Mathematical Sciences Research Collection
http://hdl.handle.net/10197/2047
Wed, 23 Apr 2014 13:21:17 GMT20140423T13:21:17ZThe approximation order of polysplines
http://hdl.handle.net/10197/5519
The approximation order of polysplines
Kounchev, Ognyan; Render, Hermann
We show that the scaling spaces de ned by the polysplines of order
p provide approximation order 2p: For that purpose we re ne the re
sults on one dimensional approximation order by Lsplines obtained
in [2].
Thu, 01 Jul 2004 00:00:00 GMThttp://hdl.handle.net/10197/551920040701T00:00:00ZPolyharmonicity and algebraic support of measures
http://hdl.handle.net/10197/5511
Polyharmonicity and algebraic support of measures
Kounchev, Ognyan; Render, Hermann
Our main result states that two signed measures μ and ν with bounded
support contained in the zero set of a polynomial P(χ) are equal if they coincide on the
subspace of all polynomials of polyharmonic degree NP where the natural number NP is
explicitly computed by the properties of the polynomial P(χ). The method of proof
depends on a definition of a multivariate Markov transform which is another major
objective of the present paper. The classical notion of orthogonal polynomial of second
kind is generalized to the multivariate setting: it is a polyharmonic function which has
similar features to those in the onedimensional case.
Thu, 01 Feb 2007 00:00:00 GMThttp://hdl.handle.net/10197/551120070201T00:00:00ZConvergence of polyharmonic splines on semiregular grids Z x aZ^n for a to 0
http://hdl.handle.net/10197/5510
Convergence of polyharmonic splines on semiregular grids Z x aZ^n for a to 0
Kounchev, Ognyan; Render, Hermann
Let
p,n
∈
N
with 2
p
≥
n
+ 2
,
and let
I
a
be a polyharmonic spline of
order
p
on the grid
Z
×
a
Z
n
which satisfies the interpolating conditions
I
a
(
j,am
) =
d
j
(
am
) for
j
∈
Z
,m
∈
Z
n
where the functions
d
j
:
R
n
→
R
and the parameter
a>
0 are given. Let
B
s
(
R
n
) be the set of all integrable
functions
f
:
R
n
→
C
such that the integral
k
f
k
s
:=
Z
R
n
b
f
(
ξ
)
(1 +

ξ

s
)
dξ
is finite. The main result states that for given
σ
≥
0 there exists a
constant
c>
0 such that whenever
d
j
∈
B
2
p
(
R
n
)
∩
C
(
R
n
)
,j
∈
Z
,
satisfy
k
d
j
k
2
p
≤
D
·
(1 +

j

σ
) for all
j
∈
Z
there exists a polyspline
S
:
R
n
+1
→
C
of order
p
on strips such that

S
(
t,y
)
−
I
a
(
t,y
)
≤
a
2
p
−
1
c
·
D
·
(1 +

t

σ
)
for all
y
∈
R
n
,t
∈
R
and all 0
<a
≤
1.
Sun, 01 Jul 2007 00:00:00 GMThttp://hdl.handle.net/10197/551020070701T00:00:00ZOn realanalytic recurrence relations for cardinal exponential Bsplines
http://hdl.handle.net/10197/5508
On realanalytic recurrence relations for cardinal exponential Bsplines
Aldaz, J. M.; Kounchev, Ognyan; Render, Hermann
Let LN+1 be a linear differential operator of order N + 1 with constant coefficients
and real eigenvalues λ 1, ..., λ N+1, let E( N+1) be the space of all C∞solutions of
LN+1 on the real line.We show that for N 2 and n = 2, ...,N, there is a recurrence
relation from suitable subspaces εn to εn+1 involving realanalytic functions, and
with εN+1 = E(Λ N+1) if and only if contiguous eigenvalues are equally spaced.
Mon, 01 Oct 2007 00:00:00 GMThttp://hdl.handle.net/10197/550820071001T00:00:00ZPadé approximation for a multivariate Markov transform
http://hdl.handle.net/10197/5503
Padé approximation for a multivariate Markov transform
Kounchev, Ognyan; Render, Hermann
Methods of Padè approximation are used to analyse a multivariate
Markov transform which has been recently introduced by the authors.
The first main result is a characterization of the rationality of the
Markov transform via Hankel determinants. The second main result
is a cubature formula for a special class of measure.
Wed, 01 Oct 2008 00:00:00 GMThttp://hdl.handle.net/10197/550320081001T00:00:00ZOn the mixed Cauchy problem with data on singular conics
http://hdl.handle.net/10197/5501
On the mixed Cauchy problem with data on singular conics
Ebenfelt, Peter; Render, Hermann
We consider a problem of mixed Cauchy type for certain holomorphic partial differential
operators with the principal part Q2p(D) essentially being the (complex) Laplace operator to
a power, Δp. We provide inital data on a singular conic divisor given by P = 0, where P is a
homogeneous polynomial of degree 2p. We show that this problem is uniquely solvable if the
polynomial P is elliptic, in a certain sense, with respect to the principal part Q2p(D).
Fri, 01 Aug 2008 00:00:00 GMThttp://hdl.handle.net/10197/550120080801T00:00:00ZThe Goursat problem for a generalized Helmholtz operator in the plane
http://hdl.handle.net/10197/5500
The Goursat problem for a generalized Helmholtz operator in the plane
Ebenfelt, Peter; Render, Hermann
We consider the Goursat problem in the plane for partial differential operators whose principal part is the pth power of the standard Laplace operator. The data is posed on a union of 2p distinct lines through the origin. We show that the solvability of this Goursat problem depends on Diophantine properties of the geometry of lines on which the data is posed.
