Quasi-exactly Solvable Lie Superalgebras of Differential Operators

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

Cost effectiveness of nusinersen for patients with infantile-onset spinal muscular atrophy in US

Background Patients with infantile-onset spinal muscular atrophy (SMA), a rare, genetic neuromuscular disease, do not achieve key motor function milestones (e.g., sitting) and have short life expectancy in the absence of treatment. Nusinersen is a disease-modifying therapy for patients with SMA. Objective The aim of this study was to estimate the cost-effectiveness of nusinersen compared to best supportive care (BSC) in patients diagnosed with infantile-onset SMA in the US. Methods A de novo economic model was developed with the following health states: “permanent ventilation”, “not sitting”, “sitting”, “walking”, and “death”. Short-term data were sourced from the pivotal clinical trials and studies of nusinersen (ENDEAR and SHINE). Motor function milestones achieved at the end of follow-up in the clinical trials were assumed to be sustained until death. Mortality risks were based on survival modelling of relevant published Kaplan–Meier data. Costs, life years (LYs), and quality-adjusted life years (QALYs) were discounted at 3% per annum, and the analyses were performed from a US health care sector perspective. Scenario analyses and sensitivity analyses were conducted to assess the robustness of the results to key parameters. Results In our base-case analysis, nusinersen treatment achieves greater QALYs and more LYs (3.24 and 7.64, respectively) compared with BSC (0.46 QALYs and 2.40 LYs, respectively), resulting in an incremental cost per QALY gained of approximately $1,112,000 and an incremental cost per LY gained of$590,000 for nusinersen compared to BSC. The incremental cost effectiveness ratios did not fall below $990,000 per QALY gained in scenario and sensitivity analyses. Results were most sensitive to the length of survival, background health care costs, and utility in the “not sitting” and “sitting” health states. Conclusions The estimated incremental cost-effectiveness of nusinersen from a US health care sector perspective exceeded traditional cost-effectiveness thresholds. Cost-effectiveness was dependent on assumptions made regarding survival, costs, utilities, and whether the motor function milestones were sustained over lifetime. Given the relatively short-term effectiveness data available for the treatment, a registry to collect long-term data of infantile-onset SMA patients is recommended

Intertwining relations of non-stationary Schr\"odinger operators

General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in a $R$-separation of variables. The Fokker-Planck and diffusion equation are briefly considered. Second-order intertwining operators are also discussed within a general approach. However, due to its complicated structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20

Block-Diagonalization and f-electron Effects in Tight-Binding Theory

We extend a tight-binding total energy method to include f-electrons, and apply it to the study of the structural and elastic properties of a range of elements from Be to U. We find that the tight-binding parameters are as accurate and transferable for f-electron systems as they are for d-electron systems. In both cases we have found it essential to take great care in constraining the fitting procedure by using a block-diagonalization procedure, which we describe in detail.Comment: 9 pages, 6 figure

INTERPERSONAL RELATIONS AND GROUP PROCESSES Putting the Brakes on Aggression Toward a Romantic Partner: The Inhibitory Influence of Relationship Commitment

Why do people behave aggressively toward romantic partners, and what can put the brakes on this aggression? Provocation robustly predicts aggression in both intimate and nonintimate relationships. Four methodologically diverse studies tested the hypothesis that provocation severity and relationship commitment interact to predict aggression toward one's romantic partner, with the aggression-promoting effects of provocation diminishing as relationship commitment increases. Across all four studies, commitment to one's romantic relationship inhibited aggression toward one's partner when individuals were severely (but not mildly) provoked. Study 4 tested the hypothesis that this Partner Provocation ϫ Commitment interaction effect would be strong among individuals high in dispositional tendencies toward retaliation but weak (perhaps even nonexistent) among individuals low in such tendencies. Discussion emphasizes the importance of understanding instigating, impelling, and inhibiting processes in the perpetration of aggression toward intimate partners. Keywords: romantic relationships, commitment, aggression, I 3 theory Although romantic relationships often begin with chocolates and roses, eventually thorns are sure to emerge. Indeed, precisely because of the deep interdependence that characterizes these relationships, romantic partners have a particularly pronounced capacity to be infuriating. Whether by flirting with others, criticizing our flaws, thoughtlessly neglecting our needs and desires, or by other omissions and commissions, romantic partners can sometimes provoke angry responses. Such provocation frequently triggers an urge toward retaliation, perhaps even toward aggression. When will provoked people aggress toward their romantic partner, and what might put the brakes on their aggression? In the current investigation, we test the hypothesis that partner provocation increases aggressive tendencies toward one's partner, especially among individuals who are weakly (vs. strongly) committed to their partner. The logic underlying this prediction is that partner provocation frequently triggers an urge toward aggressive retaliation but that relationship commitment helps individuals override this urge. Partner Provocation in Intimate Relationships Although people typically expect that romantic relationships will be rewarding, most individuals experience some amount of conflict with their romantic partner. Indeed, conflict is "an inevitable-though often unanticipated-feature of close relationships. The strong, frequent, and diverse bonds between [romantic partners] set the stage for conflicting interests to surface&quot

Planar and Poly-Arc Lombardi Drawings

In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.Comment: Expanded version of paper appearing in the 19th International Symposium on Graph Drawing (GD 2011). 16 pages, 8 figure

Hsp90 governs dispersion and drug resistance of fungal biofilms

Fungal biofilms are a major cause of human mortality and are recalcitrant to most treatments due to intrinsic drug resistance. These complex communities of multiple cell types form on indwelling medical devices and their eradication often requires surgical removal of infected devices. Here we implicate the molecular chaperone Hsp90 as a key regulator of biofilm dispersion and drug resistance. We previously established that in the leading human fungal pathogen, Candida albicans, Hsp90 enables the emergence and maintenance of drug resistance in planktonic conditions by stabilizing the protein phosphatase calcineurin and MAPK Mkc1. Hsp90 also regulates temperature-dependent C. albicans morphogenesis through repression of cAMP-PKA signalling. Here we demonstrate that genetic depletion of Hsp90 reduced C. albicans biofilm growth and maturation in vitro and impaired dispersal of biofilm cells. Further, compromising Hsp90 function in vitro abrogated resistance of C. albicans biofilms to the most widely deployed class of antifungal drugs, the azoles. Depletion of Hsp90 led to reduction of calcineurin and Mkc1 in planktonic but not biofilm conditions, suggesting that Hsp90 regulates drug resistance through different mechanisms in these distinct cellular states. Reduction of Hsp90 levels led to a marked decrease in matrix glucan levels, providing a compelling mechanism through which Hsp90 might regulate biofilm azole resistance. Impairment of Hsp90 function genetically or pharmacologically transformed fluconazole from ineffectual to highly effective in eradicating biofilms in a rat venous catheter infection model. Finally, inhibition of Hsp90 reduced resistance of biofilms of the most lethal mould, Aspergillus fumigatus, to the newest class of antifungals to reach the clinic, the echinocandins. Thus, we establish a novel mechanism regulating biofilm drug resistance and dispersion and that targeting Hsp90 provides a much-needed strategy for improving clinical outcome in the treatment of biofilm infections

Phenotypic Variation and Bistable Switching in Bacteria

Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.