bluuebunny/crossref_metadata_2025 huggingface dataset:
Bounds for multiplicative cosets over fields of prime order
Authors: Powell Corey
Published: July 2002

Let

m
m

be a positive integer and suppose that

p
p

is an odd prime with

p
≡
1
mod
m

p \equiv 1 \bmod m

. Suppose that

a
∈
(

Z

/

p

Z

)
∗

a \in (\mathbb {Z}/p\mathbb {Z})^*

and consider the polynomial

x
m

−
a

x^m-a

. If this polynomial has any roots in

(

Z

/

p

Z

)
∗

(\mathbb {Z}/p\mathbb {Z})^*

, where the coset representatives for

Z

/

p

Z

\mathbb {Z}/p\mathbb {Z}

are taken to be all integers

u
u

with

|

u

|

>
p

/

2

|u|>p/2

, then these roots will form a coset of the multiplicative subgroup

μ
m

\mu _m

of

(

Z

/

p

Z

)
∗

(\mathbb {Z}/p\mathbb {Z})^*

consisting of the

m
m

th roots of unity mod

p
p

. Let

C
C

be a coset of

μ
m

\mu _m

in

(

Z

/

p

Z

)
∗

(\mathbb {Z}/p\mathbb {Z})^*

, and define

|

C

|

=

max

u
∈
C

|

u

|

|C|=\max _{u \in C}{|u|}

. In the paper “Numbers Having

m
m

Small

m
m

th Roots mod

p
p

” (Mathematics of Computation, Vol. 61, No. 203 (1993),pp. 393-413), Robinson gives upper bounds for
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper M 1 left-parenthesis m comma p right-parenthesis equals min Underscript upper C element-of left-parenthesis double-struck upper Z slash p double-struck upper Z right-parenthesis Superscript asterisk Baseline slash mu Subscript m Baseline Endscripts StartAbsoluteValue upper C EndAbsoluteValue">

M
1

(
m
,
p
)
=

min

C
∈
(

Z

/

p

Z

)
∗

/

μ
m

|

C

|

M_1(m,p)=\min _{\tiny C \in (\mathbb {Z}/p\mathbb {Z})^* /\mu _m }{|C|}

of the form

M
1

(
m
,
p
)
>

K
m

p

1
−
1

/

ϕ
(
m
)

M_1(m,p)>K_mp^{1-1/\phi (m)}

, where

ϕ
\phi

is the Euler phi-function. This paper gives lower bounds that are of the same form, and seeks to sharpen the constants in the upper bounds of Robinson. The upper bounds of Robinson are proven to be optimal when

m
m

is a power of

2
2

or when

m
=
6.

m=6.
Further tabulation of the Erdös-Selfridge function
Authors: Lukes Richard , Scheidler Renate , Williams Hugh
Published: July 2002

For a positive integer

k
k

, the Erdös-Selfridge function is the least integer

g
(
k
)
>
k
+
1

g(k) > k+1

such that all prime factors of

(

g
(
k
)

k

)

\binom {g(k)}{k}

exceed

k
k

. This paper describes a rapid method of tabulating

g
(
k
)

g(k)

using VLSI based sieving hardware. We investigate the number of admissible residues for each modulus in the underlying sieving problem and relate this number to the size of

g
(
k
)

g(k)

. A table of values of

g
(
k
)

g(k)

for

135
≤
k
≤
200

135 \leq k \leq 200

is provided.
Approximating the number of integers free of large prime factors
Authors: Hunter Simon , Sorenson Jonathan
Published: July 2002

Define

Ψ
(
x
,
y
)

\Psi (x,y)

to be the number of positive integers

n
≤
x

n\le x

such that

n
n

has no prime divisor larger than

y
y

. We present a simple algorithm that approximates

Ψ
(
x
,
y
)

\Psi (x,y)

in

O
(
y
{

log
⁡
log
⁡
x

log
⁡
y

+

1

log
⁡
log
⁡
y

}
)

O(y\{\frac {\log \log x}{\log y} + \frac 1{\log \log y}\})

floating point operations. This algorithm is based directly on a theorem of Hildebrand and Tenenbaum. We also present data which indicate that this algorithm is more accurate in practice than other known approximations, including the well-known approximation

Ψ
(
x
,
y
)
≈
x
ρ
(
log
⁡
x

/

log
⁡
y
)

\Psi (x,y)\approx x\rho (\log x/\log y)

, where

ρ
(
u
)

\rho (u)

is Dickman’s function.
Tables of unit groups and class groups of quintic fields and a regulator bound
Authors: Pohst M. , Wildanger K.
Published: July 2002

Using a new regulator bound we determine unit groups and class groups of the 289040 quintic algebraic number fields with absolute discriminant less than

2
×

10
7

2 \times 10^7

(totally real fields), respectively

5
×

10
6

5 \times 10^6

(other signatures). We list significant data.
Exceptional units in a family of quartic number fields
Authors: Niklasch G. , Smart N.
Published: July 2002

We determine all exceptional units among the elements of certain groups of units in quartic number fields. These groups arise from a one-parameter family of polynomials with two real roots.
Computing 𝜓(𝑥)
Authors: Deléglise Marc , Rivat Joël
Published: July 2002

Let

Λ
\Lambda

denote the Von Mangoldt function and

ψ
(
x
)
=

∑

n
≤
x

Λ
(
n
)

\psi (x)=\sum _{n \leq x} \Lambda (n)

. We describe an elementary method for computing isolated values of

ψ
(
x
)

\psi (x)

. The complexity of the algorithm is

O
(

x

2

/

3

(
log
⁡
log
⁡
x

)

