bluuebunny/crossref_metadata_2025 huggingface dataset:
Equilibria and quasiequilibria for infinite collections of interacting Fleming-Viot processes
Authors: Dawson Donald A. , Greven Andreas , Vaillancourt Jean
Published: June 2012

In this paper of infinite systems of interacting measure-valued diffusions each with state space

P

(

[
0
,
1
]

)

\mathcal {P}\left ( {[0,1]} \right )

, the set of probability measures on [0, 1], is constructed and analysed (Fleming-Viot systems). These systems arise as diffusion limits of population genetics models with infinitely many possible types of individuals (labelled by [0, 1]), spatially distributed over a countable collection of sites and evolving as follows. Individuals can migrate between sites and after an exponential waiting time a colony replaces its population by a new generation where the types are assigned by resampling from the empirical distribution of types at this site. It is proved that, depending on recurrence versus transience properties of the migration mechanism, the system either clusters as

t
→
∞

t \to \infty

, that is, converges in distribution to a law concentrated on the states in which all components are equal to some

δ
u

,
 
u
∈
[
0
,
1
]

{\delta _u},\ u \in [0,1]

, or the system approaches a nontrivial equilibrium state. The properties of the equilibrium states, respectively the cluster formation, are studied by letting a parameter in the migration mechanism tend to infinity and explicitly identifying the limiting dynamics in a sequence of different space-time scales. These limiting dynamics have stationary states which are quasi-equilibria of the original system, that is, change only in longer time scales. Properties of these quasi-equilibria are derived and related to the global equilibrium process for large

N
N

. Finally we establish that the Fleming-Viot systems are the unique dynamics which remain invariant under the associated space-time renormalization procedure.
Ranges of perturbed maximal monotone and 𝑚-accretive operators in Banach spaces
Authors: Guan Zhengyuan , Kartsatos Athanassios G.
Published: June 2012

A more comprehensive and unified theory is developed for the solvability of the inclusions

S
⊂

R
(
A
+
B
)

¯

S \subset \overline {R(A + B)}

, int

S
⊂
R
(
A
+
B
)

S \subset R(A + B)

, where

A
:
X
⊃
D
(
A
)
→

2
Y

A:X \supset D(A) \to {2^Y}

,

B
:
X
⊃
D
(
B
)
→
Y

B:X \supset D(B) \to Y

and

S
⊂
X

S \subset X

. Here,

X
X

is a real Banach space and

Y
=
X

Y = X

or

Y
=

X
∗

Y = {X^*}

. Mainly,

A
A

is either maximal monotone or maccretive, and

B
B

is either pseudo-monotone or compact. Cases are also considered where

A
A

has compact resolvents and

B
B

is continuous and bounded. These results are then used to obtain more concrete sets in the ranges of sums of such operators

A
A

and

B
B

. Various results of Browder, Calvert and Gupta, Gupta, Gupta and Hess, and Kartsatos are improved and/or extended. The methods involve the application of a basic result of Browder, concerning pseudo-monotone perturbation of maximal monotone operators, and the Leray-Schauder degree theory.
On the ideal class groups of imaginary abelian fields with small conductor
Authors: Horie Kuniaki , Ogura Hiroko
Published: June 2012

Let

k
k

be any imaginary abelian field with conductor not exceeding 100, where an abelian field means a finite abelian extension over the rational field

Q

{\mathbf {Q}}

contained in the complex field. Let

C
(
k
)

C(k)

denote the ideal class group of

k
k

,

C
−

(
k
)

{C^ - }(k)

the kernel of the norm map from

C
(
k
)

C(k)

to the ideal class group of the maximal real subfield of

k
k

, and

f
(
k
)

f(k)

the conductor of

k
;
f
(
k
)
⩽
100

k;f(k) \leqslant 100

. Proving a preliminary result on

2
2

-ranks of ideal class groups of certain imaginary abelian fields, this paper determines the structure of the abelian group

C
−

(
k
)

{C^ - }(k)

and, under the condition that either

[
k
:

Q

]
⩽
23

[k:{\mathbf {Q}}] \leqslant 23

or

f
(
k
)

f(k)

is not a prime

⩾
71

\geqslant 71

, determines the structure of

C
(
k
)

C(k)

.
The derivatives of homotopy theory
Authors: Johnson Brenda
Published: June 2012

We construct a functor of spaces,

M
n

{M_n}

, and show that its multilinearization is equivalent to the

n
n

th layer of the Taylor tower of the identity functor of spaces. This allows us to identify the derivatives of the identity functor and determine their homotopy type.
On the period-two-property of the majority operator in infinite graphs
Authors: Moran Gadi
Published: June 2012