Mon, 01 Sep 2008 00:00:00 GMThttp://hdl.handle.net/10197/550020080901T00:00:00ZReproducing kernels for polyharmonic polynomials
http://hdl.handle.net/10197/5499
Reproducing kernels for polyharmonic polynomials
Render, Hermann
The reproducing kernel of the space of all homogeneous polynomi
als of degree
k
and polyharmonic order
m
is computed explicitly, solving a
question of A. Fryant and M.K. Vemuri.
Wed, 01 Oct 2008 00:00:00 GMThttp://hdl.handle.net/10197/549920081001T00:00:00ZBernstein operators for exponential polynomials
http://hdl.handle.net/10197/5498
Bernstein operators for exponential polynomials
Aldaz, J. M.; Kounchev, Ognyan; Render, Hermann
Let
L
be a linear differential operator with constant coefficients of order
n
and complex eigenvalues
λ
0
,...,λ
n
. Assume that the set
U
n
of all solutions of the
equation
Lf
= 0 is closed under complex conjugation. If the length of the interval [
a,b
]
is smaller than
π/M
n
, where
M
n
:= max
{
Im
λ
j

:
j
= 0
,...,n
}
, then there exists a basis
p
n,k
,
k
= 0
,...n
, of the space
U
n
with the property that each
p
n,k
has a zero of order
k
at
a
and a zero of order
n
−
k
at
b,
and each
p
n,k
is positive on the open interval (
a,b
)
.
Under the additional assumption that
λ
0
and
λ
1
are real and distinct, our first main
result states that there exist points
a
=
t
0
<t
1
<...<t
n
=
b
and positive numbers
α
0
,..,α
n
, such that the operator
B
n
f
:=
n
X
k
=0
α
k
f
(
t
k
)
p
n,k
(
x
)
satisfies
B
n
e
λ
j
x
=
e
λ
j
x
, for
j
= 0
,
1
.
The second main result gives a sufficient condition
guaranteeing the uniform convergence of
B
n
f
to
f
for each
f
∈
C
[
a,b
].
Wed, 01 Apr 2009 00:00:00 GMThttp://hdl.handle.net/10197/549820090401T00:00:00ZOn the Bernstein operator of S. Morigi and M. Neamtu
http://hdl.handle.net/10197/5496
On the Bernstein operator of S. Morigi and M. Neamtu
Kounchev, Ognyan; Render, Hermann
We discuss a Bernstein type operator introduced by S. Morigi and
M. Neamtu for
D
polynomials in the more general framework of exponential
polynomials
Thu, 01 Oct 2009 00:00:00 GMThttp://hdl.handle.net/10197/549620091001T00:00:00ZShape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
http://hdl.handle.net/10197/5495
Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces
Aldaz, J. M.; Kounchev, Ognyan; Render, Hermann
We study the existence and shape preserving properties of a generalized
Bernstein operator
B
n
fixing a strictly positive function
f
0
, and a second function
f
1
such
that
f
1
/f
0
is strictly increasing, within the framework of extended Chebyshev spaces
U
n
.
The first main result gives an inductive criterion for existence: suppose there exists a
Bernstein operator
B
n
:
C
[
a,b
]
→
U
n
with strictly increasing nodes, fixing
f
0
,f
1
∈
U
n
.
If
U
n
⊂
U
n
+1
and
U
n
+1
has a nonnegative Bernstein basis, then there exists a Bernstein
operator
B
n
+1
:
C
[
a,b
]
→
U
n
+1
with strictly increasing nodes, fixing
f
0
and
f
1
.
In
particular, if
f
0
,f
1
,...,f
n
is a basis of
U
n
such that the linear span of
f
0
,..,f
k
is an
extended Chebyshev space over [
a,b
] for each
k
= 0
,...,n
, then there exists a Bernstein
operator
B
n
with increasing nodes fixing
f
0
and
f
1
.
The second main result says that
under the above assumptions the following inequalities hold
B
n
f
≥
B
n
+1
f
≥
f
for all (
f
0
,f
1
)convex functions
f
∈
C
[
a,b
]
.
Furthermore,
B
n
f
is (
f
0
,f
1
)convex for all
(
f
0
,f
1
)convex functions
f
∈
C
[
a,b
]
.
Tue, 01 Dec 2009 00:00:00 GMThttp://hdl.handle.net/10197/549520091201T00:00:00ZCauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
http://hdl.handle.net/10197/5492
Cauchy, Goursat and Dirichlet problems for holomorphic partial differential equations
Render, Hermann
n this paper we survey recent results about Fischer decomposi
tions of polynomials or entire functions and their applications to holomorphic
partial di erential equations. We discuss Cauchy and Goursat problems for the
polyharmonic operator. Special emphasis is given to the KhavinsonShapiro
conjecture concerning polynomial solvability of the Dirichlet problem.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10197/549220110101T00:00:00ZThe KhavinsonShapiro conjecture and polynomial decompositions
http://hdl.handle.net/10197/5490
The KhavinsonShapiro conjecture and polynomial decompositions
Lundberg, Erik; Render, Hermann
The main result of the paper states the following: Let ψ be a polynomial
in n variables of degree t: Suppose that there exists a constant C > 0 such
that any polynomial f has a polynomial decomposition f = ψ qf + hf with
khf = 0 and deg qf deg f + C: Then deg ψ 2k. Here ∆k is the kth
iterate of the Laplace operator ∆ : As an application, new classes of domains
in Rn are identi ed for which the KhavinsonShapiro conjecture holds.
Fri, 15 Apr 2011 00:00:00 GMThttp://hdl.handle.net/10197/549020110415T00:00:00ZPolyharmonic Hardy spaces on the complexified annulus and error estimates of cubature formulas
http://hdl.handle.net/10197/5489
Polyharmonic Hardy spaces on the complexified annulus and error estimates of cubature formulas
Kounchev, Ognyan; Render, Hermann
The present paper has a twofold contribution: first, we intro
duce a new concept of Hardy spaces on a multidimensional complexified
annular domain which is closely related to the annulus of the KleinDi
rac
quadric important in Conformal Quantum Field Theory. Secondly, for
functions in these Hardy spaces, we provide error estimate for the p
oly
harmonic GaußJacobi cubature formulas, which have been introduced
in previous papers.