1

/

3

)

O(x^{2/3}(\log \log x)^{1/3})

time and

O
(

x

1

/

3

(
log
⁡
log
⁡
x

)

2

/

3

)

O(x^{1/3}(\log \log x)^{2/3})

space. A table of values of

ψ
(
x
)

\psi (x)

for

x
x

up to

10

15

10^{15}

is included, and some times of computation are given.
New results in equal sums of like powers
Authors: Ekl Randy
Published: July 2002

This paper reports on new results for the equation

∑

i
=
1

m

a

i

k

=

∑

j
=
1

n

b

j

k

,

\begin{equation*}\sum _{i=1}^{m} a_{i}^{k}=\sum _{j=1}^{n} b_{j}^{k},\end{equation*}

i.e., equal sums of like powers. Since the 1967 Lander, Parkin and Selfridge survey paper [A Survey of Equal Sums of Like Powers, Mathematics of Computation 21 (1967), 446–459], few other numeric results have been published (see Elkies [On

A

4

+

B

4

+

C

4

=

D

4

A^{4}+B^{4}+C^{4} = D^{4}

, Mathematics of Computation 51 (1988), 825-835] and Ekl [Equal Sums of Four Seventh Powers, Mathematics of Computation 65 (1996), 1755-1756]). The present paper reports on several new smallest primitive solutions. Further, search limits have been extended in many cases, and tables of solutions are presented. Additionally, new solutions to the same class of problems in distinct integers have been discovered.
Large primes and Fermat factors
Authors: Young Jeff
Published: July 2002

A systematic search for large primes has yielded the largest Fermat factors known.
Computing the rank of elliptic curves over real quadratic number fields of class number 1
Authors: Cremona J. , Serf P.
Published: July 2002

In this paper we describe an algorithm for computing the rank of an elliptic curve defined over a real quadratic field of class number one. This algorithm extends the one originally described by Birch and Swinnerton-Dyer for curves over

Q

\mathbb {Q}

. Several examples are included.
On the Sato-Tate conjecture for QM-curves of genus two
Authors: Hashimoto Ki-ichiro , Tsunogai Hiroshi
Published: July 2002

An abelian surface

A
A

is called a QM-abelian surface if its endomorphism ring includes an order of an indefinite quaternion algebra, and a curve

C
C

of genus two is called a QM-curve if its jacobian variety is a QM-abelian surface. We give a computational result about the distribution of the arguments of the eigenvalues of the Frobenius endomorphisms of QM-abelian surfaces modulo good primes, which supports an analogue of the Sato-Tate Conjecture for such abelian surfaces. We also make some remarks on the field of definition of QM-curves and their endomorphisms.
Optimal convergence for the finite element method in Campanato spaces
Authors: Dolzmann Georg
Published: July 2002

We prove a priori estimates and optimal error estimates for linear finite element approximations of elliptic systems in divergence form with continuous coefficients in Campanato spaces. The proofs rely on discrete analogues of the Campanato inequalities for the solution of the system, which locally measure the decay of the energy. As an application of our results we derive

W

1
,
p

W^{1,p}

–estimates and give a new proof of the well-known

W

1
,
∞

W^{1,\infty }

–results of Rannacher and Scott.
Stably splitting BG
Authors: Benson Dave
Published: July 2002

In the early nineteen eighties, Gunnar Carlsson proved the Segal conjecture on the stable cohomotopy of the classifying space

B
G

BG

of a finite group

G
G

. This led to an algebraic description of the ring of stable self-maps of

B
G

BG

as a suitable completion of the “double Burnside ring”. The problem of understanding the primitive idempotent decompositions of the identity in this ring is equivalent to understanding the stable splittings of

B
G

BG

into indecomposable spectra. This paper is a survey of the developments of the last ten to fifteen years in this subject.
The mathematical enterprises of Robert Thomason
Authors: Weibel Charles
Published: July 2002

During his career, Bob Thomason was involved in an interesting and varied group of mathematical endeavors. This is a retrospective survey of his contributions.
Two geometric character formulas for reductive Lie groups
Authors: Schmid Wilfried , Vilonen Kari
Published: July 2002

In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation

π
\pi

in terms of the same geometric data attached to

π
\pi

. When specialized to the case of a compact Lie group, one of them reduces to Kirillov’s character formula in the compact case, and the other, to an application of the Atiyah-Bott fixed point formula to the Borel-Weil realization of the representation

π
\pi

.
A converse to a theorem of Adamyan, Arov and Krein
Authors: Agler J. , Young N.
Published: July 2002

A well known theorem of Akhiezer, Adamyan, Arov and Krein gives a criterion (in terms of the signature of a certain Hermitian matrix) for interpolation by a meromorphic function in the unit disc with at most

m
m

poles subject to an

L
∞

L^\infty

-norm bound on the unit circle. One can view this theorem as an assertion about the Hardy space

H
2

H^2

of analytic functions on the disc and its reproducing kernel. A similar assertion makes sense (though it is not usually true) for an arbitrary Hilbert space of functions. One can therefore ask for which spaces the assertion is true. We answer this question by showing that it holds precisely for a class of spaces closely related to

H
2

H^2

.
Lower and upper bounds for the splitting of separatrices of the pendulum under a fast quasiperiodic forcing
Authors: Delshams Amadeu , Gelfreich Vassili , Jorba Àngel , Seara Tere
Published: July 2002

Quasiperiodic perturbations with two frequencies

(
1

/

ε
,
γ

/

ε
)

