Majorana Fermions and Non-Abelian Statistics in Three Dimensions

We show that three dimensional superconductors, described within a Bogoliubov de Gennes framework can have zero energy bound states associated with pointlike topological defects. The Majorana fermions associated with these modes have non-Abelian exchange statistics, despite the fact that the braid group is trivial in three dimensions. This can occur because the defects are associated with an orientation that can undergo topologically nontrivial rotations. A new feature of three dimensional systems is that there are "braidless" operations in which it is possible to manipulate the groundstate associated with a set of defects without moving or measuring them. To illustrate these effects we analyze specific architectures involving topological insulators and superconductors.Comment: 4 pages, 2 figures, published versio

The Effect of Randomized School Admissions on Voter Participation

There is little causal evidence on the effect of economic and policy outcomes on voting behavior. This paper uses randomized outcomes from a school choice lottery to examine if lottery outcomes affect voting behavior in a school board election. We show that losing the lottery has no significant impact on overall voting behavior; however, among white families, those with above median income and prior voting history, lottery losers were significantly more likely to vote than lottery winners. Using propensity score methods, we compare the voting of lottery participants to similar families who did not participate in the lottery. We find that losing the school choice lottery caused an increase in voter turnout among whites, while winning the lottery had no effect relative to non-participants. Overall, our empirical results lend support to models of expressive and retrospective voting, where likely voters are motivated to vote by past negative policy outcomes.

Waring's Theorem for Binary Powers

A natural number is a binary $k$'th power if its binary representation consists of $k$ consecutive identical blocks. We prove an analogue of Waring's theorem for sums of binary $k$'th powers. More precisely, we show that for each integer $k \geq 2$, there exists a positive integer $W(k)$ such that every sufficiently large multiple of $E_k := \gcd(2^k - 1, k)$ is the sum of at most $W(k)$ binary $k$'th powers. (The hypothesis of being a multiple of $E_k$ cannot be omitted, since we show that the $\gcd$ of the binary $k$'th powers is $E_k$.) Also, we explain how our results can be extended to arbitrary integer bases $b > 2$

Fostering Socio-Ecological Resilience to Wildfire by Interconnecting Knowledge Systems at Cal Poly Humboldt

The wildfire-related challenges of Northern California and many other regions in the western United States are daunting in scope and magnitude. Ecologically and culturally salient solutions that limit the negative impacts of wildfire and promote resilience of human and ecological systems will require newer approaches. Through Cal Poly Humboldt and the Fire Resilience Institute, there is greater emphasis on the interconnection of knowledge systems across education, training, research, and management. Here we highlight several on-going efforts that seek to enhance the fire resilience workforce, promote socio-ecological resilience through interdisciplinary projects, and inform management through monitoring and research projects that intentionally incorporate multiple knowledge systems. Shifting to a more inclusive process has many potential benefits but will also pose challenges and require modification of approaches. Here we emphasize some on-going efforts at Cal Poly Humboldt to intentionally bridge knowledge systems to make advances on wildfire-related challenges. Socio-ecological resilience and coexistence with fire can be fostered but the long-term effectiveness will greatly benefit from approaches that are inclusive, equitable, and interconnected across the many stakeholders affected and disciplines involved

Effects of expression of mammalian G alpha and hybrid mammalian-yeast G alpha proteins on the yeast pheromone response signal transduction pathway