A self-mapping

M
:
X
→
X

M:X \to X

of a nonempty set

X
X

has the Period-Two-Property (p2p) if

M
2

x
=
x

{M^2}x = x

holds for every

M
M

-periodic point

x
∈
X

x \in X

. Let

X
X

be the set of all

{
0
,
1
}

\{ 0,1\}

-labelings

x
:
V
→
{
0
,
1
}

x:V \to \{ 0,1\}

of the set of vertices

V
V

of a locally finite connected graph

G
G

. For

x
∈
X

x \in X

let

M
x
∈
X

Mx \in X

label

v
∈
V

v \in V

by the majority bit that

x
x

applies to its neighbors, retaining

υ
\upsilon

’s

x
x

-label in case of a tie. We show that

M
M

has the p2p if there is a finite bound on the degrees in

G
G

and

1
n

log
⁡

b
n

→
0

\frac {1} {n}\log {b_n} \to 0

, where

b
n

{b_n}

is the number of

υ
∈
V

\upsilon \in V

at a distance at most

n
n

from a fixed vertex

υ
0

∈
V

{\upsilon _0} \in V

.
Radially symmetric internal layers in a semilinear elliptic system
Authors: del Pino Manuel A.
Published: June 2012

Let

B
B

denote the unit ball in

R
N

,

N
⩾
1

{R^N},\quad N \geqslant 1

. We consider the problem of finding nonconstant solutions to a class of elliptic systems including the Gierer and Meinhardt model of biological pattern formation,
\[

(
1.1
)

ε
2

Δ
u
−
u
+

u
2

1
+
k

u
2

+
p
=
0

in

B
,

(1.1)\qquad {\varepsilon ^2}\Delta u - u + \frac {{{u^2}}} {{1 + k{u^2}}} + p = 0\quad {\text {in}}B,

\]

\[

(
1.2
)

D
Δ
v
−
v
+

u
2

=
0

in

B
,

(1.2)\quad D\Delta v - v + {u^2} = 0\quad {\text {in}}B,

\]

\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis 1.3 right-parenthesis StartFraction partial-differential u Over partial-differential n EndFraction equals 0 equals StartFraction partial-differential v Over partial-differential n EndFraction on partial-differential upper B comma">

(
1.3
)

∂
u

∂
n

=
0
=

∂
v

∂
n

on

∂
B
,

(1.3)\quad \frac {{\partial u}} {{\partial n}} = 0 = \frac {{\partial v}} {{\partial n}}\quad {\text {on}}\partial B,

\]
where

ε
\varepsilon

,

D
D

,

k
k

and

ρ
\rho

denote positive constants and

n
n

the unit outer normal to

∂
B

\partial B

. Assuming that the parameters

ρ
\rho

,

k
k

are small and

D
D

large, we construct a family of radially symmetric solutions to (1.1)-(1.3) indexed by the parameter

ε
\varepsilon

, which exhibits an internal layer in

B
B

, as

ε
→
0

\varepsilon \to 0

.
A categorical approach to matrix Toda brackets
Authors: Hardie K. A. , Kamps K. H. , Marcum H. J.
Published: June 2012

In this paper we give a categorical treatment of matrix Toda brackets, both in the pre- and post-compositional versions. Explicitly the setting in which we work is, à la Gabriel-Zisman, a

2
2

-category with zeros. The development parallels that in the topological setting but with homotopy groups replaced by nullity groups of invertible

2
2

-morphisms. A central notion is that of conjugation of

2
2

-morphisms. Our treatment of matrix Toda brackets is carried forward to the point of establishing appropriate indeterminacies.
Finite generalized triangle groups
Authors: Howie J. , Metaftsis V. , Thomas R. M.
Published: June 2012

We give an almost complete classification of those generalized triangle groups that are finite, building on previous results of Baumslag, Morgan and Shalen [1], Conder [4], Rosenberger [12] and Levin and Rosenberger [11]. There are precisely two groups for which we cannot decide whether or not they are finite.
The approximation theorem and the 𝐾-theory of generalized free products
Authors: Schwänzl Roland , Staffeldt Ross E.
Published: June 2012

We use methods of abstract algebraic

K
K

-theory as developed by Friedhelm Waldhausen to give a new derivation of the decomposition theorem for the algebraic

K
K

-theory of a generalized free product ring. The result takes the form of a fibration sequence which relates the algebraic

K
K

-theory of such a ring with the algebraic

K
K

-theory of its factors, plus a Nil-term.
The index of determinacy for measures and the 𝑙²-norm of orthonormal polynomials
Authors: Berg Christian , Duran Antonio J.
Published: June 2012

For determinate measures

μ
\mu

having moments of every order we define and study an index of determinacy which checks the stability of determinacy under multiplication by even powers of

|

t
−
z

|

|t - z|

for

z
z

a complex number. Using this index of determinacy, we solve the problem of determining for which

z
∈

C

z \in \mathbb {C}

the sequence

(

p
n

(
m
)

(
z
)

)
n

(
m
∈

N

)

