444 research outputs found
Review of New Music Vocabulary: A Guide to Notational Signs for Contemporary Music by Howard Risatti
 
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Cubical Models of Homotopy Type Theory - An Internal Approach
This thesis presents an account of the cubical sets model of homotopy type theory using an internal type theory for elementary topoi.
Homotopy type theory is a variant of Martin-Lof type theory where we think of types as spaces, with terms as points in the space and elements of the identity type as paths. We actualise this intuition by extending type theory with Voevodsky's univalence axiom which identifies equalities between types with homotopy equivalences between spaces.
Voevodsky showed the univalence axiom to be consistent by giving a model of homotopy type theory in the category of Kan simplicial sets in a paper with Kapulkin and Lumsdaine. However, this construction makes fundamental use of classical logic in order to show certain results. Therefore this model cannot be used to explain the computational content of the univalence axiom, such as how to compute terms involving univalence.
This problem was resolved by Cohen, Coquand, Huber and Mortberg, who presented a new model of type theory in Kan cubical sets which validated the univalence axiom using a constructive metatheory. This meant that the model provided an understanding of the computational content of univalence. In fact, the authors present a new type theory, cubical type theory, where univalence is provable using a new "glueing" type former. This type former comes with appropriate definitional equalities which explain how the univalence axiom should compute. In particular, Huber proved that any term of natural number type constructed in this new type theory must reduce to a numeral.
This thesis explores models of type theory based on the cubical sets model of Cohen et al. It gives an account of this model using the internal language of toposes, where we present a series of axioms which are sufficient to construct a model of cubical type theory, and hence a model of homotopy type theory. This approach therefore generalises the original model and gives a new and useful method for analysing models of type theory.
We also discuss an alternative derivation of the univalence axiom and show how this leads to a potentially simpler proof of univalence in any model satisfying the axioms mentioned above, such as cubical sets.
Finally, we discuss some shortcomings of the internal language approach with respect to constructing univalent universes. We overcome these difficulties by extending the internal language with an appropriate modality in order to manipulate global elements of an object.UK EPSRC PhD studentship, funded by grants EP/L504920/1, EP/M506485/1
The Role of Habitat Management in Shaping Predation, Animal Color, and Gene Flow in a Metapopulation of Florida Scrub Lizards (Sceloporus Woodi)
Anthropogenic disturbance is known to affect biological diversity at the community, species, and genetic levels. Habitat fragmentation, in particular, has been shown to impact predator abundance and distribution, impede dispersal, and augment genetic drift. In small populations, which often result from habitat fragmentation, the effects of human disturbance may be disproportionately expressed. Small populations are more susceptible to selection pressures and random drift because genetic and phenotypic frequencies can become rapidly fixed, in comparison to larger populations. In turn, fixation of maladaptive alleles or morphs can accelerate extinction. For example, cryptic color polymorphism can be maintained by apostatic selection, where detection of prey is dependent on the relative frequencies of color morphs. In the event that a conspicuous color morph becomes fixed, the probability of detection by visual predators is likely to increase, thus increasing probability of local extinction. Furthermore, events that alter habitat structure and substrate composition may also increase exposure of cryptic animals to visual predators because crypsis is substrate-dependent. A color morph that is cryptic against one visual background may be conspicuous against a different visual background. Subpopulations of Sceloporus woodi, a cryptic species of lizard, occupy managed stands of sand pine scrub and longleaf pine habitats in the Ocala National Forest. These subpopulations are subjected to prescribe burning, fire suppression, and clear-cutting. Here, I show that habitat alteration, due to management in the Ocala National Forest, results in differential predation between sampling locations. As a result, significant variation in dorsal color is observed across the metapopulation. Furthermore, subpopulations appear to experience little genetic drift, perhaps due to gene flow facilitated by anthropogenically-maintained corridors
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Models of Type Theory Based on Moore Paths
This paper introduces a new family of models of intensional Martin-Löf type theory. We use constructive ordered algebra in toposes. Identity types in the models are given by a notion of Moore path. By considering a particular gros topos, we show that there is such a model that is non-truncated, i.e. contains non-trivial structure at all dimensions. In other words, in this model a type in a nested sequence of identity types can contain more than one element, no matter how great the degree of nesting. Although inspired by existing non-truncated models of type theory based on simplicial and cubical sets, the notion of model presented here is notable for avoiding any form of Kan filling condition in the semantics of types.Orton was supported by a PhD studentship from the UK EPSRC funded by grants EP/L504920/1 and EP/M506485/1
