50 research outputs found
Computability Theory
Computability is one of the fundamental notions of mathematics, trying to capture the effective content of mathematics. Starting from GĂśdelâs Incompleteness Theorem, it has now blossomed into a rich area with strong connections with other areas of mathematical logic as well as algebra and theoretical computer science
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The Reverse Mathematics of CAC for trees
CAC for trees is the statement asserting that any infinite subtree of
has an infinite path or an infinite antichain. In
this paper, we study the computational strength of this theorem from a reverse
mathematical viewpoint. We prove that TAC for trees is robust, that is, there
exist several characterizations, some of which already appear in the
literature, namely, the tree antichain theorem (TCAC) introduced by Conidis,
and the statement SHER introduced by Dorais et al. We show that CAC for trees
is computationally very weak, in that it admits probabilistic solutions.Comment: 28 page
On the Nonexistence of a Strong Minimal Pair
Two nonzero recursively enumerable (r.e.) degrees and
form a strong minimal pair if and for any
nonzero r.e. degree . We prove that there is no
strong minimal pair in the r.e. degrees. Our construction goes beyond the usual
-priority arguments and we give some evidence to show that it
needs -priority arguments
Reducibilities in recursive function theory.
Massachusetts Institute of Technology. Dept. of Mathematics. Thesis. 1966. Ph.D.Bibliography: leaves 102-103.Ph.D
Randomness and Computability
This thesis establishes significant new results in the area of algorithmic randomness.
These results elucidate the deep relationship between randomness
and computability.
A number of results focus on randomness for finite strings. Levin introduced
two functions which measure the randomness of finite strings. One
function is derived from a universal monotone machine and the other function
is derived from an optimal computably enumerable semimeasure. Gacs
proved that infinitely often, the gap between these two functions exceeds the
inverse Ackermann function (applied to string length). This thesis improves
this result to show that infinitely often the difference between these two functions
exceeds the double logarithm. Another separation result is proved for
two different kinds of process machine.
Information about the randomness of finite strings can be used as a computational
resource. This information is contained in the overgraph. Muchnik
and Positselsky asked whether there exists an optimal monotone machine
whose overgraph is not truth-table complete. This question is answered in the
negative. Related results are also established.
This thesis makes advances in the theory of randomness for infinite binary
sequences. A variant of process machines is used to characterise computable
randomness, Schnorr randomness and weak randomness. This result is extended
to give characterisations of these types of randomness using truthtable
reducibility. The computable Lipschitz reducibility measures both the
relative randomness and the relative computational power of real numbers. It
is proved that the computable Lipschitz degrees of computably enumerable
sets are not dense.
Infinite binary sequences can be regarded as elements of Cantor space.
Most research in randomness for Cantor space has been conducted using the
uniform measure. However, the study of non-computable measures has led to
interesting results. This thesis shows that the two approaches that have been
used to define randomness on Cantor space for non-computable measures:
that of Reimann and Slaman, along with the uniform test approach first introduced
by Levin and also used by Gacs, Hoyrup and Rojas, are equivalent.
Levin established the existence of probability measures for which all infinite sequences are random. These measures are termed neutral measures. It is
shown that every PA degree computes a neutral measure. Work of Miller is
used to show that the set of atoms of a neutral measure is a countable Scott set
and in fact any countable Scott set is the set of atoms of some neutral measure.
Neutral measures are used to prove new results in computability theory. For
example, it is shown that the low computable enumerable sets are precisely
the computably enumerable sets bounded by PA degrees strictly below the
halting problem.
This thesis applies ideas developed in the study of randomness to computability
theory by examining indifferent sets for comeager classes in Cantor
space. A number of results are proved. For example, it is shown that there
exist 1-generic sets that can compute their own indifferent sets
Studies on some bovine mycoplasmas
My studies on bovine mycoplasnas fall under three
separate headings:A. ANGPLASMA MYQPI.DES VAR. MCOIDES AND CONTĂ2IOUS BOVINE
UROPNEUMONIA.