{(p_n^{(m)}(z))_n}(m \in \mathbb {N})

belongs to

ℓ
2

{\ell ^2}

, where

(

p
n

)
n

{({p_n})_n}

is the sequence of orthonormal polynomials associated with the measure

μ
\mu

.
The order bidual of almost 𝑓-algebras and 𝑑-algebras
Authors: Bernau S. J. , Huijsmans C. B.
Published: June 2012

It is shown in this paper that the second order dual

A
A

of an Archimedean (almost)

f
f

-algebra

A
A

, equipped with the Arens multiplication, is again an (almost)

f
f

-algebra. Also, the order continuous bidual

(

A
′

)
n
′

(A’)_n’

of an Archimedean

d
d

-algebra

A
A

is a

d
d

-algebra. Moreover, if the

d
d

-algebra

A
A

is commutative or has positive squares, then

A
A

is again a

d
d

-algebra.
Geometry of strictly convex domains and an application to the uniform estimate of the \overline∂-problem
Authors: Chen Ten Ging
Published: June 2012

In this paper, we construct a nice defining function

ρ
\rho

for a bounded smooth strictly convex domain

Ω
\Omega

in

R
n

{R^n}

with explicit gradient and Hessian estimates near the boundary

∂
Ω

\partial \Omega

of

Ω
\Omega

. From the approach, we deduce that any two normals through

∂
Ω

\partial \Omega

do not intersect in any tubular neighborhood of

∂
Ω

\partial \Omega

with radius which is less than

1
K

\frac {1} {K}

, where

K
K

is the maximum principal curvature of

∂
Ω

\partial \Omega

. Finally, we apply such

ρ
\rho

to obtain an explicit upper bound of the constant

C
Ω

{C_\Omega }

in the Henkin’s estimate
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper H Subscript normal upper Omega Baseline f double-vertical-bar Subscript upper L Sub Superscript normal infinity Subscript left-parenthesis normal upper Omega right-parenthesis Baseline less-than-or-slanted-equals upper C Subscript normal upper Omega Baseline double-vertical-bar f double-vertical-bar Subscript upper L Sub Superscript normal infinity Subscript left-parenthesis normal upper Omega right-parenthesis">

‖

H
Ω

f

‖

L
∞

(
Ω
)

⩽

C
Ω

‖
f
‖

L
∞

(
Ω
)

{\left \| {{H_\Omega }f} \right \|_{{L^\infty }(\Omega )}} \leqslant {C_\Omega }{\left \| f \right \|_{{L^\infty }(\Omega )}}

of the

∂
\partial

-problem on strictly convex domains

Ω
\Omega

in

C

n

{{\mathbf {C}}^n}

.
On Lamé operators which are pull-backs of hypergeometric ones
Authors: Chiarellotto Bruno
Published: June 2012

We give a method that would allow one to calculate the number of Lamé operators,

L

n

{\mathcal {L}_n}

,

n
∈

N

n \in {\mathbf {N}}

, with prescribed finite monodromy and do the calculation for the case

n
=
1

n = 1

. We find a bound for the degree over

Q

{\mathbf {Q}}

of the field of definition of the coefficients of a Lamé operator with prescribed finite monodromy and give examples of Lamé operators with finite monodromy. Finally we study Lamé operators with infinite monodromy and generic second order differential operators which are pull-backs of hypergeometric ones under algebraic maps.
Circle bundles and the Kreck-Stolz invariant
Authors: Dai Xianzhe , Zhang Wei Ping
Published: June 2012

We present a direct analytic calculation of the

s
s

-invariant of Kreck-Stolz for circle bundles, by evaluating the adiabatic limits of

η
\eta

invariants. We believe that this method should have wider applications.
Sur les structures de contact régulières en dimension trois
Authors: Hadjar Amine
Published: June 2012

Let

M

\mathcal {M}

be a compact and oriented

3
3

-manifold with boundary, endowed with a free

S

1

{\mathbb {S}^1}

action. We give a characterization of germs of invariant contact structures along

∂

M

\partial \mathcal {M}

which are extendable to

M

\mathcal {M}

as regular contact structures.
Integrally closed modules over two-dimensional regular local rings
Authors: Kodiyalam Vijay
Published: June 2012

This paper is based on work of Rees on integral closures of modules and initiates the study of integrally closed modules over two-dimensional regular local rings in analogy with the classical theory of complete ideals of Zariski. The main results can be regarded as generalizations of Zariski’s product theorem. They assert that the tensor product mod torsion of integrally closed modules is integrally closed, that the symmetric algebra mod torsion of an integrally closed module is a normal domain and that the first Fitting ideal of an integrally closed module is an integrally closed ideal. A construction of indecomposable integrally closed modules is also given. The primary technical tool is a study of the Buchsbaum-Rim multiplicity.
Harmonic diffeomorphisms between Hadamard manifolds
Authors: Li Peter , Tam Luen-Fai , Wang Jiaping
Published: June 2012

