On the relative strengths of fragments of collection

Let $\mathbf{M}$ be the basic set theory that consists of the axioms of extensionality, emptyset, pair, union, powerset, infinity, transitive containment, $\Delta_0$-separation and set foundation. This paper studies the relative strength of set theories obtained by adding fragments of the set-theoretic collection scheme to $\mathbf{M}$. We focus on two common parameterisations of collection: $\Pi_n$-collection, which is the usual collection scheme restricted to $\Pi_n$-formulae, and strong $\Pi_n$-collection, which is equivalent to $\Pi_n$-collection plus $\Sigma_{n+1}$-separation. The main result of this paper shows that for all $n \geq 1$, (1) $\mathbf{M}+\Pi_{n+1}\textrm{-collection}+\Sigma_{n+2}\textrm{-induction on } \omega$ proves the consistency of Zermelo Set Theory plus $\Pi_{n}$-collection, (2) the theory $\mathbf{M}+\Pi_{n+1}\textrm{-collection}$ is $\Pi_{n+3}$-conservative over the theory $\mathbf{M}+\textrm{strong }\Pi_n \textrm{-collection}$. It is also shown that (2) holds for $n=0$ when the Axiom of Choice is included in the base theory. The final section indicates how the proofs of (1) and (2) can be modified to obtain analogues of these results for theories obtained by adding fragments of collection to a base theory (Kripke-Platek Set Theory with Infinity and $V=L$) that does not include the powerset axiom.Comment: 22 page

Mechanism for Spontaneous Growth of Nanopillar Arrays in Ultrathin Films Subject to a Thermal Gradient

Several groups have reported spontaneous formation of periodic pillar-like arrays in molten polymer nanofilms confined within closely spaced substrates maintained at different temperatures. These formations have been attributed to a radiation pressure instability caused by acoustic phonons. In this work, we demonstrate how variations in the thermocapillary stress along the nanofilm interface can produce significant periodic protrusions in any viscous film no matter how small the initial transverse thermal gradient. The linear stability analysis of the interface evolution equation explores an extreme limit of B\'{e}nard-Marangoni flow peculiar to films of nanoscale dimensions in which hydrostatic forces are altogether absent and deformation amplitudes are small in comparison to the pillar spacing. Finite element simulations of the full nonlinear equation are also used to examine the array pitch and growth rates beyond the linear regime. Inspection of the Lyapunov free energy as a function of time confirms that in contrast to typical cellular instabilities in macroscopically thick films, pillar-like elongations are energetically preferred in nanofilms. Provided there occurs no dewetting during film deformation, it is shown that fluid elongations continue to grow until contact with the cooler substrate is achieved. Identification of the mechanism responsible for this phenomenon may facilitate fabrication of extended arrays for nanoscale optical, photonic and biological applications.Comment: 20 pages, 9 figure

On quasilinear parabolic evolution equations in weighted Lp-spaces II

Our study of abstract quasi-linear parabolic problems in time-weighted L_p-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reaction-diffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method presented here will be applicable to other parabolic systems, including free boundary problems.Comment: 21 page

Solid-state magnetic traps and lattices

We propose and analyze magnetic traps and lattices for electrons in semiconductors. We provide a general theoretical framework and show that thermally stable traps can be generated by magnetically driving the particle's internal spin transition, akin to optical dipole traps for ultra-cold atoms. Next we discuss in detail periodic arrays of magnetic traps, i.e. magnetic lattices, as a platform for quantum simulation of exotic Hubbard models, with lattice parameters that can be tuned in real time. Our scheme can be readily implemented in state-of-the-art experiments, as we particularize for two specific setups, one based on a superconducting circuit and another one based on surface acoustic waves.Comment: 18 pages, 8 figure

A Framework for Inferring Taxonomic Class of Asteroids.

