the general structure of the conserved charges is indicated, and the expression for the terms linear in the model's free parameter for all charges is derived in closed form.Comment: 79 pages in plain TeX plus 4 uuencoded figures; (uses harvmac and epsf

Theory for Superconducting Properties of the Cuprates: Doping Dependence of the Electronic Excitations and Shadow States

The superconducting phase of the 2D one-band Hubbard model is studied within the FLEX approximation and by using an Eliashberg theory. We investigate the doping dependence of $T_c$, of the gap function $\Delta ({\bf k},\omega)$ and of the effective pairing interaction. Thus we find that $T_c$ becomes maximal for $13 \; \%$ doping. In {\it overdoped} systems $T_c$ decreases due to the weakening of the antiferromagnetic correlations, while in the {\it underdoped} systems due to the decreasing quasi particle lifetimes. Furthermore, we find {\it shadow states} below $T_c$ which affect the electronic excitation spectrum and lead to fine structure in photoemission experiments.Comment: 10 pages (REVTeX) with 5 figures (Postscript

Fault-Tolerance by Graceful Degradation for Car Platoons

The key advantage of autonomous car platoons are their short inter-vehicle distances that increase traffic flow and reduce fuel consumption. However, this is challenging for operational and functional safety. If a failure occurs, the affected vehicles cannot suddenly stop driving but instead should continue their operation with reduced performance until a safe state can be reached or, in the case of temporal failures, full functionality can be guaranteed again. To achieve this degradation, platoon members have to be able to compensate sensor and communication failures and have to adjust their inter-vehicle distances to ensure safety. In this work, we describe a systematic design of degradation cascades for sensor and communication failures in autonomous car platoons using the example of an autonomous model car. We describe our systematic design method, the resulting degradation modes, and formulate contracts for each degradation level. We model and test our resulting degradation controller in Simulink/Stateflow

The Structure of Conserved Charges in Open Spin Chains

We study the local conserved charges in integrable spin chains of the XYZ type with nontrivial boundary conditions. The general structure of these charges consists of a bulk part, whose density is identical to that of a periodic chain, and a boundary part. In contrast with the periodic case, only charges corresponding to interactions of even number of spins exist for the open chain. Hence, there are half as many charges in the open case as in the closed case. For the open spin-1/2 XY chain, we derive the explicit expressions of all the charges. For the open spin-1/2 XXX chain, several lowest order charges are presented and a general method of obtaining the boundary terms is indicated. In contrast with the closed case, the XXX charges cannot be described in terms of a Catalan tree pattern.Comment: 22 pages, harvmac.tex (minor clarifications and reference corrections added

Modular classes of skew algebroid relations

Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.Comment: 20 page

Modular classes of Poisson-Nijenhuis Lie algebroids

The modular vector field of a Poisson-Nijenhuis Lie algebroid $A$ is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian $A$-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

Factors Associated with Influenza Vaccine Uptake among Pregnant Women: Analysis of the 2015 Georgia Vital Events Information System Birth Worksheet

ABSTRACT INTRODUCTION: Influenza is a public health concern each influenza season in the United States (US). Annually, about 50,000 people die due to influenza complications in the US. Pregnant women and children under the age of five are two of the most at-risk groups for influenza-related morbidity and mortality. Since 2004, the Centers for Disease Control (CDC), the Advisory Committee on Immunization Practice (ACIP), and the American College of Obstetricians and Gynecologists (ACOG) have recommended that women who will be pregnant during the influenza season get vaccinated. Vaccination of mothers also protects infants for up to the first six months of life through the active transfer of maternal antibodies in the womb. Vaccination during pregnancy is safe and is the most effective way for mothers to protect themselves and their infants from the influenza virus. PURPOSE: Vaccination rates among pregnant women in Georgia are low, despite the CDC, ACIP, and ACOG recommendation to be vaccinated for influenza during pregnancy. In 2013, only 23.7% of women in Georgia received an influenza vaccine before or during pregnancy, a number well below the national average of 55.3% for the same year. The purpose of this study is to determine which factors are positively associated with influenza vaccine uptake during 2 pregnancy in Georgia through an analysis of the 2015 Georgia Vital Events Information System (VEIS) Birth Worksheet. The author believes that by identifying which factors show an increase in vaccine uptake, clinicians will be able to beneficially direct vaccine promotion efforts among pregnant women in Georgia. METHODS: Secondary data from the 2015 VEIS Birth Worksheet was obtained from the Georgia Department of Public Health. 130,133 women between the ages of 18 – 49 completed a Birth Worksheet in 2015 and were included in the study. Variables used for regression analysis, descriptive analysis, and prevalence of vaccine uptake include: age, race, education level, perinatal region of residence, and receipt of prenatal care. An extensive review of existing literature was also conducted. RESULTS: The prevalence of influenza vaccine uptake among pregnant women varied across the variables. 13.39% of women who completed a Birth Worksheet in 2015 reported that they received an influenza vaccine during pregnancy. The prevalence of vaccine uptake was highest among white women (65.26%), women between the ages of 25 – 34 (60.16%), women with a college degree (51.03%), and women living in the Atlanta perinatal region (44.52%). Surprisingly, of all the Atlanta region respondents, only 10.32% received an influenza vaccine despite having the largest population of all the regions in Georgia. Almost all women who received an influenza vaccine during pregnancy also received prenatal care (98.48%). Of the 115,443 women who received prenatal care, 14.87% received an influenza vaccine