(1/\varepsilon ,\gamma /\varepsilon )

of a pendulum are considered, where

γ
\gamma

is the golden mean number. We study the splitting of the three-dimensional invariant manifolds associated to a two-dimensional invariant torus in a neighbourhood of the saddle point of the pendulum. Provided that some of the Fourier coefficients of the perturbation (the ones associated to Fibonacci numbers) are separated from zero, it is proved that the invariant manifolds split for

ε
\varepsilon

small enough. The value of the splitting, that turns out to be

O

(
exp
⁡

(
−

c
o
n
s
t

/

ε

)

)

\mathrm {O} \left (\exp \left (-\mathrm {const}/\sqrt {\varepsilon }\right )\right )

, is correctly predicted by the Melnikov function.
Nonlinear parabolic problems on manifolds, and a nonexistence result for the noncompact Yamabe problem
Authors: Zhang Qi
Published: July 2002

We study the Cauchy problem for the semilinear parabolic equations

Δ
u
−
R
u
+

u

p

−

u

t

=
0

\Delta u - R u + u^{p} - u_{t} =0

on

M

n

×
(
0
,
∞
)

\mathbf {M}^{n} \times (0, \infty )

with initial value

u

0

≥
0

u_{0} \ge 0

, where

M

n

\mathbf {M}^{n}

is a Riemannian manifold including the ones with nonnegative Ricci curvature. In the Euclidean case and when

R
=
0

R=0

, it is well known that

1
+

2
n

1+ \frac {2}{n}

is the critical exponent, i.e., if

p
>
1
+

2
n

p > 1 + \frac {2}{n}

and

u

0

u_{0}

is smaller than a small Gaussian, then the Cauchy problem has global positive solutions, and if

p
>
1
+

2
n

p>1+\frac {2}{n}

, then all positive solutions blow up in finite time. In this paper, we show that on certain Riemannian manifolds, the above equation with certain conditions on

R
R

also has a critical exponent. More importantly, we reveal an explicit relation between the size of the critical exponent and geometric properties such as the growth rate of geodesic balls. To achieve the results we introduce a new estimate for related heat kernels. As an application, we show that the well-known noncompact Yamabe problem (of prescribing constant positive scalar curvature) on a manifold with nonnegative Ricci curvature cannot be solved if the existing scalar curvature decays “too fast” and the volume of geodesic balls does not increase “fast enough”. We also find some complete manifolds with positive scalar curvature, which are conformal to complete manifolds with positive constant and with zero scalar curvatures. This is a new phenomenon which does not happen in the compact case.
Classification of compact complex homogeneous spaces with invariant volumes
Authors: Guan Daniel
Published: July 2002

In this note we give a classification of compact complex homogeneous spaces with invariant volume.
Wave propagation in a lattice KPP equation in random media
Authors: Lee Tzong-Yow , Torcaso Fred
Published: July 2002

We extend a result of Freidlin and Gartner (1979) for KPP (Kolmogorov-Petrovskii-Piskunov) wave fronts to the case

d
≥
2

d\ge 2

for i.i.d. (independent and identically distributed) random media. We show a wave front propagation speed is attained for the discrete-space (lattice) KPP using a large deviation approach.
Homotopy invariance of relative eta-invariants and 𝐶*-algebra 𝐾-theory
Authors: Keswani Navin
Published: July 2002

We prove a close cousin of a theorem of Weinberger about the homotopy invariance of certain relative eta-invariants by placing the problem in operator

K
K

-theory. The main idea is to use a homotopy equivalence

h
:
M
→

M
′

h:M \to M’

to construct a loop of invertible operators whose “winding number" is related to eta-invariants. The Baum-Connes conjecture and a technique motivated by the Atiyah-Singer index theorem provides us with the invariance of this winding number under twistings by finite-dimensional unitary representations of

π

1

(
M
)

\pi _{1}(M)

.
The special Schubert calculus is real
Authors: Sottile Frank
Published: July 2002

We show that the Schubert calculus of enumerative geometry is real, for special Schubert conditions. That is, for any such enumerative problem, there exist real conditions for which all the a priori complex solutions are real.
Cellular algebras and quasi-hereditary algebras: a comparison
Authors: König Steffen , Xi Changchang
Published: July 2002

Cellular algebras have been defined in a computational way by the existence of a special kind of basis. We compare them with quasi-hereditary algebras, which are known to carry much homological and categorical structure. Among the properties to be discussed here are characterizations of quasi-hereditary algebras inside the class of cellular algebras in terms of vanishing of cohomology and in terms of positivity of the Cartan determinant.
Consistency of the BIC order estimator
Authors: Csiszár Imre , Shields Paul
Published: July 2002

We announce two results on the problem of estimating the order of a Markov chain from observation of a sample path. First is that the Bayesian Information Criterion (BIC) leads to an almost surely consistent estimator. Second is that the Bayesian minimum description length estimator, of which the BIC estimator is an approximation, fails to be consistent for the uniformly distributed i.i.d. process. A key tool is a strong ratio-typicality result for empirical

k
k

-block distributions. Complete proofs are given in the authors’ article to appear in The Annals of Statistics.
Parusinski’s “Key Lemma” via algebraic geometry
Authors: Reichstein Z. , Youssin B.
Published: July 2002

The following “Key Lemma” plays an important role in the work by Parusiński on the existence of Lipschitz stratifications in the class of semianalytic sets: For any positive integer

n
n

, there is a finite set of homogeneous symmetric polynomials

W
1

,
…
,

W
N

W_1, \dots ,W_N

in

Z
[

x
1

,
…
,

x
n

]