In this paper, we study the Dirichlet problem at infinity for harmonic maps between complete hyperbolic Hadamard surfaces. We will address the existence and uniqueness questions relating to the problem. In particular, we generalize results in the work of Li-Tam and Wan.
Orbits of rank one and parallel mean curvature
Authors: Olmos Carlos
Published: June 2012

Let

M
n

(
n
⩾
2
)

{M^n}(n \geqslant 2)

be a (extrinsic) homogeneous irreducible full submanifold of Euclidean space with

r
a
n
k
(
M
)
=
k
⩾
1

rank(M) = k \geqslant 1

(i.e., it admits

k
⩾
1

k \geqslant 1

locally defined, linearly independent parallel normal vector fields). We prove that

M
M

must be contained in a sphere. This result toghether with previous work of the author about homogeneous submanifolds of higher rank imply, in particular, the following theorem: A homogeneous irreducible submanifold of Euclidean space with parallel mean curvature vector is either minimal, or minimal in a sphere, or an orbit of the isotropy representation of a simple symmetric space.
The complex zeros of random polynomials
Authors: Shepp Larry A. , Vanderbei Robert J.
Published: June 2012

Mark Kac gave an explicit formula for the expectation of the number,

ν
n

(
Ω
)

{\nu _n}(\Omega )

, of zeros of a random polynomial,
\[

P
n

(
z
)
=

∑

j
=
0

n
−
1

η
j

z
j

,

{P_n}(z) = \sum \limits _{j = 0}^{n - 1} {{\eta _j}{z^j}} ,

\]
in any measurable subset

Ω
\Omega

of the reals. Here,

η
0

,
…
,

η

n
−
1

{\eta _0}, \ldots ,{\eta _{n - 1}}

are independent standard normal random variables. In fact, for each

n
>
1

n > 1

, he obtained an explicit intensity function

g
n

{g_n}

for which
\[

E

ν
n

(
Ω
)
=

∫
Ω

g
n

(
x
)

d
x
.

{\mathbf {E}}{\nu _n}(\Omega ) = \int _\Omega {{g_n}(x)\,dx.}

\]
Here, we extend this formula to obtain an explicit formula for the expected number of zeros in any measurable subset

Ω
\Omega

of the complex plane

C

\mathbb {C}

. Namely, we show that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="bold upper E nu Subscript n Baseline left-parenthesis normal upper Omega right-parenthesis equals integral Underscript normal upper Omega Endscripts h Subscript n Baseline left-parenthesis x comma y right-parenthesis d x d y plus integral Underscript normal upper Omega intersection double-struck upper R Endscripts g Subscript n Baseline left-parenthesis x right-parenthesis d x comma">

E

ν
n

(
Ω
)
=

∫
Ω

h
n

(
x
,
y
)

d
x
d
y
+

∫

Ω
∩

R

g
n

(
x
)

d
x
,

{\mathbf {E}}{\nu _n}(\Omega ) = \int _\Omega {{h_n}(x,y)\,dxdy + \int _{\Omega \cap \mathbb {R}} {{g_n}(x)\,dx,} }

\]
where

h
n

{h_n}

is an explicit intensity function. We also study the asymptotics of

h
n

{h_n}

showing that for large

n
n

its mass lies close to, and is uniformly distributed around, the unit circle.
Discontinuous robust mappings are approximatable
Authors: Shi Shu Zhong , Zheng Quan , Zhuang Deming
Published: June 2012

The concepts of robustness of sets and and functions were introduced to form the foundation of the theory of integral global optimization. A set

A
A

of a topological space

X
X

is said to be robust iff

cl

A
=

cl

{\text {cl}}A = {\text {cl}}

int

A
A

. A mapping

f
:
X
→
Y

f:X \to Y

is said to be robust iff for each open set

U
Y

{U_Y}

of

Y
Y

,

f

−
1

(

U
Y

)

{f^{ - 1}}({U_Y})

is robust. We prove that if

X
X

is a Baire space and

Y
Y

satisfies the second axiom of countability, then a mapping

f
:
X
→
Y

f:X \to Y

is robust iff it is approximatable in the sense that the set of points of continuity of

f
f

is dense in

X
X

and that for any other point

x
∈
X

x \in X

,

(
x
,
f
(
x
)
)

(x,f(x))

is the limit of

{
(

x
α

,
f
(

x
α

)
)
}

\{ ({x_\alpha },f({x_\alpha }))\}

, where for all

α
\alpha

,

x
α

{x_\alpha }

is a continuous point of

f
f

. This result justifies the notion of robustness.
On the 𝐾-theory of crystallographic groups
Authors: Tsapogas Georgios
Published: June 2012

