On the Spectra of Real and Complex Lam\'e Operators

We study Lam\'e operators of the form $$L = -\frac{d^2}{dx^2} + m(m+1)\omega^2\wp(\omega x+z_0),$$ with $m\in\mathbb{N}$ and $\omega$ a half-period of $\wp(z)$. For rectangular period lattices, we can choose $\omega$ and $z_0$ such that the potential is real, periodic and regular. It is known after Ince that the spectrum of the corresponding Lam\'e operator has a band structure with not more than $m$ gaps. In the first part of the paper, we prove that the opened gaps are precisely the first $m$ ones. In the second part, we study the Lam\'e spectrum for a generic period lattice when the potential is complex-valued. We concentrate on the $m=1$ case, when the spectrum consists of two regular analytic arcs, one of which extends to infinity, and briefly discuss the $m=2$ case, paying particular attention to the rhombic lattices

Altering the stability of the Cdc8 overlap region modulates the ability of this tropomyosin to bind cooperatively to actin and regulate myosin.

Tropomyosin (Tm) is an evolutionarily conserved ?-helical coiled-coil protein, dimers of which form end-to-end polymers capable of associating with and stabilising actin-filaments and regulate myosin function. The fission yeast, Schizosaccharomyces pombe, possesses a single essential Tm, Cdc8, which can be acetylated on its amino terminal methionine to increase its affinity for actin and enhance its ability to regulate myosin function. We have designed and generated a number of novel Cdc8 mutant proteins with amino terminal substitutions to explore how stability of the Cdc8-polymer overlap region affects the regulatory function of this Tm. By correlating the stability of each protein, its propensity to form stable polymers, its ability to associate with actin and to regulate myosin, we have shown the stability of the amino terminal of the Cdc8 ?-helix is crucial for Tm function. In addition we have identified a novel Cdc8 mutant with increased amino-terminal stability, dimers of which are capable of forming Tm-polymers significantly longer than the wild-type protein. This protein had a reduced affinity for actin with respect to wild type, and was unable to regulate actomyosin interactions. The data presented here are consistent with acetylation providing a mechanism for modulating the formation and stability of Cdc8 polymers within the fission yeast cell. The data also provide evidence for a mechanism in which Tm dimers form end-to-end polymers on the actin-filament, consistent with a cooperative model for Tm binding to actin

Quadrilateral-octagon coordinates for almost normal surfaces

Normal and almost normal surfaces are essential tools for algorithmic 3-manifold topology, but to use them requires exponentially slow enumeration algorithms in a high-dimensional vector space. The quadrilateral coordinates of Tollefson alleviate this problem considerably for normal surfaces, by reducing the dimension of this vector space from 7n to 3n (where n is the complexity of the underlying triangulation). Here we develop an analogous theory for octagonal almost normal surfaces, using quadrilateral and octagon coordinates to reduce this dimension from 10n to 6n. As an application, we show that quadrilateral-octagon coordinates can be used exclusively in the streamlined 3-sphere recognition algorithm of Jaco, Rubinstein and Thompson, reducing experimental running times by factors of thousands. We also introduce joint coordinates, a system with only 3n dimensions for octagonal almost normal surfaces that has appealing geometric properties.Comment: 34 pages, 20 figures; v2: Simplified the proof of Theorem 4.5 using cohomology, plus other minor changes; v3: Minor housekeepin

Evaluation of myocardial ischemia using a rest metabolism/stress perfusion protocol with fluorine-18 deoxyglucose/technetium-99m MIBI and dual-isotope simultaneous-acquisition single-photon emission computed tomography

