bluuebunny/crossref_metadata_2025_split huggingface dataset:
The local Hurwitz constant and Diophantine approximation on Hecke groups
Authors: Lehner J. 
Published: June 2010

Define the Hecke group by
\[

G
q

=

⟨

(

1

a
m
p
;

λ
q

0

a
m
p
;
1

)

,

(

0

a
m
p
;

−
1

1

a
m
p
;
0

)

⟩

,

{G_q} = \left \langle {\left ( {\begin {array}{*{20}{c}} 1 & {{\lambda _q}} \\ 0 & 1 \\ \end {array} } \right ),\left ( {\begin {array}{*{20}{c}} 0 & { - 1} \\ 1 & 0 \\ \end {array} } \right )} \right \rangle ,

\]

λ
q

=
2
cos
⁡
π

/

q

{\lambda _q} = 2\cos \pi /q

,

q
=
3
,
4
,
…

q = 3,4, \ldots

. We call

G
q

(
∞
)

{G_q}(\infty )

the

G
q

{G_q}

-rationals, and

R

−

G
q

(
∞
)

\mathbb {R} - {G_q}(\infty )

the

G
q

{G_q}

-irrationals. The problem we treat here is the approximation of

G
q

{G_q}

-irrationals by

G
q

{G_q}

-rationals. Let

M
(
α
)

M(\alpha )

be the upper bound of numbers c for which

|

α
−
k

/

m

|

>
1

/

c

m
2

|\alpha - k/m| > 1/c{m^2}

for all

G
q

{G_q}

-irrationals and infinitely many

k

/

m
∈

G
q

(
∞
)

k/m \in {G_q}(\infty )

. Set

h
q
′

=

inf
α

M
(
α
)

h_q’= {\inf _\alpha }M(\alpha )

. We call

h
q
′

h_q’

the Hurwitz constant for

G
q

{G_q}

. It is known that

h
q
′

=
2

h_q’= 2

, q even;

h
q
′

=
2

(
1
+

(
1
−

λ
q

/

2

)
2

)

1

/

2

h_q’= 2{(1 + {(1 - {\lambda _q}/2)^2})^{1/2}}

, q odd. In this paper we prove this result by using

λ
q

{\lambda _q}

-continued fractions, as developed previously by D. Rosen. Write
\[

α
−

P

n
−
1

Q

n
−
1

=

(
−
1
)

n
−
1

ε
1

ε
2

⋯

ε
n

m

n
−
1

(
α
)

Q

n
−
1

2

,

\alpha - \frac {{{P_{n - 1}}}}{{{Q_{n - 1}}}} = \frac {{{{( - 1)}^{n - 1}}{\varepsilon _1}{\varepsilon _2} \cdots {\varepsilon _n}}}{{{m_{n - 1}}(\alpha )Q_{n - 1}^2}},

\]
where

ε
i

=
±
1

{\varepsilon _i} = \pm 1

and

P
i

/

Q
i

{P_i}/{Q_i}

are the convergents of the

λ
q

{\lambda _q}

-continued fraction for

α
\alpha

. Then

M
(
α
)
=

lim
¯

n

m
n

(
α
)

M(\alpha ) = {\overline {\lim } _n}{m_n}(\alpha )

. We call

m
n

(
α
)

{m_n}(\alpha )

the local Hurwitz constant. In the final section we prove some results on the local Hurwitz constant. For example (Theorem 4), it is shown that if q is odd and

ε

n
+
1

=

ε

n
+
2

=
+
1

{\varepsilon _{n + 1}} = {\varepsilon _{n + 2}} = + 1

, then

m
i

≥

(

λ
q
2

+
4

)

1

/

2

>

h
q
′

{m_i} \geq {(\lambda _q^2 + 4)^{1/2}} > h_q’

for at least one of

i
=
n
−
1
,
n
,
n
+
1

i = n - 1,n,n + 1

.
The numerical solution of first-kind logarithmic-kernel integral equations on smooth open arcs
Authors: Atkinson Kendall E. , Sloan Ian H. 
Published: June 2010

Consider solving the Dirichlet problem
\[

Δ
u
(
P
)
=
0
,

a
m
p
;

P
∈

R

2

∖
S
,

u
(
P
)
=
h
(
P
)
,

a
m
p
;