Sat, 01 Dec 2012 00:00:00 GMThttp://hdl.handle.net/10197/548920121201T00:00:00ZHarmonic divisors and rationality of zeros of Jacobi polynomials
http://hdl.handle.net/10197/5488
Harmonic divisors and rationality of zeros of Jacobi polynomials
Render, Hermann
Let
Pn
(α,β
)
(
x
)
be the Jacobi polynomial of degree
n
with parameters
αβ
The main result of the paper states the following: If
b≠
1
;
3
and
c
are nonzero rel
atively prime natural numbers then
P
(
k
+(
d
3)
=
2
;k
+(
d
3)
=
2)
n
p
b=c
6
≠ 0
for all natural
numbers
d;n
and
k
2
N
0
:
Moreover, under the above assumption, the polynomial
Q
(
x
) =
b
c
x
2
1
+
:::
+
x
2
d
1
+
b
c
1
x
2
d
is not a harmonic divisor, and the Dirichlet problem for
the cone
f
Q
(
x
)
<
0
g
has polynomial harmonic solutions for polynomial data functions.
Thu, 01 Aug 2013 00:00:00 GMThttp://hdl.handle.net/10197/548820130801T00:00:00ZRegularity of generalized Daubechies wavelets reproducing exponential polynomials with realvalued parameters
http://hdl.handle.net/10197/5484
Regularity of generalized Daubechies wavelets reproducing exponential polynomials with realvalued parameters
Dyn, Nira; Kounchev, Ognyan; Levin, David; Render, Hermann
We investigate nonstationary orthogonal wavelets based on a nonstationary
interpolatory subdivision scheme reproducing a given set of exponentials with realvalued
parameters. The construction is analogous to the construction of Daubechies wavelets
using the subdivision scheme of DeslauriersDubuc. The main result is the existence and
smoothness of these Daubechies type wavelets.
Thu, 02 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10197/548420140102T00:00:00ZConvergence of rational Bernstein operators
http://hdl.handle.net/10197/5478
Convergence of rational Bernstein operators
Render, Hermann
In this paper we discuss convergence properties and error estimates of rational
Bernstein operators introduced by P. Pit¸ul and P. Sablonni`ere. It is shown that the
rational Bernstein operators converge to the identity operator if and only if the maximal
difference between two consecutive nodes is converging to zero. Further a Voronovskaja
theorem is given based on the explicit computation of higher order moments for the
rational Bernstein operator
Tue, 01 Apr 2014 00:00:00 GMThttp://hdl.handle.net/10197/547820140401T00:00:00ZReal Bargmann spaces, Fischer decompositions and Sets of uniqueness for polyharmonic functions
http://hdl.handle.net/10197/5474
Real Bargmann spaces, Fischer decompositions and Sets of uniqueness for polyharmonic functions
Render, Hermann
In this paper a positive answer is given to the following question of W.K.
Hayman: if a polyharmonic entire function of order k vanishes on k distinct ellipsoids
in the euclidean space Rn then it vanishes everywhere. Moreover a characterization of
ellipsoids is given in terms of an extension property of solutions of entire data functions
for the Dirichlet problem answering a question of D. Khavinson and H.S. Shapiro. These
results are consequences from a more general result in the context of direct sum decompositions
(Fischer decompositions) of polynomials or functions in the algebra A(BR)
of all realanalytic functions defined on the ball BR of radius R and center 0 whose
Taylor series of homogeneous polynomials converges compactly in BR. The main result
states that for a given elliptic polynomial P of degree 2k and sufficiently large radius
R > 0 the following decomposition holds: for each function f 2 A(BR) there exist
unique q, r 2 A(BR) such that f = Pq + r and kr = 0. Another application of this
result is the existence of polynomial solutions of the polyharmonic equation ku = 0 for
polynomial data on certain classes of algebraic hypersurfaces.
2000 Mathematical Subject Classification. Primary: 31B30. Secondary: 35A20,
14P99, 12Y05
Tue, 01 Apr 2008 00:00:00 GMThttp://hdl.handle.net/10197/547420080401T00:00:00ZBoundary behaviour of universal Taylor series
http://hdl.handle.net/10197/5312
Boundary behaviour of universal Taylor series
Gardiner, Stephen J.; Khavinson, Dmitry
A power series that converges on the unit disc D is called universal if its partial sums approx
imate arbitrary polynomials on arbitrary compacta in CnD that have connected complement.
This paper shows that such series grow strongly and possess a Picardtype property near
each boundary point.
Sat, 01 Feb 2014 00:00:00 GMThttp://hdl.handle.net/10197/531220140201T00:00:00ZMetSizeR: selecting the optimal sample size for metabolomic studies using an analysis based approach.
http://hdl.handle.net/10197/5043
MetSizeR: selecting the optimal sample size for metabolomic studies using an analysis based approach.
Nyamundanda, Gift; Gormley, Isobel Claire; Fan, Yue; Gallagher, William M.; Brennan, Lorraine
Background: Determining sample sizes for metabolomic experiments is important but due to the complexity of these experiments, there are currently no standard methods for sample size estimation in metabolomics. Since pilot studies are rarely done in metabolomics, currently existing sample size estimation approaches which rely on
pilot data can not be applied.
Results: In this article, an analysis based approach called MetSizeR is developed to estimate sample size for metabolomic experiments even when experimental pilot data are not available. The key motivation for MetSizeR is that it considers the type of analysis the researcher intends to use for data analysis when estimating sample
size. MetSizeR uses information about the data analysis technique and prior expert knowledge of the metabolomic experiment to simulate pilot data from a statistical model. Permutation based techniques are then applied to the simulated pilot data to estimate the required sample size.