Objectives.This study sought to develop a dual-isotope single-acquisition single-photon emission computed tomographic (SPECT) protocol using a multihead SPECT camera equipped with an ultra-high energy collimator to evaluate rest metabolism/stress perfusion simultaneously with fluorine-18 (F-18) deoxyglucose/technetium-99m (Tc-99m) 2-hexakis-2-methoxy-2-methylpropyl isonitrile (MIBI).Background.The most accurate and logistic method of identifying injured but viable myocardium remains a diagnostic challenge.Methods.Sixty-five patients were given 25 to 50 g of glucose and, after ∼60 min, an injection of 370 MBq (10 mCi) of F-18 fluorodeoxyglucose. After a 35-min distribution phase, patients underwent exercise or pharmacologic stress followed by administration of 925 MBq (25 mCi) of Tc-99m MIBI. Five patients underwent F-18 fluorodeoxyglucose positron emission tomography before dualisotope SPECT.Results.With a window of 20% for both photopeaks and a technetium-99m/fluorine-18 concentration of 3.2: 1, the “spillover” from fluorine-18 into the technetium-99m window is <6% of the total counts in the window in patients with a normal distribution of both radiopharmaceuticals. Phantom images clearly demonstrated cardiac defects measuring 2 × 1 and 2 × 0.5 cm. There was no significant difference in the images of the five patients who underwent both positron emission tomography and SPECT. Fifty-seven patients (mean [±SD] age 55 ± 15 years, range 25 to 83; 38 men, 19 women) had satisfactory images and were included in the study. Twenty-one patients had normal study results; 15 had mismatched defects; 14 had matched defects; and 7 had both matched and mismatched defects. Twenty-three patients (mean age 54 ± 6 years, range 30 to 83; 14 men, 9 women) underwent coronary angiography within 3 months of dual-isotope SPECT. There were seven normal studies, eight with mismatched defects, one with a matched defect and seven with matched and mismatched defects. When stenosis >70% was used as the criterion for a diagnosis of coronary artery disease, dual-isotope SPECT had a sensitivity of 100%, specificity of 88%, positive predictive value of 93%, negative predictive value of 100% and an accuracy of 96%.Conclusions.Dual-isotope SPECT may provide an alternative, accurate, cost-effective method to nitrogen-13 ammonia/F-18 fluorodeoxyglucose positron emission tomography or thallium-201 reinjection for identifying injured or dysfunctional but viable myocardium

Shoot yield drives phosphorus use efficiency in Brassica oleracea and correlates with root architecture traits

The environmental and financial costs of using inorganic phosphate fertilizers to maintain crop yield and quality are high. Breeding crops that acquire and use phosphorus (P) more efficiently could reduce these costs. The variation in shoot P concentration (shoot-P) and various measures of P use efficiency (PUE) were quantified among 355 Brassica oleracea L. accessions, 74 current commercial cultivars, and 90 doubled haploid (DH) mapping lines from a reference genetic mapping population. Accessions were grown at two or more external P concentrations in glasshouse experiments; commercial and DH accessions were also grown in replicated field experiments. Within the substantial species-wide diversity observed for shoot-P and various measures of PUE in B. oleracea, current commercial cultivars have greater PUE than would be expected by chance. This may be a consequence of breeding for increased yield, which is a significant component of most measures of PUE, or early establishment. Root development and architecture correlate with PUE; in particular, lateral root number, length, and growth rate. Significant quantitative trait loci associated with shoot-P and PUE occur on chromosomes C3 and C7. These data provide information to initiate breeding programmes to improve PUE in B. oleracea

Tracking icebergs with time-lapse photography and sparse optical flow, LeConte Bay, Alaska, 2016–2017

We present a workflow to track icebergs in proglacial fjords using oblique time-lapse photos and the Lucas-Kanade optical flow algorithm. We employ the workflow at LeConte Bay, Alaska, where we ran five time-lapse cameras between April 2016 and September 2017, capturing more than 400 000 photos at frame rates of 0.5–4.0 min−1. Hourly to daily average velocity fields in map coordinates illustrate dynamic currents in the bay, with dominant downfjord velocities (exceeding 0.5 m s−1 intermittently) and several eddies. Comparisons with simultaneous Acoustic Doppler Current Profiler (ADCP) measurements yield best agreement for the uppermost ADCP levels (∼ 12 m and above), in line with prevalent small icebergs that trace near-surface currents. Tracking results from multiple cameras compare favorably, although cameras with lower frame rates (0.5 min−1) tend to underestimate high flow speeds. Tests to determine requisite temporal and spatial image resolution confirm the importance of high image frame rates, while spatial resolution is of secondary importance. Application of our procedure to other fjords will be successful if iceberg concentrations are high enough and if the camera frame rates are sufficiently rapid (at least 1 min−1 for conditions similar to LeConte Bay).This work was funded by the U.S. National Science Foundation (OPP-1503910, OPP-1504288, OPP-1504521 and OPP-1504191).Ye