Z[x_1,\dots ,x_n]

and a constant

M
>
0

M >0

such that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue d x Subscript i Baseline slash x Subscript i Baseline EndAbsoluteValue less-than-or-equal-to upper M max Underscript j equals 1 comma ellipsis comma upper N Endscripts StartAbsoluteValue d upper W Subscript j Baseline slash upper W Subscript j Baseline EndAbsoluteValue comma">

|

d

x
i

/

x
i

|

≤
M

max

j
=
1
,
…
,
N

|

d

W
j

/

W
j

|

,

|dx_i/x_i| \le M \max _{j = 1, \dots , N} |dW_j/W_j| \; ,

\]
as densely defined functions on the tangent bundle of

C

n

\mathbb {C}^n

. We give a new algebro-geometric proof of this result.
Generic central extensions and projective representations of finite groups
Authors: Quinlan Rachel
Published: July 2002

Any free presentation for the finite group

G
G

determines a central extension

(
R
,
F
)

(R,F)

for

G
G

having the projective lifting property for

G
G

over any field

k
k

. The irreducible representations of

F
F

which arise as lifts of irreducible projective representations of

G
G

are investigated by considering the structure of the group algebra

k
F

kF

, which is greatly influenced by the fact that the set of torsion elements of

F
F

is equal to its commutator subgroup and, in particular, is finite. A correspondence between projective equivalence classes of absolutely irreducible projective representations of

G
G

and

F
F

-orbits of absolutely irreducible characters of

F
′

F’

is established and employed in a discussion of realizability of projective representations over small fields.
Strictly small representations and a reduction theorem for the unitary dual
Authors: Salamanca-Riba Susana , Vogan David
Published: July 2002

To any irreducible unitary representation

X
X

of a real reductive Lie group we associate in a canonical way, a Levi subgroup

G

s
u

G_{su}

and a representation of this subgroup. Assuming a conjecture of the authors on the infinitesimal character of

X
X

, we show that

X
X

is cohomologically induced from a unitary representation of the subgroup

G

s
u

G_{su}

. This subgroup is in some cases smaller than the subgroup

G

u

G_{u}

that the authors attached to

X
X

in earlier work. In those cases this provides a further reduction to the classification problem.
Exceptional Unitary Representations Of Semisimple Lie Groups
Authors: Knapp A.
Published: July 2002

Let

G
G

be a noncompact simple Lie group with finite center, let

K
K

be a maximal compact subgroup, and suppose that

rank 
G
=
rank 
K

\text {rank }G=\text {rank }K

. If

G

/

K

G/K

is not Hermitian symmetric, then a theorem of Borel and de Siebenthal gives the existence of a system of positive roots relative to a compact Cartan subalgebra so that there is just one noncompact simple root and it occurs exactly twice in the largest root. Let

q

=

l

⊕

u

\mathfrak {q}=\mathfrak {l}\oplus \mathfrak {u}

be the

θ
\theta

stable parabolic obtained by building

l

\mathfrak {l}

from the roots generated by the compact simple roots and by building

u

\mathfrak {u}

from the other positive roots, and let

L
⊆
K

L\subseteq K

be the normalizer of

q

\mathfrak {q}

in

G
G

. Cohomological induction of an irreducible representation of

L
L

produces a discrete series representation of

G
G

under a dominance condition. This paper studies the results of this cohomological induction when the dominance condition fails. When the inducing representation is one-dimensional, a great deal is known about when the cohomologically induced representation is infinitesimally unitary. This paper addresses the question of finding Langlands parameters for the natural irreducible constituent of these representations, and also it finds some cases when the inducing representation is higher-dimensional and the cohomologically induced representation is infinitesimally unitary.
Subregular nilpotent representations of Lie algebras in prime characteristic
Authors: Jantzen Jens
Published: July 2002

We look in this paper at representations of Lie algebras of simple reductive groups in prime characteristic. We investigate those modules that have a subregular nilpotent

p
p

–character. In case all roots in the corresponding root system have the same length, we determine all simple modules in generic blocks as well as the Cartan matrices of these blocks. Our results confirm conjectures by Lusztig. We determine in these cases also extension groups between non-isomorphic simple modules. There are similar, somewhat less detailed results on non-generic blocks and the cases with two root lengths.
Differential operators on some nilpotent orbits
Authors: Levasseur T. , Stafford J.
Published: July 2002

In recent work, Astashkevich and Brylinski construct some differential operators of Euler degree

−
1

-1

(thus, they lower the degree of polynomials by one) on the coordinate ring

O

(

O

min

(

g

)
)

\mathcal {O}(\mathbb {O}_{\min }(\mathfrak {g}))

of the minimal nilpotent orbit

O

min

(

g

)

\mathbb O_{\min }(\mathfrak {g})

for any classical, complex simple Lie algebra 

g

\mathfrak {g}

. They term these operators “exotic” since there is “(apparently) no geometric or algebraic theory that explains them”. In this paper, we provide just such an algebraic theory for

s
l

(
n
)

{\mathfrak {sl}}(n)

by giving a complete description of the ring of differential operators on

O

min

(

s
l

(
n
)
)
.

\mathbb O_{\min }({\mathfrak {sl}}(n)).