Scg1, the product of the Saccharomyces cerevisiae SCG1 (also called GPA1) gene, is homologous to the alpha subunits of G proteins involved in signal transduction in mammalian cells. Scg1 negatively controls the pheromone response pathway in haploid cells. Either pheromonal activation or an scg1 null mutation relieves the negative control and leads to an arrest of cell growth in the G1 phase of the cell cycle. Expression of rat G alpha s was previously shown to complement the growth defect of scg1 null mutants while not allowing mating. We have extended this analysis to examine the effects of the short form of G alpha s (which lacks 15 amino acids present in the long form), G alpha i2, G alpha o, and Scg1-mammalian G alpha hybrids. In addition, we have found that constructs able to complement scg1 are also able to inhibit the response to pheromone and mating when expressed in a wild-type SCG1 strain. Overexpression of Scg1 has a similar inhibitory effect. These results are consistent with a model proposed for the action of Scg1 as the alpha component of a heterotrimeric G protein in which the beta gamma component (Ste4/Ste18) activates the pheromone response after dissociation from Scg1. They suggest that the G alpha constructs able to complement scg1 can interact with beta gamma to prevent activation of the pathway but are unable to interact with pheromone receptors to activate the pathway

Topological Defects and Gapless Modes in Insulators and Superconductors

We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic parameters r surrounding the defect and belong to any of the ten symmetry classes defined by time reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified, and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions and helical Majorana fermions, as well as zero dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.Comment: 27 pages, 15 figures, Published versio

Provably and Efficiently Approximating Near-cliques using the Tur\'an Shadow: PEANUTS

Clique and near-clique counts are important graph properties with applications in graph generation, graph modeling, graph analytics, community detection among others. They are the archetypal examples of dense subgraphs. While there are several different definitions of near-cliques, most of them share the attribute that they are cliques that are missing a small number of edges. Clique counting is itself considered a challenging problem. Counting near-cliques is significantly harder more so since the search space for near-cliques is orders of magnitude larger than that of cliques. We give a formulation of a near-clique as a clique that is missing a constant number of edges. We exploit the fact that a near-clique contains a smaller clique, and use techniques for clique sampling to count near-cliques. This method allows us to count near-cliques with 1 or 2 missing edges, in graphs with tens of millions of edges. To the best of our knowledge, there was no known efficient method for this problem, and we obtain a 10x - 100x speedup over existing algorithms for counting near-cliques. Our main technique is a space-efficient adaptation of the Tur\'an Shadow sampling approach, recently introduced by Jain and Seshadhri (WWW 2017). This approach constructs a large recursion tree (called the Tur\'an Shadow) that represents cliques in a graph. We design a novel algorithm that builds an estimator for near-cliques, using an online, compact construction of the Tur\'an Shadow.Comment: The Web Conference, 2020 (WWW

Hydroxychloroquine and the risk of respiratory infections among RA patients

OBJECTIVES: To determine the effect of hydroxychloroquine on the incidence of new respiratory infections in a large registry of rheumatoid arthritis (RA) patients compared with a matched cohort receiving other conventional disease-modifying antirheumatic drugs (csDMARDs). METHODS: We reviewed physician-reported infections including upper respiratory infections (URI), bronchitis and pneumonia in the Corrona RA registry from June 2008 to February 2020 with the goal of comparing infections in biologic/targeted synthetic (b/ts) DMARDs naive HCQ starts compared with starts of other csDMARDs and no HCQ. Patients on different interventions were compared using time-varying adjusted Cox models adjusting for age, sex, duration of RA, BMI, disease activity, smoking status, concurrent medications, season of the year, year of onset and history of serious infections, diabetes or cardiovascular disease (CVD). A secondary analysis in a set of propensity-matched starts were also compared adjusting for time-varying covariates. The analysis was repeated including URI and bronchitis only and also for serious respiratory infections only. RESULTS: No evidence of differences was found in the incidence of any respiratory infection (URI, bronchitis, pneumonia) in patients receiving HCQ compared with other csDMARDs: HR=0.87 (0.70 to1.07) in adjusted analyses and HR=0.90 (0.70 to 1.17) in adjusted matched analysis. Similar results were found in the analysis of URI and bronchitis only and for serious respiratory infections only. CONCLUSIONS: In patients with RA, the risk for respiratory infections was similar among patients using HCQ as compared to other non-biologic DMARDs

Residual Impact of Previous Injury on Musculoskeletal Characteristics in Special Forces Operators