For any crystallographic groupΓ\Gammawe show that the groupsKi(Γ){K_i}(\Gamma )are isomorphic, via the forget control map, to the controlledKK-groupsKi(Γ)c{K_i}{(\Gamma )_c}, for alli⩽1i \leqslant 1and for an appropriate choice of the control map. By using this result and under a mild hypothesis on the crystallographic groupΓ\Gamma, it is proved thatKi(Γ)=0{K_i}(\Gamma ) = 0for alli⩽−2i \leqslant - 2andNjKi(Γ)=0{N^j}{K_i}(\Gamma ) = 0for alli⩽−1i \leqslant - 1andj>0j > 0.
On Euler characteristics associated to exceptional divisors
Authors: Veys Willem
Published: June 2012

Let

k
k

be an algebraically closed field and

f
∈
k
[

x
1

,
…
,

x

n
+
1

]

f \in k[{x_1}, \ldots ,{x_{n + 1}}]

. Fix an embedded resolution

h
:
X
→

A

n
+
1

of

f

−
1

{
0
}

h:X \to {\mathbb {A}^{n + 1}}\quad {\text {of}}\quad {f^{ - 1}}\{ 0\}

and denote by

E
i

{E_i}

,

i
∈
S

i \in S

, the irreducible components of

h

−
1

(

f

−
1

{
0
}
)

{h^{ - 1}}({f^{ - 1}}\{ 0\} )

with multiplicity

N
i

{N_i}

in the divisor of

f

o

h

f{\text {o}}h

. Put also

E
˚

i

≔

E
i

∖

∪

j
≠
i

E
j

\mathring {E}_i \coloneq {E_i}\backslash { \cup _{j \ne i}}{E_j}

, and denote by

χ
(

E
i

)

\chi ({E_i})

its Euler characteristic. Several conjectures concerning Igusa’s local zeta function and the topological zeta function of

f
f

motivate the study of Euler characteristics associated to subsets

∪

i
∈
T

E
i

{ \cup _{i \in T}}{E_i}

of

∪

i
∈
S

E
i

{ \cup _{i \in S}}{E_i}

, which are maximal connected with respect to the property that

d

|

N
i

d|{N_i}

for all

i
∈
T

i \in T

. Here

d
∈

N

,
d
>
1

d \in \mathbb {N},d > 1

. We prove that if

h
h

maps

∪

i
∈
T

E
i

{ \cup _{i \in T}}{E_i}

to a point, then
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis negative 1 right-parenthesis Superscript n Baseline sigma-summation Underscript i element-of upper T Endscripts chi left-parenthesis ModifyingAbove upper E With ring-above Subscript i Baseline right-parenthesis greater-than-or-slanted-equals 0">

(
−
1

)
n

∑

i
∈
T

χ
(

E
˚

i

)
⩾
0

(-1)^n \sum _{i \in T} \chi (\mathring {E}_i) \geqslant 0

\]
This generalizes a well-known result for curves. We also prove some vanishing results concerning the

χ
(

E
˚

i

)

\chi (\mathring {E}_i)

for such a maximal connected subset

∪

i
∈
T

E
i

{ \cup _{i \in T}}{E_i}

and give an application on the above-mentioned zeta functions, yielding some confirmation of the holomorphy conjecture for those zeta functions.
A geometric approach to regular perturbation theory with an application to hydrodynamics
Authors: Chicone Carmen
Published: June 2012

The Lyapunov-Schmidt reduction technique is used to prove a persistence theorem for fixed points of a parameterized family of maps. This theorem is specialized to give a method for detecting the existence of persistent periodic solutions of perturbed systems of differential equations. In turn, this specialization is applied to prove the existence of many hyperbolic periodic solutions of a steady state solution of Euler’s hydrodynamic partial differential equations. Incidentally, using recent results of S. Friedlander and M. M. Vishik, the existence of hyperbolic periodic orbits implies the steady state solutions of the Eulerian partial differential equation are hydrodynamically unstable. In addition, a class of the steady state solutions of Euler’s equations are shown to exhibit chaos.
Elliptic equations of order 2𝑚 in annular domains
Authors: Dalmasso Robert
Published: June 2012

In this paper we study the existence of positive radial solutions for some semilinear elliptic problems of order

2
m

2m

in an annulus with Dirichlet boundary conditions. We consider a nonlinearity which is either sublinear or the sum of a sublinear and a superlinear term.
Lévy type characterization of stable laws for free random variables
Authors: Pata Vittorino
Published: June 2012

We give a description of stable probability measures relative to free additive convolution. The definition of domain of attraction is given, and a proof is provided of the noncommutative analogue of Lévy Theorem.
Test ideals in local rings
Authors: Smith Karen E.
Published: June 2012

It is shown that certain aspects of the theory of tight closure are well behaved under localization. Let

J
J

be the parameter test ideal for

R
R

, a complete local Cohen-Macaulay ring of positive prime characteristic. For any multiplicative system

U
⊂
R

U \subset R

, it is shown that

J

U

−
1

R

J{U^{ - 1}}R

is the parameter test ideal for

U

−
1

R

{U^{ - 1}}R

. This is proved by proving more general localization results for the here-introduced classes of "