Conclusions: The MetSizeR methodology, and a publicly available software package which implements the approach, are illustrated through real metabolomic applications. Sample size estimates, informed by the intended statistical analysis technique, and the associated uncertainty are provided.
Thu, 21 Nov 2013 00:00:00 GMThttp://hdl.handle.net/10197/504320131121T00:00:00ZJoint SpatioTemporal Modeling of Mycobacterium bovis Infections in Badgers and Cattle  Results from the Irish Four Area Project
http://hdl.handle.net/10197/4460
Joint SpatioTemporal Modeling of Mycobacterium bovis Infections in Badgers and Cattle  Results from the Irish Four Area Project
Kelly, Gabrielle E.
In Ireland and in the UK, bovine tuberculosis(bTB) infects cattle and wildlife badgers (Meles meleslinnaeus) and badgers contribute to the spread of the disease in cattle. Isotropic and anisotropic spatiotemporalmodels are fitted to cattle herd and badger settbTB incidence data from the Four Area Project using sequences of linear geostatistical models. An association was found between the spatial distribution of the disease in cattle and badgers in two of three areas. The limited association may be due to irregularity of sett territories,fragmentation of farms, TBtest insensitivity, temporal lags associated with transmission or nonspatial transmission. A statistical methodology is outlined whereby hypotheses related to spatial correlation structure may be tested.
Sat, 01 Jun 2013 00:00:00 GMThttp://hdl.handle.net/10197/446020130601T00:00:00ZAnisotropic spatial clustering of TB in cattle  the implications for control policy
http://hdl.handle.net/10197/4288
Anisotropic spatial clustering of TB in cattle  the implications for control policy
Kelly, Gabrielle E.
Bovine TB is a disease that affects cattle and the wildlife badger, species Meles meles, in Ireland and the UK, and badgers have been implicated in the spread of the disease in cattle. Efforts to eradicate the disease that have included localized badger culling, have not been successful. In a study to understand how the disease spreads, Kelly and More [1] determined that the disease spatially clusters in cattle herds and estimated the practical spatial ranges at which this occurs. We extend this work by examining possible anisotropy in clustering and the consequences for TB control policy.
1st Conference on Spatial Statistics 2011 – Mapping Global Change, Enschede, The Netherlands, March, 2011
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10197/428820110101T00:00:00ZClustering Ordinal Data via Latent Variable Models
http://hdl.handle.net/10197/4284
Clustering Ordinal Data via Latent Variable Models
McParland, Damien; Gormley, Isobel Claire
Item response modelling is a well established method for analysing ordinal response data. Ordinal data are typically collected as responses to a number
of questions or items. The observed data can be viewed as discrete versions of an
underlying latent Gaussian variable. Item response models assume that this latent
variable (and therefore the observed ordinal response) is a function of both respondent specific and item specific parameters. However, item response models assume
a homogeneous population in that the item specific parameters are assumed to be
the same for all respondents. Often a population is heterogeneous and clusters of
respondents exist; members of different clusters may view the items differently. A
mixture of item response models is developed to provide clustering capabilities in
the context of ordinal response data. The model is estimated within the Bayesian
paradigm and is illustrated through an application to an ordinal response data set
resulting from a clinical trial involving selfassessment of arthritis.
IFCS 2013 Conference of the International Federation of Classification Societies, Tilburg University, The Netherlands, from July 1417, 2013
Mon, 01 Apr 2013 00:00:00 GMThttp://hdl.handle.net/10197/428420130401T00:00:00ZA long term observational study of the impact of badger removal on herd restrictions due to bovine TB in the Irish midlands during 19892004
http://hdl.handle.net/10197/4280
A long term observational study of the impact of badger removal on herd restrictions due to bovine TB in the Irish midlands during 19892004
Kelly, Gabrielle E.; Condon, J.; More, Simon John; Dolan, L.; Higgins, I.; Eves, J.
An observational study was carried out, using data collected from four areas in the Irish midlands, between 1989 and 2004, to critically evaluate the longterm effects of proactive badger culling and to provide insights into reactive badger culling tuberculosis (TB) prevalence in cattle. Confirmed cattle herd TB incidence is the outcome measure used throughout. Relative to reactive culling, proactive badger culling was associated with a decrease in incidence in each of the 16 years of observation, which encompassed periods of both intensive and lessintensive badger removal. By 2004, we observed a decrease of 22% [95% confidence interval (CI) 1529, P<0.001] in the entire proactive and 37% (95% CI 25–47, P<0.001), in the inner proactive removal areas. The size of the decrease increased with time (P=0.055). There was a decrease (constant over time) of at least 14% (95% CI 76–97, P=0.013) in incidence in the inner compared to the outer control area (herds ≤2 km, >2 km, from proactive removal area boundaries, respectively). Incidence in the outer proactive removal area (herds <1.6 km from the proactive removal boundary) was similar to the inner control area (P=0.890). Incidence in the outer control area and total control area, compared to a neighbouring area some distance away, increased over the course of the study. Differences with the total control area were not statistically significant but the outer control area was 11% higher than the neighbouring area by 2004 (borderline significance P=0.057).
Wed, 01 Oct 2008 00:00:00 GMThttp://hdl.handle.net/10197/428020081001T00:00:00ZBody mass index and height over three generations: evidence from the Lifeways crossgenerational cohort study
http://hdl.handle.net/10197/4279
Body mass index and height over three generations: evidence from the Lifeways crossgenerational cohort study
Murrin, Celine; Kelly, Gabrielle E.; Tremblay, Richard E.; Kelleher, Cecily
Background: Obesity and its measure of body mass index are strongly determined by parental body size. Debate continues as to whether both parents contribute equally to offspring body mass which is key to understanding the aetiology of the disease. The aim of this study was to use cohort data from three generations of one family to
examine the relative maternal and paternal associations with offspring body mass index and how these associations compare with family height to demonstrate evidence of genetic or environmental crossgenerational transmission.