An investigation was undertaken to determine whether
the allergic reaction could be developed as a useful diagnostic test for contagious bovine pleuropneumonia. Using
antigens obtained from M. mycoides var. n coides two types
of reaction were observed, an immediate reaction associated
with lipopolysaccharide material and a delayed reaction
associated with protein. It was impossible to separate the
protein completely from the lipopolysaccharide, which
elicited some non-specific reactions, and the test was
abandoned.A comparison of various serological tests employed in
contagious bovine pleuropneumonia diagnosis revealed that
no single test was entirely satisfactory, but the complement fixation test was the best available. Growth inhibition of M. mycoides var. mycoides by serum was examined as
a diagnostic test and as a measure of immunity. Two tests
were evolved, one on solid medium and the other in liquid
medium, and both proved to be of potential value for contagious bovine pleuropneumonia diagnosis, but their value
in measuring immunity was not determined. Inhibition was
observed, to occur in the absence of agglutination and
heat-labile accessory factors.The lipopolysaccharide from M. mycoides var. mycoides,
responsible for the immediate allergic reaction, was
shown to be serologically related to a galactan extracted
from normal bovine lung. This lipopolysaccharide was also
shown to be aritigenically related to polysaccharides from
a number of different sources including other microorganisms and this relationship was considered to be responsible for non-specific reactions discerned in diagnostic tests.It was suggested that the serological relationship
between the lipopolysaccharide of M. Ayssides vay_t_mycoides
and the galactan from bovine lung might play a role in the
pathogenesis of contagious bovine pleuropneumonia. A preliminary examination of this percept was inconclusive, but
it was shown, fortuitously, that immunity could be transferred passively.Electronmicroscopic examination of ItmmixleamaEl.
ycoides, treated with specific antiserum, revealed a capsule or slime layer round the organisms. This capsule is
probably composed of galactan.A method devised for the production, testing and
transport of a modified Ti contagious bovine pleuropneumonia vaccine is described.Chicken embryos, from hens previously inoculated with
M. mycoides var. mycoides, were immune to challenge with
this organism, suggesting that the chicken embryo might be
a suitable host for studying immunity to contagious bovine
pleuropneumonia.B. MYCOPLASMAS WITH CALF NEUMONIA AND BOVINE
KERATOCON'UNCTIVITIS.
Material from pneumonic lungs cultured in special
media resulted in the isolation of two species of xaycoplasma hitherto unrecorded from lungs. One was a new
species of mycoplasma, subsequently named M. dispar, and
the other was T-mycoplasna. Mycoplasmas were isolated
from 75% of 65 pneumonic lungs examined; these comprised
T-mycoplasmas from 58.5% of lungs, M. dispar from 51% and
M. bovirhinis from 23%.The pathogenicity of the T-mycoplasmas was tested by
inoculating cultures endobronchially into 3-week-old
calves. Gross pneumonic lesions were observed in 14 out of
the 16 calves at slaughter, compared with 2 out of 9 that
revealed lesions following inoculation of control materials
(P<0.01). Certain T-mycoplasmas also produced mastitis in
the mammary glands of cows when inoculated via the teat
canal. Strains both virulent and avirulent for the bovine
mammary gland could be isolated from cattle, but human,
canine and simian strains of T-mycoplasmas were avirulent.
Bovine T-mycoplasmas were shown to be serologically heterogeneous.T-mycoplasmas, M. bovirhinis, Acholejlasma laidlawii
and an unidentifiable species of mycoplasma were isolated
from eyes of cattle suffering from keratoconjunctivitis.C. MYCOPLASMATALES VIRUSES
Three distinct viruses have been isolated. All infect
A. laidlawii producing visible plaques on 'lawns' of this
organism. The first virus isolated, named Mycoplasmatales
virus - laidlawii 1 (MV-L1), is a small (16 x 90 nm.)