F

{\text {F}}

-ideals" of

R
R

and "

F

{\text {F}}

-submodules of the canonical module" of

R
R

, which are annihilators of

R
R

modules with an action of Frobenius. It also follows that the parameter test ideal cannot be contained in any parameter ideal of

R
R

.
Continuous functions on extremally disconnected spaces
Authors: Vermeer J.
Published: June 2012

Using results and techniques due to Abramovich, Arenson and Kitover it is shown that each fixed-point set of a selfmap of a compact extremally disconnected space is a retract of that space, and that the retraction can be constructed from the particular selfmap itself. Also, the closure of the set of periodic points turns out to be a retract of the space. Several decomposition theorems for arbitrary selfmaps on extremally disconnected spaces are obtained similar to the theorem of Frolík on embeddings. Conditions are obtained under which the set of fixed points is clopen.
Sharp inequalities, the functional determinant, and the complementary series
Authors: Branson Thomas P.
Published: June 2012

Results in the spectral theory of differential operators, and recent results on conformally covariant differential operators and on sharp inequalities, are combined in a study of functional determinants of natural differential operators. The setting is that of compact Riemannian manifolds. We concentrate especially on the conformally flat case, and obtain formulas in dimensions

2
2

,

4
4

, and

6
6

for the functional determinants of operators which are well behaved under conformal change of metric. The two-dimensional formulas are due to Polyakov, and the four-dimensional formulas to Branson and Ørsted; the method is sufficiently streamlined here that we are able to present the sixdimensional case for the first time. In particular, we solve the extremal problems for the functional determinants of the conformal Laplacian and of the square of the Dirac operator on

S
2

{S^2}

, and in the standard conformal classes on

S
4

{S^4}

and

S
6

{S^6}

. The

S
2

{S^2}

results are due to Onofri, and the

S
4

{S^4}

results to Branson, Chang, and Yang; the

S
6

{S^6}

results are presented for the first time here. Recent results of Graham, Jenne, Mason, and Sparling on conformally covariant differential operators, and of Beckner on sharp Sobolev and Moser-Trudinger type inequalities, are used in an essential way, as are a computation of the spectra of intertwining operators for the complementary series of

S

O

0

(
m
+
1
,
1
)

{\text {S}}{{\text {O}}_0}(m + 1,1)

, and the precise dependence of all computations on the dimension. In the process of solving the extremal problem on

S
6

{S^6}

, we are forced to derive a new and delicate conformally covariant sharp inequality, essentially a covariant form of the Sobolev embedding

L
1
2

(

S
6

)
↪

L
3

(

S
6

)

L_1^2({S^6})\hookrightarrow {L^3}({S^6})

for section spaces of trace free symmetric two-tensors.
On invariants for 𝜔₁-separable groups
Authors: Eklof Paul C. , Foreman Matthew , Shelah Saharon
Published: June 2012

We study the classification of

ω
1

{\omega _1}

-separable groups by using Ehrenfeucht-Fraïssé games and prove a strong classification result assuming PFA, and a strong non-structure theorem assuming

♢
\diamondsuit

.
Periodic orbits of 𝑛-body type problems: the fixed period case
Authors: Riahi Hasna
Published: June 2012

This paper gives a proof of the existence and multiplicity of periodic solutions to Hamiltonian systems of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper A right-parenthesis StartLayout Enlarged left-brace 1st Row m Subscript i Baseline ModifyingAbove q With two-dots Subscript i Baseline plus StartFraction partial-differential upper V Over partial-differential q Subscript i Baseline EndFraction left-parenthesis t comma q right-parenthesis equals 0 2nd Row q left-parenthesis t plus upper T right-parenthesis equals q left-parenthesis t right-parenthesis comma for-all t element-of normal fraktur upper R period EndLayout">

(

A

)

 

{

m
i

q
¨

i

+

∂
V

∂

q
i

(
t
,
q
)
=
0

q
(
t
+
T
)
=
q
(
t
)
,

∀
t
∈
ℜ
.

({\text {A}})\quad {\text { }}\left \{ {\begin {array}{*{20}{c}} {{m_i}{{\ddot q}_i} + \frac {{\partial V}} {{\partial {q_i}}}(t,q) = 0} \\ {q(t + T) = q(t),\quad \forall t \in \Re .} \\ \end {array} } \right .