P
∈
S
,

sup

|

u
(
P
)

|

>
∞
,

a
m
p
;

P
∈

R

2

a
m
p
;

\begin {array}{*{20}{c}} {\Delta u(P) = 0,} \hfill & {P \in {\mathbb {R}^2}\backslash S,} \hfill \\ {u(P) = h(P),} \hfill & {P \in S,} \hfill \\ {\sup |u(P)| > \infty ,} \hfill & {} \hfill \\ {P \in {\mathbb {R}^2}} \hfill & {} \hfill \\ \end {array}

\]
with S a smooth open curve in the plane. We use single-layer potentials to construct a solution

u
(
P
)

u(P)

. This leads to the solution of equations of the form
\[

∫
S

g
(
Q
)
log
⁡

|

P
−
Q

|

d
S
(
Q
)
=
h
(
P
)
,

P
∈
S
.

\int _S {g(Q)\log |P - Q|dS(Q) = h(P),\quad P \in S.}

\]
This equation is reformulated using a special change of variable, leading to a new first-kind equation with a smooth solution function. This new equation is split into a principal part, which is explicitly invertible, and a compact perturbation. Then a discrete Galerkin method that takes special advantage of the splitting of the integral equation is used to solve the equation numerically. A complete convergence analysis is given; numerical examples conclude the paper.
On a certain (mod 2) identity and a method of proof by expansion
Authors: Blecksmith Richard , Brillhart John , Gerst Irving 
Published: June 2010

We prove the congruence
\[

∏

n
=
1

n

≢

7

(
mod

14
)

∞

(
1
−

x
n

)
≡

∑

−
∞

∞

(

x

n
(
3
n
+
2
)

+

x

7
n
(
3
n
+
2
)
+
2

)

(
mod

2
)

\prod \limits _{\begin {array}{*{20}{c}} {n = 1} \\ {n \nequiv 7\;\pmod {14}} \\ \end {array} }^\infty {(1 - {x^n}) \equiv \sum \limits _{ - \infty }^\infty {({x^{n(3n + 2)}} + {x^{7n(3n + 2) + 2}})\;\pmod 2} }

\]
by first establishing a related equation, which reduces to the congruence modulo 2. The method of proof (called "expanding zero") is based on a formula of the authors for expanding the product of two triple products. A second proof of the result more fully explicates the various aspects of the method. A parity result for an associated partition function is also included.
On the densest lattice packing of centrally symmetric octahedra
Authors: Chaładus Stefan 
Published: June 2010

The main purpose of this paper is the calculation of the critical determinant, and therefore the packing constant, for any centrally symmetric octahedron. The results are obtained partially by a numerical computation that is not rigorous. As an application, we prove that the lattice of integer vectors perpendicular to any integer vector

n

=
[

n
1

,

n
2

,

n
3

,

n
4

]

(
0
≤

n
1

≤

n
2

≤

n
3

≤

n
4

,

n
4

>
0
)

{\mathbf {n}} = [{n_1},{n_2},{n_3},{n_4}]\;(0 \leq {n_1} \leq {n_2} \leq {n_3} \leq {n_4},{n_4} > 0)

contains a nonzero vector

m

∈

Z

4

{\mathbf {m}} \in {{\mathbf {Z}}^4}

, the height

(
h
(

m

)
=
max

|

m
i

|

)

(h({\mathbf {m}}) = \max |{m_i}|)

of which satisfies
\[

(i)

(ii)

(iii)

h
(

m

)
>

(

4
3

h
(

n

)
)

1

/

3

if

n
4

≤
−
2

n
1

+

n
2

+

n
3

,

h
(

m

)
>

(

27

19

h
(

n

)
)

1

/

3

in any case,

h
(

m

)
≤
h

(

n

)

1

/

3

if

n
4

≥

n
1

+

n
2

+

n
3

.