The method of proof also works for various related varieties, notably for the Lagrangian submanifolds of the minimal orbit of classical Lie algebras for which Kostant and Brylinski have constructed exotic differential operators.
Geometric intersection numbers on a four-punctured sphere
Authors: Chiang Yungyen
Published: July 2002

Let

G

4

\mathcal {G}_{4}

be the space of all simple closed geodesics on the punctured sphere

Σ

4

\Sigma _{4}

. We construct an explicit homeomorphism of the completion of

G

4

\mathcal {G}_{4}

onto a circle by using geometric intersection numbers. Also, we relate these geometric intersection numbers to trace polynomials of transformations corresponding to geodesics in

G

4

\mathcal {G}_{4}

in a representation of

π

1

(

Σ

4

)

\pi _{1}(\Sigma _{4})

into

P
S
L
(
2
,

C

)

PSL(2,\mathbf {C})

.
The shape of the Ford domains for Γ₀(𝑁)
Authors: Lascurain Orive Antonio
Published: July 2002

This is a second paper on the Ford domains for the Hecke congruence subgroups
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Gamma 0 left-parenthesis upper N right-parenthesis equals left-brace Start 2 By 2 Matrix 1st Row 1st Column a 2nd Column a m p semicolon a m p semicolon b 2nd Row 1st Column c 2nd Column a m p semicolon a m p semicolon d EndMatrix element-of normal upper S normal upper L left-parenthesis 2 comma double-struck upper Z right-parenthesis bar c identical-to 0 mod upper N right-brace period">

Γ
0

(
N
)
=

{

(

a

a
m
p
;
a
m
p
;
b

c

a
m
p
;
a
m
p
;
d

)

∈

S
L

(
2
,

Z

)
∣
c
≡
0

mod

N
}

.

\begin{equation*} \Gamma _0(N) = \left \{ \begin {pmatrix} a & b \\ c & d \end{pmatrix} \in \mathrm {SL}(2, \mathbb {Z}) \mid c\equiv 0 \mod N \right \}. \end{equation*}

The author establishes techniques to calculate the number of sides of these domains; in the process the shape of such polygons becomes apparent in many cases. Explicit formulas are given for numbers which have no more than four prime factors. The main result (Theorem 1) exhibits the existence of a universal symmetric polynomial which evaluated at

p
1

,

p
2

,
…
,

p
r

p_1,p_2,\dots ,p_r

yields the number of finite vertices of the Ford polygon for

Γ
0

(
N
)

\Gamma _0(N)

, for all numbers

N
=

p
1

p
2

⋯

p
r

N=p_1\,p_2\dotsb p_r

whose prime factors are larger than a constant which depends only on

r
r

. In all cases the formulas are in terms of symmetric polynomials which generalize the Euler

ϕ
\phi

function. The techniques developed to count the number of visible isometric circles show that the study of these circles might also be a useful tool to simplify or solve problems in number theory.
Examples of uniformly quasiregular mappings
Authors: Peltonen Kirsi
Published: July 2002

In this paper we construct examples of uniformly quasiregular (uqr) mappings. These provide counterexamples for a rigidity conjecture in quasiregular dynamics. It states that a closed manifold of dimension at least three, which admits a branched uqr mapping, is quasiconformally equivalent to an ordinary sphere

S
n

S^n

.
The Small GTPase Rab13 Regulates Assembly of Functional Tight Junctions in Epithelial Cells
Authors: Marzesco Anne-Marie , Dunia Irene , Pandjaitan Rudy , Recouvreur Michel , Dauzonne Daniel , Benedetti Ennio Lucio , Louvard Daniel , Zahraoui Ahmed
Published: July 2002

Junctional complexes such as tight junctions (TJ) and adherens junctions are required for maintaining cell surface asymmetry and polarized transport in epithelial cells. We have shown that Rab13 is recruited to junctional complexes from a cytosolic pool after cell–cell contact formation. In this study, we investigate the role of Rab13 in modulating TJ structure and functions in epithelial MDCK cells. We generate stable MDCK cell lines expressing inactive (T22N mutant) and constitutively active (Q67L mutant) Rab13 as GFP-Rab13 chimeras. Expression of GFP-Rab13Q67L delayed the formation of electrically tight epithelial monolayers as monitored by transepithelial electrical resistance (TER) and induced the leakage of small nonionic tracers from the apical domain. It also disrupted the TJ fence diffusion barrier. Freeze-fracture EM analysis revealed that tight junctional structures did not form a continuous belt but rather a discontinuous series of stranded clusters. Immunofluorescence studies showed that the expression of Rab13Q67L delayed the localization of the TJ transmembrane protein, claudin1, at the cell surface. In contrast, the inactive Rab13T22N mutant did not disrupt TJ functions, TJ strand architecture nor claudin1 localization. Our data revealed that Rab13 plays an important role in regulating both the structure and function of tight junctions.
The platypus is not a rodent: DNA hybridization, amniote phylogeny and the palimpsest theory
Authors: Kirsch John A. W. , Mayer Gregory C.
Published: July 2002

We present DNA–hybridization data on 21 amniotes and two anurans showing that discrimination is obtained among most of these at the class and lower levels. Trees generated from these data largely agree with conventional views, for example in not associating birds and mammals. However, the sister relationships found here of the monotremes to marsupials, and of turtles to the alligator, are surprising results which are nonetheless consistent with the results of some other studies. The Marsupionta hypothesis of Gregory is reviewed, as are opinions about the placement of chelonians. Anatomical and reproductive data considered by Gregory do not unequivocally preclude a marsupial–monotreme special relationship, and there is other recent evidence for placing turtles within the Diapsida. We conclude that the evidential meaning of the molecular data is as shown in the trees, but that the topologies may be influenced by a base–compositional bias producing a seemingly slow evolutionary rate in monotremes, or by algorithmic artefacts (in the case of turtles as well).
CAG repeat instability, cryptic sequence variation and pathogeneticity: evidence from different loci
Authors: Frontali M. , Novelletto A. , Annesi G. , Jodice C.
Published: July 2002