Methods: 669 of 1082 families were followed up in 2007/8 as part of the Lifeways study, a prospective observational crossgeneration linkage cohort. Height and weight were measured in 529 Irish children aged 5 to 7 years and were selfreported by parents and grandparents. All adults provided information on selfrated health, education status, and indicators of income, diet and physical activity. Associations between the weight, height, and body mass index of family members were examined with mixed models and heritability estimates computed using linear regression analysis.
Results: Selfrated health was associated with lower BMI for all family members, as was age for children. When these effects were accounted for evidence of familial associations of BMI from one generation to the next was more apparent in the maternal line. Heritability estimates were higher (h2 = 0.40) for motheroffspring pairs compared to fatheroffspring pairs (h2 = 0.22). In the previous generation, estimates were higher between mothersparents (h2 = 0.540.60) but not between fathersparents (h2 = 0.040.17). Correlations between mother and offspring across two generations remained significant when modelled with fixed variables of socioeconomic status, health, and lifestyle. A similar analysis of height showed strong familial associations from maternal and paternal lines across each generation.
Conclusions: This is the first family cohort study to report an enduring association between mother and offspring BMI over three generations. The evidence of BMI transmission over three generations through the maternal line in an observational study corroborates the findings of animal studies. A more detailed analysis of geno and
phenotypic data over three generations is warranted to understand the nature of this maternaloffspring relationship.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10197/427920120101T00:00:00ZSpatial clustering of TBinfected cattle herds prior to and following proactive badger removal
http://hdl.handle.net/10197/4278
Spatial clustering of TBinfected cattle herds prior to and following proactive badger removal
Kelly, Gabrielle E.; More, Simon John
Bovine tuberculosis (TB) is primarily a disease of cattle. In both Ireland and the UK, badgers (Meles meles) are an important wildlife reservoir of infection. This paper examined the hypothesis that TB is spatially correlated in cattle herds, established the range of correlation and the effect, if any, of proactive badger removal on this. We also reanalysed data from the Four Area Project in Ireland, a largescale intervention study aimed at assessing the effect of proactive badger culling on bovine TB incidence in cattle herds, taking possible spatial correlation into account. We established that infected herds are spatially correlated (the scale of spatial correlation is presented), but at a scale that varies with time and in different areas. Spatial correlation persists following proactive badger removal.
Mon, 01 Aug 2011 00:00:00 GMThttp://hdl.handle.net/10197/427820110801T00:00:00ZEstimating the extent of spatial association of Mycobacterium bovis infection in badgers in Ireland
http://hdl.handle.net/10197/4275
Estimating the extent of spatial association of Mycobacterium bovis infection in badgers in Ireland
Kelly, Gabrielle E.; McGrath, Guy; More, Simon John
Mycobacterium bovis infects the wildlife species badgers Meles meles who are linked with the spread of the associated disease tuberculosis (TB) in cattle. Control of livestock infections depends in part on the spatial and social structure of the wildlife host. Here we describe spatial association of M. bovis infection in a badger population using data from the first year of the Four Area Project in Ireland. Using secondorder intensity functions, we show there is strong evidence of clustering of TB cases in each the four areas, i.e. a global tendency for infected cases to occur near other infected cases. Using estimated intensity functions, we identify locations where particular strains of TB cluster. Generalized linear geostatistical models are used to assess the practical range at which spatial correlation occurs and is found to exceed 6 in all areas. The study is of relevance concerning the scale of localized badger culling in the control of the disease in cattle.
Mon, 01 Feb 2010 00:00:00 GMThttp://hdl.handle.net/10197/427520100201T00:00:00ZSpatioTemporal Modelling of TB in Cattle Herds
http://hdl.handle.net/10197/4273
SpatioTemporal Modelling of TB in Cattle Herds
Kelly, Gabrielle E.
We examine spatial association of bovine TB in cattle herds using data from Ireland. Badgers (Meles meles), a protected species under the Wildlife Act 1976 (OAG 2012), have been implicated in the spread of the disease in cattle. Current disease control policies include reactive culling (in response to TB outbreaks) of badgers in the index and neighbouring farms. Kelly and More (2011) using generalized linear geostatistical models, established that TB clusters in cattle herds and estimated the practical spatial ranges at which this occurs. Here this work is extended by taking into account possible anisotropy. Changes in spatial association over two time periods are also examined. The results have direct implications for establishing scale and direction in reactive culling. They are also of import regarding the evaluation of vaccines for badgers and cattle.
Wed, 01 Aug 2012 00:00:00 GMThttp://hdl.handle.net/10197/427320120801T00:00:00ZBoundary behaviour of functions which possess universal Taylor series
http://hdl.handle.net/10197/4220
Boundary behaviour of functions which possess universal Taylor series
Gardiner, Stephen J.
It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\ Ω that have connected complement. This paper establishes a strong unboundedness property for such functions near every boundary point. The result is new even in the case of the disc, where it strengthens work of several authors.