\begin {array}{*{20}{c}} {{\text {(i)}}} \\ {{\text {(ii)}}} \\ {{\text {(iii)}}} \\ \end {array} \quad \begin {array}{*{20}{c}} {h({\mathbf {m}}) > {{(\tfrac {4}{3}h({\mathbf {n}}))}^{1/3}}\quad {\text {if}}\;{n_4} \leq - 2{n_1} + {n_2} + {n_3},} \hfill \\ {h({\mathbf {m}}) > {{(\tfrac {{27}}{{19}}h({\mathbf {n}}))}^{1/3}}\quad {\text {in any case,}}} \hfill \\ {h({\mathbf {m}}) \leq h{{({\mathbf {n}})}^{1/3}}\quad {\text {if}}\;{n_4} \geq {n_1} + {n_2} + {n_3}.} \hfill \\ \end {array}

\]
The closing examples show that the above estimations cannot be improved.
On the distribution of a scaled condition number
Authors: Edelman Alan 
Published: June 2010

In this note, we give the exact distribution of a scaled condition number used by Demmel to model the probability that matrix inversion is difficult. Specifically, consider a random matrix A and the scaled condition number

κ
D

(
A
)
=

‖
A
‖

F

∙

‖

A

−
1

‖

{\kappa _D}(A) = {\left \| A \right \|_F} \bullet \left \| {{A^{ - 1}}} \right \|

. Demmel provided bounds for the condition number distribution when A has real or complex normally distributed elements. Here, we give the exact formula.
On the Diophantine equation 𝑥⁶₁+𝑥⁶₂+𝑥⁶₃=𝑦⁶₁+𝑦⁶₂+𝑦⁶₃
Authors: Delorme Jean-Joël 
Published: June 2010

In this paper, we develop an elementary method for producing parametric solutions of the equation

x
1
6

+

x
2
6

+

x
3
6

=

y
1
6

+

y
2
6

+

y
3
6

x_1^6 + x_2^6 + x_3^6 = y_1^6 + y_2^6 + y_3^6

by reducing the resolution of a system including it to that of the equation
\[

(

s
1
2

+

(

s
1

+

t
1

)

2

)
(

s
2
2

+

(

s
2

+

t
2

)

2

)
(

s
3
2

+

(

s
3

+

t
3

)

2

)

=
(

t
1
2

+

(

s
1

+

t
1

)

2

)
(

t
2
2

+

(

s
2

+

t
2

)

2

)
(

t
3
2

+

(

s
3

+

t
3

)

2

)
.

\begin {array}{*{20}{c}} {(s_1^2 + {{({s_1} + {t_1})}^2})(s_2^2 + {{({s_2} + {t_2})}^2})(s_3^2 + {{({s_3} + {t_3})}^2})} \\ { = (t_1^2 + {{({s_1} + {t_1})}^2})(t_2^2 + {{({s_2} + {t_2})}^2})(t_3^2 + {{({s_3} + {t_3})}^2}).} \\ \end {array}

\]
We give such solutions of degrees 4, 5, 7, 8, 9, and 11.
The Monte Carlo complexity of Fredholm integral equations
Authors: Heinrich Stefan , Mathé Peter 
Published: June 2010

A complexity study of Monte Carlo methods for Fredholm integral equations is carried out. We analyze the problem of computing a functional

μ
(
y
)

\mu (y)

, where y is the solution of a Fredholm integral equation
\[

y
(
s
)
=

∫

I
m

k
(
s
,
t
)
y
(
t
)

d
t
+
f
(
s
)
,

s
∈

I
m

y(s) = \int _{{I^m}} {k(s,t)y(t)\;dt + f(s),\quad s \in {I^m}}

\]
, on the m-dimensional unit cube

I
m

{I^m}

, where the kernel k and right-hand side f are given r times differentiable functions. We permit stochastic numerical methods which can make use of function evaluations of k and f only. All Monte Carlo methods known to the authors for solving the above problem are of the order

n

−
1

/

2

{n^{ - 1/2}}

, while the optimal deterministic methods yield rate

n

−
r

/

(
2
m
)

{n^{ - r/(2m)}}

, thus taking into account the given smoothness of the data. Here, n denotes the (average) number of function evaluations performed. The optimal algorithm we present combines deterministic and stochastic methods in an optimal way. It can be seen that both rates—the standard Monte Carlo rate for general continuous data and the deterministic rate for r-smooth data—multiply. This provides the smallest error that stochastic methods of given computational cost can achieve.
On the minimal elements for the sequence of all powers in the Lemoine-Kátai algorithm
Authors: Pihko Jukka 
Published: June 2010