Different aspects of expanded polyglutamine tracts and of their pathogenetic role are taken into consideration here. (i) The (CAG)
n
length of wild-type alleles of the Huntington disease gene was analysed in instability-prone tumour tissue from colon cancer patients to test whether the process leading to the elongation of alleles towards the expansion range involves single-unit stepwise mutations or larger jumps. The analysis showed that length changes of a single unit had a relatively low frequency. (ii) The observation of an expanded spinocerebellar ataxia (SCA)1 allele with an unusual pattern of multiple CAT interruptions showed that cryptic sequence variations are critical not only for sequence length stability but also for the expression of the disease phenotype. (iii) Small expansions of the (CAG)
n
sequence at the
CACNA1A
gene have been reported as causing SCA6. The analysis of families with SCA6 and episodic ataxia type 2 showed that these phenotypes are, in fact, expressions of the same disorder caused either by point mutations or by small (CAG)
n
expansions. A gain of function has been hypothesized for all proteins containing an expanded polyglutamine stretch, including the α
1A
subunit of the voltage-gated calcium channel type P/Q coded by the
CACNA1A
gene. Because point mutations at the same gene with similar phenotypic consequences are highly unlikely to have this effect, an alternative common pathogenetic mechanism for all these mutations, including small expansions, can be hypothesized.
Development and evaluation of a 27 MHz multielectrode current‐source interstitial hyperthermia system
Authors: Kaatee Robert S. J. P.
Published: July 2002

Hyperthermia is a cancer therapy, which is mostly applied in combination with radiotherapy. The aim of hyperthermia is to increase tumor temperatures to 40 °C−45 °C. One of the heating techniques that has been developed to be combined with afterloading interstitial radiotherapy (IRT) is 27 MHz current‐source interstitial hyperthermia (IHT). A four‐channel version of a current‐source IHT system had been developed to study the effectiveness of interstitial hyperthermia in combination with IRT in tumors growing in the flank of a rat. Temperatures up to 46 °C at the edges of various solid tumors with volumes in the range 1500–2000 are easily reached within 4–10 min. Furthermore, in a collaboration between the University Hospital Utrecht and the Daniel den Hoed Cancer Center in Rotterdam, a multielectrode current‐source (MECS) IHT‐system for clinical use has been developed. Basically, this system consists of three units. First, the actual heating system, including a 27 MHz electromagnetic power unit and multielectrode applicators. Second, a 196‐channel thermometry system with manganin–constantan thermcouple thermometers. Third, a computer plus treatment control software that provides the connection between the first two units and the operator. The power unit has 2 groups of 32 channels with opposite phase. The power can be controlled separately for each channel. Temperatures are measured with seven‐point thermocouple probes inside applicators or inside extra nonheating catheters. The performance of the MECS‐IHT system was examined, focusing on the efficiency of the power deposition in tissue, the homogeneity of the temperature distribution, and on thermometry accuracy.
An algorithm for automatic, computed‐tomography‐based source localization after prostate implant
Authors: Li Zuofeng , Nalcacioglu Ismail A. , Ranka Sanjay , Sahni Sartaj K. , Palta Jatinder R. , Tomé Wolfgang , Kim Siyong
Published: July 2002

Permanent implant of the prostate using I‐125 and Pd‐103 seeds is a popular choice of treatment for early‐stage prostate cancer in the United States. Evaluation of the quality of the implant is best based on the calculated dose distribution from postimplant computed tomography (CT) images. This task, however, has been time‐consuming and inaccurate. We have developed an algorithm for automatic source localization from postimplant CT images. The only requirement of this algorithm is knowledge of the number of seeds present in the prostate, thus minimizing the need for human intervention. The algorithm processes volumetric CT data from the patient, and pixels of higher CT numbers are categorized into classes of definite and potential source pixels. A multithresholding technique is used to further determine the number of seeds and their precise locations in the CT volume data. A graphic user interface was developed to facilitate operator review of and intervention in the calculation and the results of the algorithm. This algorithm was tested on two phantoms containing nonradioactive seeds, one with 20 seeds in discrete locations and another with 100 seeds with small distances between seeds. The tests showed that the algorithm was able to identify the seed locations to within 1 mm of their physical locations for discrete seed locations. It was further able to separate seeds at close proximity to each other while maintaining an average seed localization error of less than 2 mm, with no operator intervention required.
Evaluation of protective shielding thickness for diagnostic radiology rooms: Theory and computer simulation
Authors: Costa Paulo R. , Caldas Linda V. E.
Published: July 2002

This work presents the development and evaluation using modern techniques to calculate radiation protection barriers in clinical radiographic facilities. Our methodology uses realistic primary and scattered spectra. The primary spectra were computer simulated using a waveform generalization and a semiempirical model (the Tucker–Barnes–Chakraborty model). The scattered spectra were obtained from published data. An analytical function was used to produce attenuation curves from polycromatic radiation for specified kVp, waveform, and filtration. The results of this analytical function are given in ambient dose equivalent units. The attenuation curves were obtained by application of Archer's model to computer simulation data. The parameters for the best fit to the model using primary and secondary radiation data from different radiographic procedures were determined. They resulted in an optimized model for shielding calculation for any radiographic room. The shielding costs were about 50% lower than those calculated using the traditional method based on Report No. 49 of the National Council on Radiation Protection and Measurements.
Fiducial‐based targeting accuracy for external‐beam radiotherapy
Authors: Murphy Martin J.
Published: July 2002