rod-shaped DNA containing virus. The second virus,
named MV-L2, is roughly spherical, apparently enveloped
and about 80 nm, in diameter (range 50-125 nm.). It
appears to contain DNA and is serologically distinct from
MV-Ll. The third virus (MV-L3), only recently isolated,
is polyhedral and uniform in size (about 54 nm, diameter)
and is serologically distinct from both MV-Li and MV-L2.PUBLICATIONS IN SUPPORT OF CANDIDATURE:
A MYCOPLASMA MYCOIDES VAR. MYCOIDES AND CONTAGIOUS
BOVINE PLEUROPNEUMONIA
1. GOURLAY, R. N. (1964). The allergic reaction in
contagious bovine pleuropneumonia. Journal of
EsylpĂĄratiae2211-22122x 74, 286-299. ||
2. & PALMER, R. F. (1965). Further studies
on the allergic reaction in contagious bovine
pleuropneumonia. Journal of Comparative Pathology 75, 89-95. ||
3. & SHIFRINE, M. (1965) . Comparison
between methods of antigen preparation and the use
of adjuvant in the delayed allergic skin reaction
in contagious bovine pleuropneumonia. Journal of
Comparative Pathology 75, 375-380. ||
4. SHIFRINE, M. & GOURLAY,. R. N. (1965). The immediate
type allergic skin reaction in contagious bovine
pleuropneumonia. Journal of Comparative Pathology
75, 381-385. ||
5. & (1967). Serological
relationships between Mycoplasma mycoides and other
bacteria. Annals of the New York Academy of
Science. 143, 311-324. ||
6. GOURLAY, R. N. (1935). Comparison between some diagnostic tests for contagious bovine pleuropneumonia.
Journal of Comparative Pathology 75, 97-109. ||
7. SHIFRINE M. & GOURLAY, R. N. (1967). Evaluation of
diagnostic tests for contagious bovine pleuropneumonia. ER112Iinafpizootic Diseases of
Africa 15, 7-10, ||
8. DOMERMUTH, C. H. & GOURLAY, R. N. (1967). A solid
medium test for measuring growth inhibition and
neutralisation of ypyARxçc2LdMcolasxes by immune
bovine serum. Journal of General Microbiology
47, 289-294. ||
9. GOURLAY, R. N. & DOMERMUTH, C. H. (1967). Growth
inhibition and 'neutralisation' of Mycoplasma
mycoides by immune bovine serum. Annals of the
New York Academ of Science 143, 325-336. ||
10. SHIFRINE, M. & GOURLAY, R. N. (1965). Serological
relationship between galactans from normal bovine
lung and Mycoplasma Nature, London
208, 498-499. ||
11. GOURLAY, R. N. & SHIFRINE, M. (1966). Antigenic
cross-reactions between the galactan from
plasmanasoides and polysaccharides from other
sources. Journal of Corn arative Patholoc 76,
417-425. ||
12. & BROCKLESBY, D. W. (1967). Preliminary experiments with antigens of Theileria
pĂĄLya (Theiler, 1904). British Veterinary_lamIlL
123, 533-540. ||
13. & SHIFRINE, M. (1966). Passive transfer of immunity and formation of lung lesions
following intravenous inoculation of Mycoplasma nix,21.sisa and immune bovine serum. Bulletin of
Epiaslotic Diseases of Africa 14, 369-372. ||
14. GOURLAY, R. N. & THROWER, K. J. (1968). Morl,hology
of Llysgpjau_uarzlxcoides thread-phase growth.
Journal of General Microbiology 54, 155-159. ||
15. BROWN, R. D., GOURLAY, R. N. & MACLEOD, A. K. (1965).
The production of Ti broth culture contagious
bovine pleuropneumonia vaccine. Bulletin of
E izootic Diseases of Africa 13, 149-155. ||
16. GOURLAY, R. N. & MACLEOD, A. K. (1966). Fermentation
of glucose by Mys2212sma mycoides and its effect
on viability. Bulletin of E izootic Diseases of
Africa 14, 373-381. ||
17. & SHIFRINE, M. (1966). The use of
embryonated chicken eggs for the study of immunity to MYcoplasma Tycoides. Veterinary Record 78,
256-257. ||
18. & (1968). The virulence
and viability of Mycoplasma mycoides strains in
chicken embryos from normal and immunised hens.