It is proved, with the help of a computer, that form=20m = 20the firstmminimal elements for the sequence of all powers in an integer-representing algorithm are given byyi=i,i=1,2,3,yi+1=(yi2+6yi+1)/4,i=3,…,m−1{y_i} = i,i = 1,2,3,{y_{i + 1}} = (y_i^2 + 6{y_i} + 1)/4,i = 3, \ldots ,m - 1. This extends an earlier result of the author (form=10m = 10).
Stability of the discretized pantograph differential equation
Authors: Buhmann Martin , Iserles Arieh 
Published: June 2010

In this paper we study discretizations of the general pantograph equation
\[

y
′

(
t
)
=
a
y
(
t
)
+
b
y
(
θ
(
t
)
)
+
c

y
′

(
ϕ
(
t
)
)
,

t
≥
0
,

y
(
0
)
=

y
0

,

y’(t) = ay(t) + by(\theta (t)) + cy’(\phi (t)),\quad t \geq 0,\quad y(0) = {y_0},

\]
, where a, b, c, and

y
0

{y_0}

are complex numbers and where

θ
\theta

and

ϕ
\phi

are strictly increasing functions on the nonnegative reals with

θ
(
0
)
=
ϕ
(
0
)
=
0

\theta (0) = \phi (0) = 0

and

θ
(
t
)
>
t
,
ϕ
(
t
)
>
t

\theta (t) > t, \phi (t) > t

for positive t. Our purpose is an analysis of the stability of the numerical solution with trapezoidal rule discretizations, and we will identify conditions on a, b, c and the stepsize which imply that the solution sequence

{

y
n

}

n
=
0

∞

\{ {y_n}\} _{n=0}^\infty

is bounded or that it tends to zero algebraically, as a negative power of n.
The minimum discriminant of totally real algebraic number fields of degree 9 with cubic subfields
Authors: Fujita Hiroyuki 
Published: June 2010

With the help of the computer language UBASIC86, the minimum discriminant

d
(
K
)

d(K)

of totally real algebraic number fields K of degree 9 with cubic subfields F is determined. It is given by

d
(
K
)
=
16240385609

d(K) = 16240385609

. The defining equation for K is given by

f
(
x
)
=

x
9

−

x
8

−
9

x
7

+
4

x
6

+
26

x
5

−
2

x
4

−
25

x
3

−

x
2

+
7
x
+
1

f(x) = {x^9} - {x^8} - 9{x^7} + 4{x^6} + 26{x^5} - 2{x^4} - 25{x^3} - {x^2} + 7x + 1

, and K is uniquely determined by

d
(
K
)

d(K)

up to Q-isomorphism. The field K has the cubic subfield F with

d
(
F
)
=
49

d(F) = 49

defined by the polynomial

f
(
x
)
=

x
3

+

x
2

−
2
x
−
1

f(x) = {x^3} + {x^2} - 2x - 1

.
On a problem of Erdős concerning primitive sequences
Authors: Zhang Zhen Xiang 
Published: June 2010

A sequence

A
=
{

a
i

}

A = \{ {a_i}\}

of positive integers

a
1

>

a
2

>
⋯

{a_1} > {a_2} > \cdots

is said to be primitive if no term of A divides any other. Let

Ω
(
a
)

\Omega (a)

denote the number of prime factors of a counted with multiplicity. Let

p
(
a
)

p(a)

denote the least prime factor of a and

A
(
p
)

A(p)

denote the set of

a
∈
A

a \in A

with

p
(
a
)
=
p

p(a) = p

. The set

A
(
p
)

A(p)

is called homogeneous if there is some integer

s
p

{s_p}

such that either

A
(
p
)
=
∅

A(p) = \emptyset

or

Ω
(
a
)
=

s
p

\Omega (a) = {s_p}

for all

a
∈
A
(
p
)

a \in A(p)

. Clearly, if

A
(
p
)

A(p)

is homogeneous, then

A
(
p
)

A(p)

is primitive. The main result of this paper is that if A is a positive integer sequence such that

1
∉
A

1 \notin A

and each

A
(
p
)

A(p)

is homogeneous, then
\[

∑

a
≤
n
,
a
∈
A

1

a
log
⁡
a

≤

∑

p
≤
n
,
p

prime

1

p
log
⁡
p

for

n
>
1.