Introduction: Taxonomic classification of asteroids based on their visible / near-infrared spectra or multi band photometry has proven to be a useful tool to infer other properties about asteroids. Meteorite analogs have been identified for several taxonomic classes, permitting detailed inference about asteroid composition. Trends have been identified between taxonomy and measured asteroid density. Thanks to NEOWise (Near-Earth-Object Wide-field Infrared Survey Explorer) and Spitzer (Spitzer Space Telescope), approximately twice as many asteroids have measured albedos than the number with taxonomic classifications. (If one only considers spectroscopically determined classifications, the ratio is greater than 40.) We present a Bayesian framework that provides probabilistic estimates of the taxonomic class of an asteroid based on its albedo. Although probabilistic estimates of taxonomic classes are not a replacement for spectroscopic or photometric determinations, they can be a useful tool for identifying objects for further study or for asteroid threat assessment models. Inputs and Framework: The framework relies upon two inputs: the expected fraction of each taxonomic class in the population and the albedo distribution of each class. Luckily, numerous authors have addressed both of these questions. For example, the taxonomic distribution by number, surface area and mass of the main belt has been estimated and a diameter limited estimate of fractional abundances of the near earth asteroid population was made. Similarly, the albedo distributions for taxonomic classes have been estimated for the combined main belt and NEA (Near Earth Asteroid) populations in different taxonomic systems and for the NEA population specifically. The framework utilizes a Bayesian inference appropriate for categorical data. The population fractions provide the prior while the albedo distributions allow calculation of the likelihood an albedo measurement is consistent with a given taxonomic class. These inputs allows calculation of the probability an asteroid with a specified albedo belongs to any given taxonomic class

Formation of Nanopillar Arrays in Ultrathin Viscous Films: The Critical Role of Thermocapillary Stresses

Experiments by several groups during the past decade have shown that a molten polymer nanofilm subject to a large transverse thermal gradient undergoes spontaneous formation of periodic nanopillar arrays. The prevailing explanation is that coherent reflections of acoustic phonons within the film cause a periodic modulation of the radiation pressure which enhances pillar growth. By exploring a deformational instability of particular relevance to nanofilms, we demonstrate that thermocapillary forces play a crucial role in the formation process. Analytic and numerical predictions show good agreement with the pillar spacings obtained in experiment. Simulations of the interface equation further determine the rate of pillar growth of importance to technological applications.Comment: 5 pages, 4 figure

A new method for the spectroscopic identification of stellar non-radial pulsation modes. II. Mode identification of the Delta Scuti star FG Virginis

We present a mode identification based on new high-resolution time-series spectra of the non-radially pulsating Delta Scuti star FG~Vir (HD 106384, V = 6.57, A5V). From 2002 February to June a global Delta Scuti Network (DSN) campaign, utilizing high-resolution spectroscopy and simultaneous photometry has been conducted for FG~Vir in order to provide a theoretical pulsation model. In this campaign we have acquired 969 Echelle spectra covering 147 hours at six observatories. The mode identification was carried out by analyzing line profile variations by means of the Fourier parameter fit method, where the observational Fourier parameters across the line are fitted with theoretical values. This method is especially well suited for determining the azimuthal order m of non-radial pulsation modes and thus complementary with the method of Daszynska-Daszkiewicz (2002) which does best at identifying the degree l. 15 frequencies between 9.2 and 33.5 c/d were detected spectroscopically. We determined the azimuthal order m of 12 modes and constrained their harmonic degree l. Only modes of low degree (l <= 4) were detected, most of them having axisymmetric character mainly due to the relatively low projected rotational velocity of FG Vir. The detected non-axisymmetric modes have azimuthal orders between -2 and 1. We derived an inclination of 19 degrees, which implies an equatorial rotational rate of 66 km/s.Comment: 14 pages, 26 figure