The accuracy of fiducial‐based alignment of external radiotherapy beams is analyzed. The study considers three basic computational methods to determine the target position—the exact closed‐form solution for three fiducials, the solution via singular value decomposition for four or more fiducials, and the iterative solution for any number of fiducials—and assesses their accuracy, robustness, and efficiency. Particular attention is paid to inaccuracies arising from the variability of fiducial positions in soft tissue. In nearly every test case it is found that all three solution methods, when properly implemented, yield the same result for the target position, but that the method of singular value decomposition must be modified to distinguish rotations from reflections. When an accurate measure of the rotation of the target site is needed, four fiducials give much better results than three, while more than five fiducials gain little further improvement.
Effect of phantom voxelization in CT simulations
Authors: Goertzen Andrew L. , Beekman Freek J. , Cherry Simon R.
Published: July 2002

In computer simulations of x‐ray CT systems one can either use continuous geometrical descriptions for phantoms or a voxelized representation. The voxelized approach allows arbitrary phantoms to be defined without being confined to geometrical shapes. The disadvantage of the voxelized approach is that inherent errors are introduced due to the phantom voxelization. To study effects of phantom discretization, analytical CT simulations were run for a fan‐beam geometry with phantom voxel sizes ranging from 0.0625 to 2 times the reconstructed pixel size and noise levels corresponding to photons per detector pixel prior to attenuation. The number of rays traced per detector element was varied from 1 to 16. Differences in the filtered backprojection images caused by changing the phantom matrix sizes and number of rays traced were assessed by calculating the difference between reconstructions based on the finest matrix and coarser matrix simulations. In noise free simulations, all phantom matrix sizes produced a measurable difference in comparison with the finest phantom matrix used. When even a small amount of noise was added to the projection data, the differences due to the phantom discretization were masked by the noise, and in all cases there was almost no improvement by using a phantom matrix that was more than twice as fine as the reconstruction matrix. No substantial improvement was achieved by tracing more than 4 rays per detector pixel.
Multislice helical computed tomography: Image reconstruction algorithms, implementations, and clinical evaluations
Authors: Taguchi Katsuyuki
Published: July 2002

The development of multislice computed tomography (MSCT), which incorporates a multirow detector, has been desired for higher longitudinal (z) spatial resolution, longer volume coverage, shorter scan time, and other clinical requirements. Therefore, the purpose of this study was to develop one of the key technologies, image reconstruction algorithms, that cover most scanning applications: (1) step‐and‐shoot (nonhelical) scan, (2) standard helical reconstruction, (3) higher temporal resolution and dynamic volumetric (ciné) imaging, and (4) better in‐plane (trans‐axial) spatial resolution. First, applying the fan‐beam reconstruction algorithm was validated for the step‐and‐shoot mode: there is no practical problem in MSCT with narrow cone angle. Second, helical filter interpolation (HFI) with z filtering was proposed for standard helical reconstruction after a unique z‐sampling pattern in multislice helical CT was investigated. HFI can increase the helical pitch three times as fast as the single‐slice CT while keeping the same image quality. Clinical evaluation demonstrated the usefulness of HFI. This method has been implemented on most of the multislice helical CT scanners available worldwide. Third, helical half‐scanning with time‐shift (TS) technique was used to overcome the insufficient in‐plane temporal resolution of HFI. This improved the image quality of cardiac, lung, and vascular imaging substantially. TS not only allows us to take full advantage of the high temporal resolution but also enables ciné imaging even in helical scanning. Last, two algorithms were proposed for improving the in‐plane spatial resolution. They successfully depict fine structures such as the otitis chain in the middle ear.
Experimental determination of the anisotropy function for the Model 200 “light seed” and derivation of the anisotropy constant based upon the linear quadratic model
Authors: Yue Ning , Nath Ravinder
Published: July 2002

Since the publication of the AAPM Task Group 43 report in 1995, Model 200 seed, which has been widely used in prostate seed implants and other brachytherapy procedures, has undergone some changes in its internal geometry resulting from the manufacturer's transition from lower specific activity reactor‐produced (“heavy seeds”) to higher specific activity accelerator‐produced radioactive material (“light seeds”). Based on previously reported theoretical calculations and measurements, the dose rate constants and the radial dose functions of the two types of seeds are nearly the same and have already been reported. In this work, the anisotropy function of the “light seed” was experimentally measured and an averaging method for the determination of the anisotropy constant from distance‐dependent values of anisotropy factors is presented based upon the continuous low dose rate irradiation linear quadratic model for cell killing. The anisotropy function of Model 200 “light seeds” was measured in a Solid Water™ phantom using\s micro LiF TLD chips at radial distances of 1, 2, 3, 4, 5, and 6 cm and at angles from 0 to 90° with respect to the longitudinal axis of the seeds. At a radial distance of 1 cm, the measured anisotropy function of the “light seed” is considerably lower than that of the “heavy seed” reported in the TG 43 report. Our measured values at all radial distances are in excellent agreement with the results of a Monte Carlo simulation reported by Weaver, except for points along and near the seed longitudinal axis. The anisotropy constant of the “light seed” was calculated using the linear quadratic biological model for cell killing in 30 clinical implants. For the model 200 “light seed,” it has a value of 0.865. However, our biological model calculations lead us to conclude that if the anisotropy factors of an interstitial brachytherapy seed vary significantly over radial distances anisotropy constant should not be used as an approximation for anisotropy characteristics of a brachytherapy seed.
Analysis of the temporal response of computed tomography fluoroscopy
Authors: Hsieh Jiang
Published: July 2002