\sum \limits _{a \leq n,a \in A} {\frac {1}{{a\log a}} \leq } \sum \limits _{p \leq n,p\;{\text {prime}}} {\frac {1}{{p\log p}}} \quad {\text {for}}\;n > 1.

\]
This would then partially settle a question of Erdős who asked if this inequality holds for any primitive sequence A.
Finite element approximation of the 𝑝-Laplacian
Authors: Barrett John W. , Liu W. B. 
Published: June 2010

In this paper we consider the continuous piecewise linear finite element approximation of the following problem: Given

p
∈
(
1
,
∞
)

p \in (1,\infty )

, f, and g, find u such that
\[

−
∇
⋅
(

|

∇
u

|

p
−
2

∇
u
)
=
f

in

Ω
⊂

R

2

,

u
=
g

on

∂
Ω
.

- \nabla \cdot (|\nabla u{|^{p - 2}}\nabla u) = f\quad {\text {in}}\;\Omega \subset {\mathbb {R}^2},\quad u = g\quad {\text {on}}\;\partial \Omega .

\]
The finite element approximation is defined over

Ω
h

{\Omega ^h}

, a union of regular triangles, yielding a polygonal approximation to

Ω
\Omega

. For sufficiently regular solutions u, achievable for a subclass of data f, g, and

Ω
\Omega

, we prove optimal error bounds for this approximation in the norm

W

1
,
q

(

Ω
h

)
,
q
=
p

{W^{1,q}}({\Omega ^h}),q = p

for

p
>
2

p > 2

and

q
∈
[
1
,
2
]

q \in [1,2]

for

p
>
2

p > 2

, under the additional assumption that

Ω
h

⊆
Ω

{\Omega ^h} \subseteq \Omega

. Numerical results demonstrating these bounds are also presented.
A fundamental modular identity and some applications
Authors: Blecksmith Richard , Brillhart John , Gerst Irving 
Published: June 2010

We prove a six-parameter identity whose terms have the form

x
α

T
(

k
1

,

l
1

)
T
(

k
2

,

l
2

)

{x^\alpha }T({k_1},{l_1})T({k_2},{l_2})

, where

T
(
k
,
l
)
=

∑

−
∞

∞

x

k

n
2

+
l

n

T(k,l) = \sum \nolimits _{ - \infty }^\infty {{x^{k{n^2} + l\,n}}}

. This identity is then used to give a new proof of the familiar Ramanujan identity

H
(
x
)
G
(

x

11

)
−

x
2

G
(
x
)
H
(

x

11

)
=
1

H(x)G({x^{11}}) - {x^2}G(x)H({x^{11}}) = 1

, where

G
(
x
)
=

∏

n
=
0

∞

[
(
1
−

x

5
n
+
1

)
(
1
−

x

5
n
+
4

)
]

−
1

G(x) = \prod \nolimits _{n = 0}^\infty {{{[(1 - {x^{5n + 1}})(1 - {x^{5n + 4}})]}^{ - 1}}}

and

H
(
x
)
=

∏

n
=
0

∞

[
(
1
−

x

5
n
+
2

)
(
1
−

x

5
n
+
3

)
]

−
1

H(x) = \prod \nolimits _{n = 0}^\infty {{{[(1 - {x^{5n + 2}})(1 - {x^{5n + 3}})]}^{ - 1}}}

. Two other identities, called "balanced

Q
2

{Q^2}

identities", are also established through its use.
Error bounds for Gauss-Kronrod quadrature formulae
Authors: Ehrich Sven 
Published: June 2010

The Gauss-Kronrod quadrature formula

Q

2
n
+
1

G
K

Q_{2n + 1}^{GK}

, is used for a practical estimate of the error

R
n
G

R_n^G

of an approximate integration using the Gaussian quadrature formula

Q
n
G

Q_n^G

. Studying an often-used theoretical quality measure, for

Q

2
n
+
1

G
K

Q_{2n + 1}^{GK}

we prove best presently known bounds for the error constants
\[

c
s

(

R

2
n
+
1

G
K

)
=

sup

‖

f

(
s
)