\]
where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q Subscript i Baseline element-of normal fraktur upper R Superscript script l Baseline comma script l greater-than-or-slanted-equals 3 comma 1 less-than-or-slanted-equals i less-than-or-slanted-equals n comma q equals left-parenthesis q 1 comma ellipsis comma q Subscript n Baseline right-parenthesis">

q
i

∈

ℜ
ℓ

,
ℓ
⩾
3
,
1
⩽
i
⩽
n
,
q
=
(

q
1

,
…
,

q
n

)

{q_i} \in {\Re ^\ell },\ell \geqslant 3,1 \leqslant i \leqslant n,q = ({q_1}, \ldots ,{q_n})

and with

V

i
j

(
t
,
ξ
)

{V_{ij}}(t,\xi )

T
T

-periodic in

t
t

and singular in

ξ
\xi

at

ξ
=
0

\xi = 0

Under additional hypotheses on

V
V

, when (A) is posed as a variational problem, the corresponding functional,

I
I

, is shown to have an unbounded sequence of critical values if the singularity of

V
V

at

0
0

is strong enough. The critical points of

I
I

are classical

T
T

-periodic solutions of (A). Then, assuming that

I
I

has only non-degenerate critical points, up to translations, Morse type inequalities are proved and used to show that the number of critical points with a fixed Morse index

k
k

grows exponentially with

k
k

, at least when

k
≡
0
,
1
(

mod

ℓ
−
2
)

k \equiv 0,1( \mod \ell - 2)

. The proof is based on the study of the critical points at infinity done by the author in a previous paper and generalizes the topological arguments used by A. Bahri and P. Rabinowitz in their study of the

3
3

-body problem. It uses a recent result of E. Fadell and S. Husseini on the homology of free loop spaces on configuration spaces. The detailed proof is given for the

4
4

-body problem then generalized to the

n
n

-body problem.
Test problems for operator algebras
Authors: Azoff Edward A.
Published: June 2012

Kaplansky’s test problems, originally formulated for abelian groups, concern the relationship between isomorphism and direct sums. They provide a "reality check" for purported structure theories. The present paper answers Kaplansky’s problems in operator algebraic contexts including unitary equivalence of von Neumann algebras and equivalence of representations of (non self-adjoint) matrix algebras. In particular, it is shown that matrix algebras admitting similar ampliations are themselves similar.
The Kechris-Woodin rank is finer than the Zalcwasser rank
Authors: Ki Haseo
Published: June 2012

For each differentiable function

f
f

on the unit circle, the Kechris-Woodin rank measures the failure of continuity of the derivative function

f
′

f’

while the Zalcwasser rank measures how close the Fourier series of

f
f

is to being a uniformly convergent series. We show that the Kechris-Woodin rank is finer than the Zalcwasser rank. Roughly speaking, small ranks mean the function is well behaved and big ranks imply bad behavior. For each countable ordinal, we explicitly construct a continuous function with everywhere convergent Fourier series such that the Zalcwasser rank of the function is bigger than the ordinal.
Courbures scalaires des variétés d’invariant conforme négatif
Authors: Rauzy Antoine
Published: June 2012

In this paper, we are interested in the problem of prescribing the scalar curvature on a compact riemannian manifold of negative conformal invariant. We give a necessary and sufficient condition when the prescribed function

f
f

is nonpositive. When

sup
(
f
)
>
0

\sup (f) > 0

, we merely find a sufficient condition. This is the subject of the first theorem. In the second one, we prove the multiplicity of the solutions of subcritical (for the Sobolev imbeddings) elliptic equations. In another article [8], we will prove the multiplicity of the solutions of the prescribing curvature problem, i.e. for a critical elliptic equation.
Bayesian model-based clustering of temporal gene expression using autoregressive panel data approach
Authors: Nascimento Moysés , Sáfadi Thelma , Silva Fabyano Fonseca e , Nascimento Ana Carolina C.
Published: June 2012

Motivation: In a microarray time series analysis, due to the large number of genes evaluated, the first step toward understanding the complex time network is the clustering of genes that share similar expression patterns over time. Up until now, the proposed methods do not point simultaneously to the temporal autocorrelation of the gene expression and the model-based clustering. We present a Bayesian method that considers jointly the fit of autoregressive panel data models and hierarchical gene clustering.

Results: The proposed methodology was able to cluster genes that share similar expression over time, which was determined jointly by the estimates of autoregression parameters, by the average level of expression) and by the quality of the fitted model.

Availability and implementation: The R codes for implementation of the proposed clustering method and for simulation study, as well as the real and simulated datasets, are freely accessible on the Web http://www.det.ufv.br/~moyses/links.php.

Contact:  moysesnascim@ufv.br
Genomic dark matter: the reliability of short read mapping illustrated by the genome mappability score
Authors: Lee Hayan , Schatz Michael C.
Published: June 2012

Motivation: Genome resequencing and short read mapping are two of the primary tools of genomics and are used for many important applications. The current state-of-the-art in mapping uses the quality values and mapping quality scores to evaluate the reliability of the mapping. These attributes, however, are assigned to individual reads and do not directly measure the problematic repeats across the genome. Here, we present the Genome Mappability Score (GMS) as a novel measure of the complexity of resequencing a genome. The GMS is a weighted probability that any read could be unambiguously mapped to a given position and thus measures the overall composition of the genome itself.