Research in Veterinary Science 9, 185-186. ||
B MYCOPLASMAS ASSOCIATED WITH CALF PNEUMONIA AND
BOVINE KERATOCONJUNCTIVITIS:
19. GOURLAY, R. N. (1969). Isolation of a mycoplasma-like
organism from pneumonic calf lungs. Veterinary
Record 84, 229-230. ||
20. & LEACH, R. H. (1970). A new mycoplasma species isolated from pneumonic lungs of
calves (Mycoplasma dispar, Sp. Nov.) Journal of
Medical Microbioloq 3, 111-123. ||
21. (1968). The isolation of T-strains of
Mycoplasma from pneumonic calf lungs. Research
in Veterinar Science 9, 376-378. ||
22. & THOMAS, L. H. (1969). The isolation
of large colony and T-strain mycoplasmas from
cases of bovine kerato-conjunctivitis.
Veterinary Record 84, 416-417. ||
23. & MACKENZIE, A. & COOPER, J. E. (1970).
Studies of the microbiology and pathology of
pneumonic lungs of calves. Journal of comparatitive Pathology 80, 575-584. ||
24. & THOMAS, L. H. (1970). The experimental production of pneumonia in calves by the
endobronchial inoculation of T-mycoplasmas.
Journal of Com arative Patholoca 80, 585-594. ||
25. HOWARD, C. J. & BROWNLIE, J. (1972).
The production of mastitis in cows by the intramammary inoculation of T-mycoplasmas. Journal of
Hygiene, Cambridge 70, 511-521. ||
26. HOWARD, C. J. & GOURLAY, R. N. (1972). Serology of
bovine T-mycoplasmas. British Veterinary
Journal 128, XXXVII-XL. ||
27. ______, _______ & BROWNLIE, J. (1973).
The virulence of T-mycoplasmas, isolated from
various animal species, assayed by intramammary
inoculation in cattle. journal of Hygiene, Cambridge 71, 163-170. ||
C MYCOPLASMATALES VIRUSES:
28. GOURLAY, R. N. (1970). Isolation of a virus infecting a strain of MycopIasma laidlawii. Nature,
London 225, 1165. ||
29. , BRUCE, JUDY & GARWES , D. J. (1971).
Characterisation of Mycoplasmatales virus
laidlawii 1. Nature New Biolaay 229, 118-119. ||
30. (1972). Ultrastructural studies of
Mycoplasmatales viruses. MedicALILlIg.
and Immunology 157, 172, ||
31. BRUCE, J., GOURLAY R. N., HULL, R. & GARWES, D. J.
(1972). Ultrastructure of Mycoplasmatales
virus - laidlawii 1. Journal of
16, 215-221. ||
32. GOURLAY, R. N. & WYLD, SARA G. (1972). Some biological characteristics of Mycoplasmatales virus
laidlawii 1. Journal of General Virolgaz 14,
15-23. ||
33. (1971). Mycoplasmatales virus - laidlawii 2, a new virus isolated from Acholeplasma laidlawii. Journal of General Virology
12, 65-67. ||
34. (1972). Isolation and characterisation
of mycoplasma viruses. In PathougaisilyssmlĂĄsmIla
Ciba Foundation Symposium. Amsterdam. ASP. 145-156. ||
35. 4.11 GARWES, D. J., BRUCF J. & WYLD, S. G.
(1973). Further studies on the morphology and
composition of Mycoplasmatales virus - laidlawii
45
2. Journal of General Virolooy 18, 127-133. ||
36. & WYLD, S. G. (1973). Isolation of
Mycoplasmatales virus laidlawii 3, a new virus
infecting Acholeolasma laidlawii.
Journal of General Virology (in press)