‖

∞

≤
1

|

R

2
n
+
1

G
K

[
f
]

|

{c_s}(R_{2n + 1}^{GK}) = \sup \limits _{{{\left \| {{f^{(s)}}} \right \|}_\infty } \leq 1} |R_{2n + 1}^{GK}[f]|

\]
in the case

s
=
3
n
+
2
+
κ
,
κ
=

⌊

n
+
1

2

⌋

−

⌊

n
2

⌋

s = 3n + 2 + \kappa ,\kappa = \left \lfloor {\frac {{n + 1}}{2}} \right \rfloor - \left \lfloor {\frac {n}{2}} \right \rfloor

. A comparison with the Gaussian quadrature formula

Q

2
n
+
1

G

Q_{2n + 1}^G

shows that there exist quadrature formulae using the same number of nodes but having considerably better error constants.
A special extension of Wieferich’s criterion
Authors: Cikánek Petr 
Published: June 2010

The following theorem is proved in this paper: "If the first case of Fermat’s Last Theorem does not hold for sufficiently large prime l, then
\[

∑
x

x

l
−
2

[

k
l

N

>
x
>

(
k
+
1
)
l

N

]

≡
0

(
mod

l
)

\sum \limits _x {{x^{l - 2}}} \left [ {\frac {{kl}}{N} > x > \frac {{(k + 1)l}}{N}} \right ] \equiv 0\quad \pmod l

\]
for all pairs of positive integers

N
,
k
,
N
≤
94
,
0
≤
k
≤
N
−
1

N, k,N \leq 94, 0 \leq k \leq N - 1

." The proof of this theorem is based on a recent paper of Skula and uses computer techniques.
Some remarks on the 𝑎𝑏𝑐-conjecture
Authors: Browkin J. , Brzeziński J. 
Published: June 2010

Let

r
(
x
)

r(x)

be the product of all distinct primes dividing a nonzero integer x . The abc-conjecture says that if a, b, c are nonzero relatively prime integers such that

a
+
b
+
c
=
0

a + b + c = 0

, then the biggest limit point of the numbers
\[

log
⁡
max
(

|

a

|

,

|

b

|

,

|

c

|

)

log
⁡
r
(
a
b
c
)

\frac {{\log \max (|a|,|b|,|c|)}}{{\log r(abc)}}

\]
equals 1. We show that in a natural anologue of this conjecture for

n
≥
3

n \geq 3

integers, the largest limit point should be replaced by at least

2
n
−
5

2n - 5

. We present an algorithm leading to numerous examples of triples a, b, c for which the above quotients strongly deviate from the conjectural value 1.
Precise solution of Laplace’s equation
Authors: Shi Zhixin , Hassard Brian 
Published: June 2010

An approximate method is described for solving Laplace’s equation
\[

{

Δ
u
=
0

u

|

∂
Ω

=
g

in

Ω
=
(
0
,
1
)
×
(
0
,
1
)
,

on

∂
Ω

\left \{ {\begin {array}{*{20}{c}} {\Delta u = 0} \\ {u{|_{\partial \Omega }} = g} \\ \end {array} \quad \begin {array}{*{20}{c}} {{\text {in}}\;\Omega = (0,1) \times (0,1),} \hfill \\ {{\text {on}}\;\partial \Omega } \hfill \\ \end {array} } \right .

\]
precisely in the sense of Aberth’s 1988 monograph. The algorithm uses singularity extraction, Fourier series methods, Taylor series methods, and interval analysis to construct an approximation

U
(
x
,
y
)

U(x,y)

to the solution

u
(
x
,
y
)

u(x,y)

at points in the square, and a uniform bound on the error

|

U
(
x
,
y
)
−
u
(
x
,
y
)

|

|U(x,y) - u(x,y)|

. The algorithm applies to problems in which the boundary data g is specified in terms of four elementary functions. The boundary data may be discontinuous at the corners.
A recursive method to calculate the number of solutions of quadratic equations over finite fields
Authors: Iyanaga Kenichi 
Published: June 2010

The number

S
m

(
α
)

{S_m}(\alpha )

of solutions of the quadratic equation
\[

x
1
2

+

x
2
2

+
⋯
+

x
m
2

=
α

(

x
i
2

≠
±

x
j
2

for

i
≠
j
)

x_1^2 + x_2^2 + \cdots + x_m^2 = \alpha \quad (x_i^2 \ne \pm x_j^2\quad {\text {for}}\;i \ne j)