Fri, 01 Feb 2013 00:00:00 GMThttp://hdl.handle.net/10197/422020130201T00:00:00ZDetermination of a universal series
http://hdl.handle.net/10197/4035
Determination of a universal series
Mouze, Augustin; Nestoridis, Vassili; Papadoperakis, Ioannis; Tsirivas, Nikolaos
The known proofs for universal Taylor series do not determine a specific universal
Taylor series. In the present paper, we isolate a specific universal Taylor series by
modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific
universal Taylor series on the disc or on a polygonal domain. Furthermore in non
simply connected domains, when universal Taylor series exist, we can construct a
sequence of specific rational functions converging to a universal function, provided
the boundary is good enough. The solution uses an infinite denumerable procedure
and a finite number of steps is not sufficient. However we solve a Runge's type
problem in a finite number of steps.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10197/403520120101T00:00:00ZOstrowskitype theorems for harmonic functions
http://hdl.handle.net/10197/4034
Ostrowskitype theorems for harmonic functions
Manolaki, Myrto
Ostrowski showed that there are intimate connections between the gap structure of a Taylor series and the behaviour of its partial sums outside the disk of convergence. This paper investigates the corresponding problem for the homogeneous polynomial expansion of a harmonic function. The results for harmonic functions display new features in the case of higher dimensions.
Sun, 15 Jul 2012 00:00:00 GMThttp://hdl.handle.net/10197/403420120715T00:00:00ZTwophase quadrature domains
http://hdl.handle.net/10197/4028
Twophase quadrature domains
Gardiner, Stephen J.; Sjödin, Tomas
Recent work on twophase free boundary problems has led to the investigation of a new type of quadrature domain for harmonic functions. This paper develops a method of constructing such quadrature domains based on the technique of partial balayage, which has proved to be a useful tool in the study of onephase quadrature domains and HeleShaw flows.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10197/402820120101T00:00:00ZSentiment Analysis of Online Media
http://hdl.handle.net/10197/3964
Sentiment Analysis of Online Media
SalterTownshend, Michael; Murphy, Thomas Brendan
A joint model for annotation bias and document classification is presented
in the context of media sentiment analysis. We consider an Irish online media data
set comprising online news articles with user annotations of negative, positive or
irrelevant impact on the Irish economy. The joint model combines a statistical model
for user annotation bias and a Naive Bayes model for the document terms. An EM
algorithm is used to estimate the annotation bias model, the unobserved biases in the
user annotations, the classifier parameters and the sentiment of the articles. The joint
modeling of both the user biases and the classifier is demonstrated to be superior to
estimation of the bias followed by the estimation of the classifier parameters.
GfKl 2011: Joint Conference of the German Classification Society (GfKl)
and the German Association for Pattern Recognition (DAGM) August 31 to September 2, 2011 and the IFCS 2011: Symposium of the International Federation of Classification Societies (IFCS) August 30, 2011, Frankfurt am Main, Germany
Tue, 18 Dec 2012 00:00:00 GMThttp://hdl.handle.net/10197/396420121218T00:00:00ZRecent progress on fine differentiability and fine harmonicity
http://hdl.handle.net/10197/3961
Recent progress on fine differentiability and fine harmonicity
Gardiner, Stephen J.
This paper describes recent results concerning the notions of differentiability and harmonicity with respect to the ne topology of classical potential theory.
Complex Analysis and Potential Theory : a conference in honour of Paul M. Gauthier and Kohur Gowrisankaran, Montreal, June 2023, 2011
Sat, 15 Dec 2012 00:00:00 GMThttp://hdl.handle.net/10197/396120121215T00:00:00ZA generalization of universal Taylor series in simply connected domains
http://hdl.handle.net/10197/3893
A generalization of universal Taylor series in simply connected domains
Tsirivas, Nikolaos
Let Ω be a simply connected proper subdomain of the complex plane and z0 be a point in Ω. It is known that there are holomorphic functions f on Ω for which the partial sums (Sn(f,z0)) of the Taylor series about z0 have universal approximation properties outside Ω. In this paper we investigate what can be said for the sequence (βnSn(f,z0)) when (βn) is a sequence of complex numbers. We also study a related analogue of a classical theorem of Seleznev concerning the case where the radius of convergence of the universal power series is zero.
Sun, 01 Apr 2012 00:00:00 GMThttp://hdl.handle.net/10197/389320120401T00:00:00ZExistence of universal Taylor series for nonsimply connected domains
http://hdl.handle.net/10197/3842
Existence of universal Taylor series for nonsimply connected domains
Gardiner, Stephen J.
It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in ℂ\Ω that have connected complement. This paper shows, for nonsimply connected domains Ω, how issues of capacity, thinness and topology affect the existence of holomorphic functions on Ω that have universal Taylor series expansions about a given point.
Sun, 27 May 2012 00:00:00 GMThttp://hdl.handle.net/10197/384220120527T00:00:00ZPositivity properties for the clamped plate boundary problem on the ellipse and strip
http://hdl.handle.net/10197/3820
Positivity properties for the clamped plate boundary problem on the ellipse and strip
Render, Hermann; Ghergu, Marius
The positivity preserving property for the biharmonic operator with Dirichlet boundary condition is investigated. We discuss here the case where the domain is an ellipse (that may degenerate to a strip) and the data is a
polynomial function. We provide various conditions for which the positivity is preserved.
Fri, 01 Jun 2012 00:00:00 GMThttp://hdl.handle.net/10197/382020120601T00:00:00ZSpatiotemporal modeling of TB in cattle herds
http://hdl.handle.net/10197/3704
Spatiotemporal modeling of TB in cattle herds
Kelly, Gabrielle E.
We examine spatial association of bovine TB in cattle herds using data from Ireland.
Badgers (Meles meles), a protected species under the Wildlife Act 1976 (OAG 2012),
have been implicated in the spread of the disease in cattle. Current disease control policies include reactive culling (in response to TB outbreaks) of badgers in the index and neighbouring farms. Kelly and More (2011) using generalized linear geostatistical models, established that TB clusters in cattle herds and estimated the practical spatial ranges at which this occurs. Here this work is extended by taking into account possible anisotropy. Changes in spatial association over two time periods are also examined. The results have direct implications for establishing scale and direction in reactive culling. They are also
of import regarding the evaluation of vaccines for badgers and cattle.