Collapse of an ecological network in Ancient Egypt

The dynamics of ecosystem collapse are fundamental to determining how and why biological communities change through time, as well as the potential effects of extinctions on ecosystems. Here we integrate depictions of mammals from Egyptian antiquity with direct lines of paleontological and archeological evidence to infer local extinctions and community dynamics over a 6000-year span. The unprecedented temporal resolution of this data set enables examination of how the tandem effects of human population growth and climate change can disrupt mammalian communities. We show that the extinctions of mammals in Egypt were nonrandom, and that destabilizing changes in community composition coincided with abrupt aridification events and the attendant collapses of some complex societies. We also show that the roles of species in a community can change over time, and that persistence is predicted by measures of species sensitivity, a function of local dynamic stability. Our study is the first high-resolution analysis of the ecological impacts of environmental change on predator-prey networks over millennial timescales, and sheds light on the historical events that have shaped modern animal communities

Sex-partitioning of the <i>Plasmodium falciparum</i> stage V gametocyte proteome provides insight into <i>falciparum</i>-specific cell biology

One of the critical gaps in malaria transmission biology and surveillance is our lack of knowledge about Plasmodium falciparum gametocyte biology, especially sexual dimorphic development and how sex ratios that may influence transmission from the human to the mosquito. Dissecting this process has been hampered by the lack of sex-specific protein markers for the circulating, mature stage V gametocytes. The current evidence suggests a high degree of conservation in gametocyte gene complement across Plasmodium, and therefore presumably for sex-specific genes as well. To better our understanding of gametocyte development and subsequent infectiousness to mosquitoes, we undertook a Systematic Subtractive Bioinformatic analysis (filtering) approach to identify sex-specific P. falciparum NF54 protein markers based on a comparison with the Dd2 strain, which is defective in producing males, and with syntenic male and female proteins from the reanalyzed and updated P. berghei (related rodent malaria parasite) gametocyte proteomes. This produced a short list of 174 male- and 258 female-enriched P. falciparum stage V proteins, some of which appear to be under strong diversifying selection, suggesting ongoing adaptation to mosquito vector species. We generated antibodies against three putative female-specific gametocyte stage V proteins in P. falciparum and confirmed either conserved sex-specificity or the lack of cross-species sex-partitioning. Finally, our study provides not only an additional resource for mass spectrometry-derived evidence for gametocyte proteins but also lays down the foundation for rational screening and development of novel sex-partitioned protein biomarkers and transmission-blocking vaccine candidates

Combination GLP-1 and Insulin Treatment Fails to Alter Myocardial Fuel Selection Versus Insulin Alone in Type 2 Diabetes

Context Glucagon-like peptide-1 (GLP-1) and the clinically available GLP-1 agonists have been shown to exert effects on the heart. It is unclear whether these effects occur at clinically used doses in vivo in humans, possibly contributing to CVD risk reduction. Objective To determine whether liraglutide at clinical dosing augments myocardial glucose uptake alone or in combination with insulin compared to insulin alone in metformin-treated Type 2 diabetes mellitus. Design Comparison of myocardial fuel utilization after 3 months of treatment with insulin detemir, liraglutide, or combination detemir+liraglutide. Setting Academic hospital Participants Type 2 diabetes treated with metformin plus oral agents or basal insulin. Interventions Insulin detemir, liraglutide, or combination added to background metformin Main Outcome Measures Myocardial blood flow, fuel selection and rates of fuel utilization evaluated using positron emission tomography, powered to demonstrate large effects. Results We observed greater myocardial blood flow in the insulin-treated groups (median[25th, 75th percentile]: detemir 0.64[0.50, 0.69], liraglutide 0.52[0.46, 0.58] and detemir+liraglutide 0.75[0.55, 0.77] mL/g/min, p=0.035 comparing 3 groups and p=0.01 comparing detemir groups to liraglutide alone). There were no evident differences between groups in myocardial glucose uptake (detemir 0.040[0.013, 0.049], liraglutide 0.055[0.019, 0.105], detemir+liraglutide 0.037[0.009, 0.046] µmol/g/min, p=0.68 comparing 3 groups). Similarly there were no treatment group differences in measures of myocardial fatty acid uptake or handling, and no differences in total oxidation rate. Conclusions These observations argue against large effects of GLP-1 agonists on myocardial fuel metabolism as mediators of beneficial treatment effects on myocardial function and ischemia protection