\]
for given m, with

α
\alpha

and

x
i

{x_i}

belonging to a finite field, is studied and a recursive method to compute

S
m

(
α
)

{S_m}(\alpha )

is established.
Deciphering subcellular processes in live imaging datasets via dynamic probabilistic networks
Authors: Letinic Kresimir , Sebastian Rafael , Barthel Andrew , Toomre Derek 
Published: June 2010

AbstractMotivation: Designing mathematical tools that can formally describe the dynamics of complex intracellular processes remains a challenge. Live cell imaging reveals changes in the cellular states, but current simple approaches extract only minimal information of a static snapshot.Results: We implemented a novel approach for analyzing organelle behavior in live cell imaging data based on hidden Markov models (HMMs) and showed that it can determine the number and evolution of distinct cellular states involved in a biological process. We analyzed insulin-mediated exocytosis of single Glut4-vesicles, a process critical for blood glucose homeostasis and impaired in type II diabetes, by using total internal reflection fluorescence microscopy (TIRFM). HMM analyses of movie sequences of living cells reveal that insulin controls spatial and temporal dynamics of exocytosis via the exocyst, a putative tethering protein complex. Our studies have validated the proof-of-principle of HMM for cellular imaging and provided direct evidence for the existence of complex spatial-temporal regulation of exocytosis in non-polarized cells. We independently confirmed insulin-dependent spatial regulation by using static spatial statistics methods.Conclusion: We propose that HMM-based approach can be exploited in a wide avenue of cellular processes, especially those where the changes of cellular states in space and time may be highly complex and non-obvious, such as in cell polarization, signaling and developmental processes.Contact: kresimir.letinic@yale.edu; derek.toomre@yale.eduSupplementary information: Supplementary data are available at Bioinformatics online.
Ekphrasis and the Creative Process in Henri Michaux's
En rêvant à partir de peintures énigmatiques
(1972)
Authors: Keohane Elizabeth Geary 
Published: June 2010

Abstract

Ekphrasis is examined here in terms of the creative process behind Henri Michaux's
En rêvant à partir de peintures énigmatiques
(1972), a collection of prose poems inspired by the paintings of René Magritte. Ekphrasis will be primarily understood as a verbal description of a visual work of art; Michaux's use of this technique will be seen to question its traditional boundaries and limitations. Analysing Michaux's exploration of the processes of literary creation through ekphrasis in this text also highlights Magritte's similarly playful interrogation of representation. A central concern here is the ekphrastic work's constant struggle to
dis
engage from its source of inspiration whilst being in itself a prolonged engagement with this source. Michaux's interpretation and manipulation of images (Magritte's paintings) and the literary form (the prose poem) are also explored in terms of his dual status as artist-writer. Given that grainy photographs are the basis of Michaux's initial encounter with many of the paintings described, what is the status of the painting and its potential to generate ekphrasis in the age of mechanical reproduction? How might the ‘visual poetry’ of Magritte be recreated or interpreted in a poetic work?
Translating Non-Figuration: Heather Dohollau's Poems on ‘Pure Visuality’
Authors: O'Connor Clémence 
Published: June 2010

Abstract

This article explores the dialogue between poems by Heather Dohollau and art forms that seem particularly alien to verbal ordering, namely so-called ‘abstract’ canvases by Joan Mitchell (
No Daisies
) and Geneviève Asse (
Sans titre
, 1988). Dohollau's ekphrastic texts relate to the painting's verbal element — its title — which teases us into identifying objects in the painting even as it forbids us to do so. Representational instability is reflected in the free circulation of metaphors set in motion. Words do not aim to dominate their visual counterpart, thus challenging views of ekphrasis as rivalry that are traced from Lessing to the critical rhetoric of W. J. T. Mitchell and his followers. Rather, I argue that Dohollau's poems seek to translate the painting's very resistance to language through specifically poetic resources. Words also aim to recreate art perception in its sensorial, preverbal fabric by emphasizing the haptic involvement of sight. Thus Dohollau's poems gesture towards a visual–verbal bilingualism, transcending the limits of what a single semiotic system can express. In the process, both the form and the ethos of ekphrasis are reinvented.