Wed, 01 Aug 2012 00:00:00 GMThttp://hdl.handle.net/10197/370420120801T00:00:00ZIsotropy over function fields of Pfister forms
http://hdl.handle.net/10197/3616
Isotropy over function fields of Pfister forms
O'Shea, James
The question of which quadratic forms become isotropic when extended to the function field of a given form is studied. A formula for the minimum dimension of the minimal isotropic forms associated to such extensions is given, and some consequences thereof are outlined. Especial attention is devoted to function fields of Pfister forms. Here, the relationship between excellence concepts and the isotropy question is explored. Moreover, in the case where the ground field is formally real and has finite Hasse number, the isotropy question is answered for forms of sufficiently large dimension.
Sun, 01 Jul 2012 00:00:00 GMThttp://hdl.handle.net/10197/361620120701T00:00:00ZSentiment analysis of online media
http://hdl.handle.net/10197/3574
Sentiment analysis of online media
SalterTownshend, Michael; Murphy, Thomas Brendan
A joint model for annotation bias and document classification is presented in the context of media sentiment analysis. We consider an Irish online media data set comprising online news articles with user annotations of negative, positive or irrelevant impact on the Irish economy. The joint model combines a statistical model
for user annotation bias and a Naive Bayes model for the document terms. An EM algorithm is used to estimate the annotation bias model, the unobserved biases in the
user annotations, the classifier parameters and the sentiment of the articles. The joint
modeling of both the user biases and the classifier is demonstrated to be superior to
estimation of the bias followed by the estimation of the classifier parameters.
Paper presented at the DAGMGfKl/IFCS 2011, Joint Conference of the German Classification Society (GfKl)
and the German Association for Pattern Recognition (DAGM), August 31 to September 2, 2011 and at the IFCS 2011 Symposium of the International Federation of Classification Societies (IFCS), August 30, 2011, Frankfurt am Main, Germany
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10197/357420120101T00:00:00ZSemisupervised linear discriminant analysis
http://hdl.handle.net/10197/3455
Semisupervised linear discriminant analysis
Toher, Deirdre; Downey, Gerard; Murphy, Thomas Brendan
Fisher's linear discriminant analysis is one of the most commonly used and studied classification methods in chemometrics. The method finds a projection of multivariate data into a lower dimensional space so that the groups in the data are well separated. The resulting projected values are subsequently used to classify unlabeled observations into the groups.
A semisupervised version of Fisher's linear discriminant analysis is developed, so that the unlabeled observations are also used in the model fitting procedure. This approach is advantageous when few labeled and many unlabeled observations are available.
The semisupervised linear discriminant analysis method is demonstrated on a number of data sets where it is shown to yield better separation of the groups and improved classification over Fisher's linear discriminant analysis.
Thu, 01 Dec 2011 00:00:00 GMThttp://hdl.handle.net/10197/345520111201T00:00:00ZReducing errors of wind speed forecasts by an
optimal combination of postprocessing methods
http://hdl.handle.net/10197/3403
Reducing errors of wind speed forecasts by an
optimal combination of postprocessing methods
Sweeney, Conor; Lynch, Peter; Nolan, Paul
Seven adaptive approaches to postprocessing wind speed forecasts are discussed and compared. 48hour forecasts are run at horizontal resolutions of 7 km and 3 km for a domain centred over Ireland. Forecast wind speeds over a two year period are compared to observed wind speeds at seven synoptic stations around Ireland and skill scores calculated. Two automatic methods for combining forecast streams are applied. The forecasts produced by the combined methods give bias and root mean squared errors that are better than the numerical weather prediction forecasts at all station locations. One of the combined forecast methods results in skill scores that are equal to or better than all of its component forecast streams. This method is straightforward to apply and should prove beneficial in operational wind forecasting.
Tue, 13 Sep 2011 00:00:00 GMThttp://hdl.handle.net/10197/340320110913T00:00:00ZThe twochild paradox : dichotomy and ambiguity
http://hdl.handle.net/10197/3258
The twochild paradox : dichotomy and ambiguity
Lynch, Peter
Given that one of the children in a twochild family is a boy, what are the chances that the other is also a boy. The intuitive answer is 50 : 50. More careful investigation leads us to a 1in3 chance. We investigate circumstances under which these answers are correct. The imposition of further conditions yields some very surprising results.
Fri, 01 Jul 2011 00:00:00 GMThttp://hdl.handle.net/10197/325820110701T00:00:00ZInitialization
http://hdl.handle.net/10197/3023
Initialization
Lynch, Peter; Huang, XiangYu
The spectrum of atmospheric motions is vast, encompassing phenomena having periods ranging
from seconds to millennia. The motions of interest to the forecaster typically have timescales of a day or longer, but the mathematical models used for numerical prediction describe a broader span
of dynamical features than those of direct concern. For many purposes these higher frequency
components can be regarded as noise contaminating the motions of meteorological interest.
The elimination of this noise is achieved by adjustment of the initial fields, a process called
initialization.
Sun, 01 Aug 2010 00:00:00 GMThttp://hdl.handle.net/10197/302320100801T00:00:00ZWeather and climate forecasting : chronicle of a revolution
http://hdl.handle.net/10197/2956
Weather and climate forecasting : chronicle of a revolution
Lynch, Peter
Remarkable advances in weather forecasts
during the past halfcentury
have brought great benefits to humanity.
Accurate forecasts save many
lives, and early warnings mitigate
the worst effects of extreme weather
events, when they are available.
Detailed, accurate forecasts are of
huge economic value, with numerous
studies showing that the benefits of
forecasts outweigh the costs many
times over.
Advances in climate modeling over
the past fifty years have also been
outstanding. General circulation
models have been developed and
applied to examine the factors causing
changes in our climate, and their
likely timing and severity.