Slow roll in simple non-canonical inflation

We consider inflation using a class of non-canonical Lagrangians for which the modification to the kinetic term depends on the field, but not its derivatives. We generalize the standard Hubble slow roll expansion to the non-canonical case and derive expressions for observables in terms of the generalized slow roll parameters. We apply the general results to the illustrative case of ``Slinky'' inflation, which has a simple, exactly solvable, non-canonical representation. However, when transformed into a canonical basis, Slinky inflation consists of a field oscillating on a multi-valued potential. We calculate the power spectrum of curvature perturbations for Slinky inflation directly in the non-canonical basis, and show that the spectrum is approximately a power law on large scales, with a ``blue'' power spectrum. On small scales, the power spectrum exhibits strong oscillatory behavior. This is an example of a model in which the widely used solution of Garriga and Mukhanov gives the wrong answer for the power spectrum.Comment: 9 pages, LaTeX, four figures. (V2: minor changes to text. Version submitted to JCAP.

How Trade Liberalization and Labor Development Could Coincide in the Philippines

As the world adapts to the rapid pace of globalization in the 21st century, countries ease trade restrictions by gradually removing tariffs and non-tariff barriers to incentivize the free flow of goods across nations. This prevalence of trade liberalization policies propelled policymakers and economists to investigate the relationship between trade reforms and economic outcomes including wage inequality around the world. They found that trade liberalization, on average, has had a positive impact on economic growth, but prior studies that examine the effects of trade liberalization on wage inequality in developing countries have found mixed results. Recently, Murakami (2021) examined the impact of trade liberalization on wage inequality in Chile through the reduction in effective tariffs brought about by the regional trade agreements of the country. Following his empirical strategy, we examine the impact of trade liberalization on wage inequality in the Philippines. In this policy brief, we provide insights on our findings and policy recommendations that the Philippines can undertak

Systems biology and ecology of microbial mat communities

Microbial mat communities consist of dense populations of microorganisms embedded in exopolymers and/or biomineralized solid phases, and are often found in mm-cm thick assemblages, which can be stratified due to environmental gradients such as light, oxygen or sulfide. Microbial mat communities are commonly observed under extreme environmental conditions, deriving energy primarily from light and/or reduced chemicals to drive autotrophic fixation of carbon dioxide. Microbial mat ecosystems are regarded as living analogues of primordial systems on Earth, and they often form perennial structures with conspicuous stratifications of microbial populations that can be studied in situ under stable conditions for many years. Consequently, microbial mat communities are ideal natural laboratories and represent excellent model systems for studying microbial community structure and function, microbial dynamics and interactions, and discovery of new microorganisms with novel metabolic pathways potentially useful in future industrial and/or medical applications. Due to their relative simplicity and organization, microbial mat communities are often excellent testing grounds for new technologies in microbiology including micro-sensor analysis, stable isotope methodology and modern genomics. Integrative studies of microbial mat communities that combine modern biogeochemical and molecular biological methods with traditional microbiology, macro-ecological approaches, and community network modeling will provide new and detailed insights regarding the systems biology of microbial mats and the complex interplay among individual populations and their physicochemical environment. These processes ultimately control the biogeochemical cycling of energy and/or nutrients in microbial systems. Similarities in microbial community function across different types of communities from highly disparate environments may provide a deeper basis for understanding microbial community dynamics and the ecological role of specific microbial populations. Approaches and concepts developed in highly-constrained, relatively stable natural communities may also provide insights useful for studying and understanding more complex microbial communities