Background: Musculoskeletal injuries are a significant burden to United States Army Special Operations Forces. The advanced tactical skill level and physical training required of Army Special Operators highlights the need to optimize musculoskeletal characteristics to reduce the likelihood of suffering a recurrent injury. Purpose: To identify the residual impact of previous injury on musculoskeletal characteristics. Study Design: Cross-sectional study; Level of evidence, 3. Methods: Isokinetic strength of the knee, shoulder, and back and flexibility of the shoulder and hamstrings were assessed as part of a comprehensive human performance protocol, and self-reported musculoskeletal injury history was obtained. Subjects were stratified based on previous history of low back, knee, or shoulder injury, and within-group and between-group comparisons were made for musculoskeletal variables. Results: Knee injury analysis showed no significant strength or flexibility differences. Shoulder injury analysis found internal rotation strength of the healthy subjects (H) was significantly higher compared with injured (I) and uninjured (U) limbs of the injured group (H, 60.8 ± 11.5 percent body weight [%BW]; I, 54.5 ± 10.5 %BW; U, 55.5 ± 11.3 %BW) (P = .014 [H vs I] and P = .05 [H vs U]). The external rotation/internal rotation strength ratio was significantly lower in the healthy subjects compared with injured and uninjured limbs of the injured group (H, 0.653 ± 0.122; I, 0.724 ± 0.121; U, 0.724 ± 0.124) (P = .026 [H vs I] and P = .018 [H vs U]). Posterior shoulder tightness was significantly different between the injured and uninjured limb of the injured group (I, 111.6° ± 9.4°; U, 114.4° ± 9.3°; P = .008). The back injury analysis found no significant strength differences between the healthy and injured groups. Conclusion: Few physical differences existed between operators with prior knee or back injury. However, operators with a previous history of shoulder injury demonstrated significantly less shoulder strength than uninjured operators as well as decreased shoulder flexibility on the injured side. All operators, regardless of prior injury, must perform the same tasks; therefore, a targeted injury rehabilitation/human performance training specifically focused on internal rotation strength and tightness of the posterior capsule may help reduce the risk for recurrence of injury. Operators presenting with musculoskeletal asymmetries and/or insufficient strength ratios may be predisposed to musculoskeletal injury. Clinical Relevance: Specific fitness programs to compensate for deficiencies in strength and flexibility need to be designed that may reduce the risk of injuries in Special Forces Operators

Exoplanet Catalogues

One of the most exciting developments in the field of exoplanets has been the progression from 'stamp-collecting' to demography, from discovery to characterisation, from exoplanets to comparative exoplanetology. There is an exhilaration when a prediction is confirmed, a trend is observed, or a new population appears. This transition has been driven by the rise in the sheer number of known exoplanets, which has been rising exponentially for two decades (Mamajek 2016). However, the careful collection, scrutiny and organisation of these exoplanets is necessary for drawing robust, scientific conclusions that are sensitive to the biases and caveats that have gone into their discovery. The purpose of this chapter is to discuss and demonstrate important considerations to keep in mind when examining or constructing a catalogue of exoplanets. First, we introduce the value of exoplanetary catalogues. There are a handful of large, online databases that aggregate the available exoplanet literature and render it digestible and navigable - an ever more complex task with the growing number and diversity of exoplanet discoveries. We compare and contrast three of the most up-to-date general catalogues, including the data and tools that are available. We then describe exoplanet catalogues that were constructed to address specific science questions or exoplanet discovery space. Although we do not attempt to list or summarise all the published lists of exoplanets in the literature in this chapter, we explore the case study of the NASA Kepler mission planet catalogues in some detail. Finally, we lay out some of the best practices to adopt when constructing or utilising an exoplanet catalogue.Comment: 14 pages, 6 figures. Invited review chapter, to appear in "Handbook of Exoplanets", edited by H.J. Deeg and J.A. Belmonte, section editor N. Batalh