Tue, 01 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10197/295620100601T00:00:00ZOn resonant RossbyHaurwitz triads
http://hdl.handle.net/10197/2897
On resonant RossbyHaurwitz triads
Lynch, Peter
The dynamics of nondivergent flow on a rotating sphere are described by the conservation of absolute vorticity. The
analytical study of the nonlinear barotropic vorticity equation is greatly facilitated by the expansion of the solution in
spherical harmonics and truncation at low order. The normal modes are the wellknown Rossby–Haurwitz (RH) waves,
which represent the natural oscillations of the system. Triads of RH waves, which satisfy conditions for resonance, are
of critical importance for the distribution of energy in the atmosphere.
We show how nonlinear interactions of resonant RH triads may result in dynamic instability of largescale components.
We also demonstrate a mathematical equivalence between the equations for an orographically forced triad
and a simple mechanical system, the forceddamped swinging spring. This equivalence yields insight concerning the
bounded response to a constant forcing in the absence of damping. An examination of triad interactions in atmospheric
reanalysis data would be of great interest.
Fri, 01 May 2009 00:00:00 GMThttp://hdl.handle.net/10197/289720090501T00:00:00ZA latent space mapping for link prediction
http://hdl.handle.net/10197/2895
A latent space mapping for link prediction
Brew, Anthony; SalterTownshend, Michael
Network modeling can be approached using either discriminative or probabilistic
models. In the task of link prediction a probabilistic model will give a probability
for the existence of a link; while in some scenarios this may be beneficial, in others
a hard discriminative boundary needs to be set. Hence the use of a discriminative
classifier is preferable. In domains such as image analysis and speaker recognition,
probabilistic models have been used as a mechanism from which features
can be extracted. This paper examines using a probabilistic model built on the
entire graph to extract features to predict the existence of unknown links between
two nodes. It demonstrates how features extracted from the model as well as the
predicted probability of a link existing can aid the classification process.
NIPS Workshop on Networks across Disciplines in Theory and Applications, 11th December 2010, Whistler BC, Canada
Sat, 11 Dec 2010 00:00:00 GMThttp://hdl.handle.net/10197/289520101211T00:00:00ZPrecession and recession of the rock'n'roller
http://hdl.handle.net/10197/2893
Precession and recession of the rock'n'roller
Lynch, Peter; Bustamante, Miguel
We study the dynamics of a spherical rigid body that rocks and rolls on a plane
under the effect of gravity. The distribution of mass is nonuniform and the
centre of mass does not coincide with the geometric centre. The symmetric case,
with moments of inertia I1 = I2 < I3, is integrable and themotion is completely
regular. Three known conservation laws are the total energy E, Jellett’s quantity
QJ and Routh’s quantity QR. When the inertial symmetry I1 = I2 is broken,
even slightly, the character of the solutions is profoundly changed and new
types of motion become possible. We derive the equations governing the
general motion and present analytical and numerical evidence of the recession,
or reversal of precession, that has been observed in physical experiments. We
present an analysis of recession in terms of critical lines dividing the (QR,QJ )
plane into four dynamically disjoint zones. We prove that recession implies
the lack of conservation of Jellett’s and Routh’s quantities, by identifying
individual reversals as crossings of the orbit (QR(t ),QJ (t)) through the critical
lines. Consequently, a method is found to produce a large number of initial
conditions so that the system will exhibit recession.
Wed, 30 Sep 2009 00:00:00 GMThttp://hdl.handle.net/10197/289320090930T00:00:00ZAdaptive postprocessing of shortterm wind forecasts for energy applications
http://hdl.handle.net/10197/2892
Adaptive postprocessing of shortterm wind forecasts for energy applications
Sweeney, Conor; Lynch, Peter
We present a new method of reducing the error in predicted wind speed, thus enabling better management of wind energy
facilities. A numerical weather prediction model, COSMO, was used to produce 48 h forecast data every day in 2008 at
horizontal resolutions of 10 and 3 km. A new adaptive statistical method was applied to the model output to improve the
forecast skill. The method applied corrective weights to a set of forecasts generated using several postprocessing methods.
The weights were calculated based on the recent skill of the different forecasts. The resulting forecast data were compared
with observed data, and skill scores were calculated to allow comparison between different postprocessing methods. The
total root mean square error performance of the composite forecast is superior to that of any of the individual methods.
Fri, 01 Apr 2011 00:00:00 GMThttp://hdl.handle.net/10197/289220110401T00:00:00ZFrom Richardson to early numerical weather prediction
http://hdl.handle.net/10197/2891
From Richardson to early numerical weather prediction
Lynch, Peter
The development of computer models for numerical simulation of the atmosphere
and oceans is one of the great scientific triumphs of the past fifty years. These
models have added enormously to our understanding of the complex processes in
the atmosphere and oceans. The consequences for humankind of ongoing climate
change will be farreaching. Earth system models are the best means we have of
predicting the future of our climate.
The basic ideas of numerical forecasting and climate modeling were developed
about a century ago, long before the first electronic computer was constructed.
However, advances on several fronts were necessary before numerical prediction
could be put into practice. A fuller understanding of atmospheric dynamics allowed
the development of simplified systems of equations; regular observations of the
free atmosphere provided the initial conditions; stable finite difference schemes
were developed; and powerful electronic computers provided a practical means of
carrying out the calculations required to predict the changes in the weather.
In this chapter, we trace the history of computer forecasting from Richardson’s
prodigious manual computation, through the ENIAC (Electronic Numerical
Integrator and Computer) integrations to the early days of operational numerical
weather prediction and climate modeling. The useful range of deterministic prediction
is increasing by about one day each decade. We set the scene for the story
of the remarkable progress in weather forecasting and in climate modeling over
the past fifty years, which will be treated in subsequent chapters.
Wed, 01 Dec 2010 00:00:00 GMThttp://hdl.handle.net/10197/289120101201T00:00:00Z