Genetic diversity, infection prevalence, and possible transmission routes of Bartonella spp. in vampire bats
Bartonella spp. are globally distributed bacteria that cause endocarditis in humans and domestic animals. Recent work has suggested bats as zoonotic reservoirs of some human Bartonella infections; however, the ecological and spatiotemporal patterns of infection in bats remain largely unknown. Here we studied the genetic diversity, prevalence of infection across seasons and years, individual risk factors, and possible transmission routes of Bartonella in populations of common vampire bats (Desmodus rotundus) in Peru and Belize, for which high infection prevalence has previously been reported. Phylogenetic analysis of the gltA gene for a subset of PCR-positive blood samples revealed sequences that were related to Bartonella described from vampire bats from Mexico, other Neotropical bat species, and streblid bat flies. Sequences associated with vampire bats clustered significantly by country but commonly spanned Central and South America, implying limited spatial structure. Stable and nonzero Bartonella prevalence between years supported endemic transmission in all sites. The odds of Bartonella infection for individual bats was unrelated to the intensity of bat flies ectoparasitism, but nearly all infected bats were infested, which precluded conclusive assessment of support for vector-borne transmission. While metagenomic sequencing found no strong evidence of Bartonella DNA in pooled bat saliva and fecal samples, we detected PCR positivity in individual saliva and feces, suggesting the potential for bacterial transmission through both direct contact (i.e., biting) and environmental (i.e., fecal) exposures. Further investigating the relative contributions of direct contact, environmental, and vector-borne transmission for bat Bartonella is an important next step to predict infection dynamics within bats and the risks of human and livestock exposures
Seasonal Variability of Saturn's Tropospheric Temperatures, Winds and Para-H from Cassini Far-IR Spectroscopy
Far-IR 16-1000 m spectra of Saturn's hydrogen-helium continuum measured
by Cassini's Composite Infrared Spectrometer (CIRS) are inverted to construct a
near-continuous record of upper tropospheric (70-700 mbar) temperatures and
para-H fraction as a function of latitude, pressure and time for a third of
a Saturnian year (2004-2014, from northern winter to northern spring). The
thermal field reveals evidence of reversing summertime asymmetries superimposed
onto the belt/zone structure. The temperature structure that is almost
symmetric about the equator by 2014, with seasonal lag times that increase with
depth and are qualitatively consistent with radiative climate models. Localised
heating of the tropospheric hazes (100-250 mbar) create a distinct perturbation
to the temperature profile that shifts in magnitude and location, declining in
the autumn hemisphere and growing in the spring. Changes in the para-H
() distribution are subtle, with a 0.02-0.03 rise over the spring
hemisphere (200-500 mbar) perturbed by (i) low- air advected by both the
springtime storm of 2010 and equatorial upwelling; and (ii) subsidence of
high- air at northern high latitudes, responsible for a developing
north-south asymmetry in . Conversely, the shifting asymmetry in the
para-H disequilibrium primarily reflects the changing temperature structure
(and the equilibrium distribution of ), rather than actual changes in
induced by chemical conversion or transport. CIRS results interpolated to
the same point in the seasonal cycle as re-analysed Voyager-1 observations show
qualitative consistency, with the exception of the tropical tropopause near the
equatorial zones and belts, where downward propagation of a cool temperature
anomaly associated with Saturn's stratospheric oscillation could potentially
perturb tropopause temperatures, para-H and winds. [ABRIDGED]Comment: Preprint accepted for publication in Icarus, 29 pages, 18 figure
Investigating intra-host and intra-herd sequence diversity of foot-and-mouth disease virus
Due to the poor-fidelity of the enzymes involved in RNA genome replication, foot-and-mouth disease (FMD) virus samples comprise of unique polymorphic populations. In this study, deep sequencing was utilised to characterise the diversity of FMD virus (FMDV) populations in 6 infected cattle present on a single farm during the series of outbreaks in the UK in 2007. A novel RT–PCR method was developed to amplify a 7.6 kb nucleotide fragment encompassing the polyprotein coding region of the FMDV genome. Illumina sequencing of each sample identified the fine polymorphic structures at each nucleotide position, from consensus level changes to variants present at a 0.24% frequency. These data were used to investigate population dynamics of FMDV at both herd and host levels, evaluate the impact of host on the viral swarm structure and to identify transmission links with viruses recovered from other farms in the same series of outbreaks. In 7 samples, from 6 different animals, a total of 5 consensus level variants were identified, in addition to 104 sub-consensus variants of which 22 were shared between 2 or more animals. Further analysis revealed differences in swarm structures from samples derived from the same animal suggesting the presence of distinct viral populations evolving independently at different lesion sites within the same infected animal
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