Computed tomography fluoroscopy (CTF) has found many applications in interventional procedures. The advantage of CTF is its ability to remove overlapping structures in the human anatomy and, thereby, provide accurate spatial information. Another advantage is its ability to reconstruct images in a short period of time so that “real‐time” information can be provided. In this paper, we perform theoretical analysis and computer simulations to evaluate the temporal response of the CTF. We investigate the impact of various reconstruction algorithms on CTF and demonstrate the inherent limitations of the CTF in terms of the time lag and delay. The analysis provides a useful guidance to the CTF operators to avoid potential pitfalls.
Real and simulated clustered microcalcifications in digital mammograms. ROC study of observer performance
Authors: Lado María J. , Tahoces Pablo G. , Souto Miguel , Méndez Arturo J. , Vidal Juan J.
Published: July 2002

We have developed a model to simulate clustered microcalcifications on digital mammograms. Wavelet transform techniques were used to detect real clustered microcalcifications. A feature analysis process was applied to automatically extract the features describing the individual simulated microcalcifications and clusters from the values of the real clustered microcalcifications present in the mammogram. Subsequently, a database of simulated and real clustered microcalcifications was created. Clusters of microcalcifications from this database were tested for indistinguishability from real ones. Two radiologists and one physicist were asked to indicate whether the microcalcifications were either real or simulated. The responses of the readers were evaluated with a ROC analysis and the area under the curve was calculated. The average ROC area was 0.54±0.03, indicating there was no statistical difference between real and simulated clustered microcalcifications. The method allows for the creations of simulated clustered microcalcifications that are virtually indistinguishable from real microcalcifications in digital mammograms and could be used to evaluate different image processing techniques.
Writing software for the clinic
Authors: Rosen Isaac I.
Published: July 2002

Medical physicists often write computer programs to support scientific, educational, and clinical endeavors. Errors in scientific and educational software can waste time and effort by producing meaningless results, but errors in clinical software can contribute to patient injuries. Although the ultimate goal of error‐free software is impossible to achieve except in very small programs, there are many good design, implementation, and testing practices that can be used by small development groups to significantly reduce errors, improve quality, and reduce maintenance. The software development process should include four basic steps: specifications, design, implementation, and testing. A specifications document defining what the software is intended to do is valuable for clearly delimiting the scope of the project and providing a benchmark for evaluating the final product. Keep the software design simple and straightforward. Document assumptions, and check them. Emphasize maintainability, portability, and reliability rather than speed. Use layers to isolate the application from hardware and the operating system. Plan for upgrades. Expect the software to be used in unplanned ways. Whenever possible, be generous with RAM and disk storage; hardware is cheaper than development and maintenance. During implementation, use well‐known algorithms whenever possible. Use prototypes to try out ideas. Use generic modules, version numbering, unique file names, defensive programming, and operating system and language/compiler defaults. Avoid binary data files and clever tricks. Remember that real numbers are not exact in a computer. Get it right before making it faster. Document the software extensively. Test continuously during development; the later a problem is found, the more it costs to fix. Use a written procedure to test the final product exactly as a typical user would run it. Allow no changes after clinical release. Expect to spend at least an additional 50% of the initial development effort on testing, fixing errors, and getting the software into routine operation.
Diagnostic imaging of focal calvarial bone lesions. Comparison of statistical and neural network models [in Spanish]
Authors: Arana Estanislao
Published: July 2002

This thesis assesses the accuracy of logistic regression (LR) and artificial neural networks (ANN) in the diagnosis of calvarial lesions using computed tomography (CT). The importance of the different features needed for the diagnosis in both models is also analyzed. The models were developed from CT images of 167 patients (aged 0.5–84 years) with calvarial lesions as their only known disease. All patients were studied with plain films and CT. Other imaging techniques were used when available. The clinical and CT data were used for developing LR and ANN models. Both models were tested with the jacknife (leave‐out‐one) method. The best ANNs were obtained varying iterations and hidden neurons by selecting the one with higher area under the receiver operating characteristic curve (ROC). The final results of each model were compared by means of area under ROC curves. The lesions were 73.1% benign and 26.9% malignant, although there was no statistically significant difference between LR and ANN in differentiating benign and malignant lesions. In characterizing every histologic diagnosis, ANN was statistically superior to LR (<0.001). ANNs were demonstrated to be adequate in diagnosing the most common lesions in the cranial vault and in helping the radiologist with misleading and infrequent appearances. ANN discovered hidden interactions among variables that were missed in the statistical analysis.
Neutron/photon physics investigation of brain tumor treatments with BNCT
Authors: Ye Sung‐Joon
Published: July 2002

In boron neutron capture therapy (BNCT) for brain tumor treatments, a computational method to calculate the tumor cell survival probability versus treatment conditions is developed as a preclinical neutron beam evaluation. A treatment condition is characterized by the spectrum and lateral size of neutron beams, single or bilateral exposure, and the choice of boron carrier drugs (BPA‐F and BSH). The radiation transport from the neutron source to tumors is carried out using Monte Carlo methods: (1) reactor‐based BNCT facility modeling to yield the neutron spectra at an irradiation port; (2) dosimetry to limit the neutron fluence below a tolerance dose (10.5 Gy Eq); (3) calculation of the reaction density in tumors. Finally, from a cell‐killing yield per reaction, the cell survival probability distribution across the tumor is calculated for various treatment conditions. A shallow surface tumor could be effectively treated by single exposure with the volume‐averaged cell survival probability of while a deep tumor will require bilateral exposure to avoid a high cell survival at depth. With pure epithermal beams eliminating low‐ and high‐energy neutrons, the cell survival can be decreased by factors of 2–10, compared to the unmodified neutron spectrum.