Takeuti's Well-Ordering Proof: Finitistically Fine?

If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form. The paper begins with a historically informed discussion of finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to

Autocatalytic plume pinch-off

A localized source of buoyancy flux in a non-reactive fluid medium creates a plume. The flux can be provided by either heat, a compositional difference between the fluid comprising the plume and its surroundings, or a combination of both. For autocatalytic plumes produced by the iodate-arsenous acid reaction, however, buoyancy is produced along the entire reacting interface between the plume and its surroundings. Buoyancy production at the moving interface drives fluid motion, which in turn generates flow that advects the reaction front. As a consequence of this interplay between fluid flow and chemical reaction, autocatalytic plumes exhibit a rich dynamics during their ascent through the reactant medium. One of the more interesting dynamical features is the production of an accelerating vortical plume head that in certain cases pinches-off and detaches from the upwelling conduit. After pinch-off, a new plume head forms in the conduit below, and this can lead to multiple generations of plume heads for a single plume initiation. We investigated the pinch-off process using both experimentation and simulation. Experiments were performed using various concentrations of glycerol, in which it was found that repeated pinch-off occurs exclusively in a specific concentration range. Autocatalytic plume simulations revealed that pinch-off is triggered by the appearance of accelerating flow in the plume conduit.Comment: 10 figures. Accepted for publication in Phys Rev E. See also http://www.physics.utoronto.ca/nonlinear/papers_chemwave.htm

Effect of stress and temperature on the optical properties of silicon nitride membranes at 1550 nm

Future gravitational-wave detectors operated at cryogenic temperatures are expected to be limited by thermal noise of the highly reflective mirror coatings. Silicon nitride is an interesting material for such coatings as it shows very low mechanical loss, a property related to low thermal noise, which is known to further decrease under stress. Low optical absorption is also required to maintain the low mirror temperature. Here, we investigate the effect of stress on the optical properties at 1,550 nm of silicon nitride membranes attached to a silicon frame. Our approach includes the measurement of the thermal expansion coefficient and the thermal conductivity of the membranes. The membrane and frame temperatures are varied, and translated into a change in stress using finite element modeling. The resulting product of the optical absorption and thermo-optic coefficient (dn/dT) is measured using photothermal common-path interferometry

Precocial juvenile lizards show adult level learning and behavioural flexibility

This project was funded by an ARC Discovery grant (DP130102998) to M.J.W. and R.W.B. and by Macquarie University.In altricial species, young rely on parental care and brain maturation mainly occurs after birth. In precocial species, young are born at a more advanced developmental stage in need of less or no parental care and brain development is mostly completed at the time of birth. We therefore predicted early maturation of learning ability in precocial species. We used a series of visual discrimination and reversal stages to investigate the ability of the precocial eastern blue-tongue lizard, Tiliqua scincoides scincoides, a long-lived Australian lizard species with slow-developing young, to respond to changes in stimulus relevance and test for behavioural flexibility. To test whether age affects learning in this species, we compared juveniles (23–56 days) with adults (sexually mature, at least 2 years). In accordance with our expectations, adults and juveniles performed similarly well in all stages, suggesting that juveniles of this precocial species learn at adult levels from an early age. Both age classes performed well during reversals showing good behavioural flexibility. This is the first study in lizards to directly compare juvenile and adult behavioural flexibility. Importantly, we demonstrate that precocial lizards can begin life with an advanced cognitive ability already in place.In altricial species, young rely on parental care and brain maturation mainly occurs after birth. In precocial species, young are born at a more advanced developmental stage in need of less or no parental care and brain development is mostly completed at the time of birth. We therefore predicted early maturation of learning ability in precocial species. We used a series of visual discrimination and reversal stages to investigate the ability of the precocial eastern blue-tongue lizard, Tiliqua scincoides scincoides, a long-lived Australian lizard species with slow-developing young, to respond to changes in stimulus relevance and test for behavioural flexibility. To test whether age affects learning in this species, we compared juveniles (23–56 days) with adults (sexually mature, at least 2 years). In accordance with our expectations, adults and juveniles performed similarly well in all stages, suggesting that juveniles of this precocial species learn at adult levels from an early age. Both age classes performed well during reversals showing good behavioural flexibility. This is the first study in lizards to directly compare juvenile and adult behavioural flexibility. Importantly, we demonstrate that precocial lizards can begin life with an advanced cognitive ability already in place.In altricial species, young rely on parental care and brain maturation mainly occurs after birth. In precocial species, young are born at a more advanced developmental stage in need of less or no parental care and brain development is mostly completed at the time of birth. We therefore predicted early maturation of learning ability in precocial species. We used a series of visual discrimination and reversal stages to investigate the ability of the precocial eastern blue-tongue lizard, Tiliqua scincoides scincoides, a long-lived Australian lizard species with slow-developing young, to respond to changes in stimulus relevance and test for behavioural flexibility. To test whether age affects learning in this species, we compared juveniles (23–56 days) with adults (sexually mature, at least 2 years). In accordance with our expectations, adults and juveniles performed similarly well in all stages, suggesting that juveniles of this precocial species learn at adult levels from an early age. Both age classes performed well during reversals showing good behavioural flexibility. This is the first study in lizards to directly compare juvenile and adult behavioural flexibility. Importantly, we demonstrate that precocial lizards can begin life with an advanced cognitive ability already in place.In altricial species, young rely on parental care and brain maturation mainly occurs after birth. In precocial species, young are born at a more advanced developmental stage in need of less or no parental care and brain development is mostly completed at the time of birth. We therefore predicted early maturation of learning ability in precocial species. We used a series of visual discrimination and reversal stages to investigate the ability of the precocial eastern blue-tongue lizard, Tiliqua scincoides scincoides, a long-lived Australian lizard species with slow-developing young, to respond to changes in stimulus relevance and test for behavioural flexibility. To test whether age affects learning in this species, we compared juveniles (23–56 days) with adults (sexually mature, at least 2 years). In accordance with our expectations, adults and juveniles performed similarly well in all stages, suggesting that juveniles of this precocial species learn at adult levels from an early age. Both age classes performed well during reversals showing good behavioural flexibility. This is the first study in lizards to directly compare juvenile and adult behavioural flexibility. Importantly, we demonstrate that precocial lizards can begin life with an advanced cognitive ability already in place.PostprintPeer reviewe

