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

Definable orthogonality classes in accessible categories are small

We lower substantially the strength of the assumptions needed for the validity of certain results in category theory and homotopy theory which were known to follow from Vopenka's principle. We prove that the necessary large-cardinal hypotheses depend on the complexity of the formulas defining the given classes, in the sense of the Levy hierarchy. For example, the statement that, for a class S of morphisms in a locally presentable category C of structures, the orthogonal class of objects is a small-orthogonality class (hence reflective) is provable in ZFC if S is \Sigma_1, while it follows from the existence of a proper class of supercompact cardinals if S is \Sigma_2, and from the existence of a proper class of what we call C(n)-extendible cardinals if S is \Sigma_{n+2} for n bigger than or equal to 1. These cardinals form a new hierarchy, and we show that Vopenka's principle is equivalent to the existence of C(n)-extendible cardinals for all n. As a consequence, we prove that the existence of cohomological localizations of simplicial sets, a long-standing open problem in algebraic topology, is implied by the existence of arbitrarily large supercompact cardinals. This result follows from the fact that cohomology equivalences are \Sigma_2. In contrast with this fact, homology equivalences are \Sigma_1, from which it follows (as is well known) that the existence of homological localizations is provable in ZFC.Comment: 38 pages; some results have been improved and former inaccuracies have been correcte

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

Magnetotransport in the Kondo model with ferromagnetic exchange interaction

We consider the transport properties in an applied magnetic field of the spin S=1/2 Kondo model with ferromagnetic exchange coupling to electronic reservoirs, a description relevant for the strong coupling limit of underscreened spin S=1 Kondo impurities. Because the ferromagnetic Kondo interaction is marginally irrelevant, perturbative methods should prove accurate down to low energies. For the purpose of this study, we use a combination of Majorana diagrammatic theory with Density Matrix Numerical Renormalization Group simulations. In the standard case of antiferromagnetic Kondo exchange, we first show that our technique recovers previously obtained results for the T-matrix and spin relaxation at weak coupling (above the Kondo temperature). Considering then the ferromagnetic case, we demonstrate how the low-energy Kondo anomaly splits for arbitrary small values of the Zeeman energy, in contrast to fully screened Kondo impurities near the strong coupling Fermi liquid fixed point, and in agreement with recent experimental findings for spin S=1 molecular quantum dots.Comment: 14 pages, 13 figures, minor changes in V

Selfdual 2-form formulation of gravity and classification of energy-momentum tensors

It is shown how the different irreducibility classes of the energy-momentum tensor allow for a Lagrangian formulation of the gravity-matter system using a selfdual 2-form as a basic variable. It is pointed out what kind of difficulties arise when attempting to construct a pure spin-connection formulation of the gravity-matter system. Ambiguities in the formulation especially concerning the need for constraints are clarified.Comment: title changed, extended versio

The Discovery of Stellar Oscillations in the Planet Hosting Giant Star Beta Geminorum

We present the results of a long time series of precise stellar radial velocity measurements of the planet hosting K giant star Beta Geminorum. A total of 20 hours of observations spanning three nights were obtained and the radial velocity variations show the presence of solar-like stellar oscillations. Our period analysis yields six significant pulsation modes that have frequencies in the range of 30 - 150 microHz. The dominant mode is at a frequency of 86.9 microHz and has an amplitude of 5.3 m/s. These values are consistent with stellar oscillations for a giant star with a stellar mass of approximately 2 solar masses. This stellar mass implies a companion minimum mass of 2.6 Jupiter masses. Beta Gem is the first planet hosting giant star in which multi-periodic stellar oscillations have been detected. The study of stellar oscillations in planet hosting giant stars may provide an independent, and more accurate determination of the stellar mass.Comment: 12 pages preprint, 2 figures, accepted by ApJ Letter

Kinematic studies of transport across an island wake, with application to the Canary islands

Transport from nutrient-rich coastal upwellings is a key factor influencing biological activity in surrounding waters and even in the open ocean. The rich upwelling in the North-Western African coast is known to interact strongly with the wake of the Canary islands, giving rise to filaments and other mesoscale structures of increased productivity. Motivated by this scenario, we introduce a simplified two-dimensional kinematic flow describing the wake of an island in a stream, and study the conditions under which there is a net transport of substances across the wake. For small vorticity values in the wake, it acts as a barrier, but there is a transition when increasing vorticity so that for values appropriate to the Canary area, it entrains fluid and enhances cross-wake transport.Comment: 28 pages, 13 figure

Small-worlds: How and why

We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network architecture. In situations such as neural or transportation networks, where a physical distance between the nodes of the network exists, we study whether the small-world topology arises as a consequence of a tradeoff between maximal connectivity and minimal wiring. Using simulated annealing, we study the properties of a randomly rewired network as the relative tradeoff between wiring and connectivity is varied. When the network seeks to minimize wiring, a regular graph results. At the other extreme, when connectivity is maximized, a near random network is obtained. In the intermediate regime, a small-world network is formed. However, unlike the model of Watts and Strogatz (Nature {\bf 393}, 440 (1998)), we find an alternate route to small-world behaviour through the formation of hubs, small clusters where one vertex is connected to a large number of neighbours.Comment: 20 pages, latex, 9 figure

The Wonder of Colors and the Principle of Ariadne

The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne and proposes the Ariadne Game, showing that the Principle of Ariadne, corresponds precisely to a winning strategy for the Ariadne Game. Some relations to other alternative. set-theoretical principles are also briefly discussed