Quaternion-Octonion SU(3) Flavor Symmetry

Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different iso-spin multiplets i.e. I, U and V- spins. Keywords: SU(3), Quaternions, Octonions and Gell Mann matrices PACS NO: 11.30.Hv: Flavor symmetries; 12.10-Dm: Unified field theories and models of strong and electroweak interaction

Takeuti's Well-Ordering Proof: Finitistically Fine?

If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form. The paper begins with a historically informed discussion of finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to

Top Background Extrapolation for H -> WW Searches at the LHC

A leading order (LO) analysis is presented that demonstrates that key top backgrounds to H -> W^+W^- -> l^\pm l^\mp \sla{p}_T decays in weak boson fusion (WBF) and gluon fusion (GF) at the CERN Large Hadron Collider can be extrapolated from experimental data with an accuracy of order 5% to 10%. If LO scale variation is accepted as proxy for the theoretical error, parton level results indicate that the tt~j background to the H -> WW search in WBF can be determined with a theoretical error of about 5%, while the tt~ background to the H -> WW search in GF can be determined with a theoretical error of better than 1%. Uncertainties in the parton distribution functions contribute an estimated 3% to 10% to the total error.Comment: 17 pages, 9 tables, 4 figures; LO caveat emphasized, version to be published in Phys. Rev.

Discovery of mating in the major African livestock pathogen Trypanosoma congolense

The protozoan parasite, Trypanosoma congolense, is one of the most economically important pathogens of livestock in Africa and, through its impact on cattle health and productivity, has a significant effect on human health and well being. Despite the importance of this parasite our knowledge of some of the fundamental biological processes is limited. For example, it is unknown whether mating takes place. In this paper we have taken a population genetics based approach to address this question. The availability of genome sequence of the parasite allowed us to identify polymorphic microsatellite markers, which were used to genotype T. congolense isolates from livestock in a discrete geographical area of The Gambia. The data showed a high level of diversity with a large number of distinct genotypes, but a deficit in heterozygotes. Further analysis identified cryptic genetic subdivision into four sub-populations. In one of these, parasite genotypic diversity could only be explained by the occurrence of frequent mating in T. congolense. These data are completely inconsistent with previous suggestions that the parasite expands asexually in the absence of mating. The discovery of mating in this species of trypanosome has significant consequences for the spread of critical traits, such as drug resistance, as well as for fundamental aspects of the biology and epidemiology of this neglected but economically important pathogen