Results: We have developed the Genome Mappability Analyzer to compute the GMS of every position in a genome. It leverages the parallelism of cloud computing to analyze large genomes, and enabled us to identify the 5–14% of the human, mouse, fly and yeast genomes that are difficult to analyze with short reads. We examined the accuracy of the widely used BWA/SAMtools polymorphism discovery pipeline in the context of the GMS, and found discovery errors are dominated by false negatives, especially in regions with poor GMS. These errors are fundamental to the mapping process and cannot be overcome by increasing coverage. As such, the GMS should be considered in every resequencing project to pinpoint the ‘dark matter’ of the genome, including of known clinically relevant variations in these regions.

Availability: The source code and profiles of several model organisms are available at http://gma-bio.sourceforge.net

Contact:  hlee@cshl.edu

Supplementary Information: Supplementary data are available at Bioinformatics online.
VIGOR extended to annotate genomes for additional 12 different viruses
Authors: Wang Shiliang , Sundaram Jaideep P. , Stockwell Timothy B.
Published: June 2012

A gene prediction program, VIGOR (Viral Genome ORF Reader), was developed at J. Craig Venter Institute in 2010 and has been successfully performing gene calling in coronavirus, influenza, rhinovirus and rotavirus for projects at the Genome Sequencing Center for Infectious Diseases. VIGOR uses sequence similarity search against custom protein databases to identify protein coding regions, start and stop codons and other gene features. Ribonucleicacid editing and other features are accurately identified based on sequence similarity and signature residues. VIGOR produces four output files: a gene prediction file, a complementary DNA file, an alignment file, and a gene feature table file. The gene feature table can be used to create GenBank submission. VIGOR takes a single input: viral genomic sequences in FASTA format. VIGOR has been extended to predict genes for 12 viruses: measles virus, mumps virus, rubella virus, respiratory syncytial virus, alphavirus and Venezuelan equine encephalitis virus, norovirus, metapneumovirus, yellow fever virus, Japanese encephalitis virus, parainfluenza virus and Sendai virus. VIGOR accurately detects the complex gene features like ribonucleicacid editing, stop codon leakage and ribosomal shunting. Precisely identifying the mat_peptide cleavage for some viruses is a built-in feature of VIGOR. The gene predictions for these viruses have been evaluated by testing from 27 to 240 genomes from GenBank.
Development of Viral Vectors Based on Citrus leaf blotch virus to Express Foreign Proteins or Analyze Gene Function in Citrus Plants
Authors: Agüero Jesús , Ruiz-Ruiz Susana , del Carmen Vives María , Velázquez Karelia , Navarro Luis , Peña Leandro , Moreno Pedro , Guerri José
Published: June 2012

Viral vectors have been used to express foreign proteins in plants or to silence endogenous genes. This methodology could be appropriate for citrus plants that have long juvenile periods and adult plants that are difficult to transform. We developed viral vectors based on Citrus leaf blotch virus (CLBV) by duplicating a minimum promoter (92 bp) either at the 3′ untranslated region (clbv3′pr vector) or at the intergenic region between the movement and coat protein (CP) genes (clbvINpr vector). The duplicated fragment (–42/+50) around the transcription start site of the CP subgenomic RNA (sgRNA) had the full promoter activity and induced synthesis of a new sgRNA in infected plants. Agroinoculation with these vectors resulted in systemic infection of Nicotiana benthamiana and the resulting virions systemically infected citrus plants. A clbvINpr vector carrying the green fluorescent protein (GFP) gene expressed GFP in citrus plants and triggered gfp silencing in gfp-transgenic citrus plants, and vectors carrying fragments of the phytoene desaturase or the magnesium chelatase genes incited a silencing phenotype in citrus plants. These silenced phenotypes persisted in successive flushes. Because CLBV infections are symptomless in most citrus species, the effective silencing induced by CLBV-derived vectors will be helpful to analyze citrus gene function.
First Report of Black Spot Disease Caused by Alternaria alternata on Cherry Fruits in China
Authors: Zhao Y. Z. , Liu Z. H.
Published: June 2012

Cherry (Cerasus pseudocerasus) has become an economically important fruit in China in recent years. In June 2010, fruit spots were discovered on fruit grown in Dalian City, Liaoning Province, China and 30% of local-orchard trees were infected with the disease, reducing yield and fruit quality. Disease incidence increased up to 75% in 2011. At the initial stage of the infection, some small, light brown spots appeared on the fruit that gradually became round or irregular and dark brown, and a black-brown concentric ring formed in the advanced stage of the infection. As disease progressed, the lesions expanded, causing the fruit surface to become pitted, withered, and dead. The pathogen was isolated from infected fruit of four orchards by a tissue isolation method (1) and cultured on potato dextrose agar (PDA) at 25°C in the dark for one week. Colonies on PDA were initially white and became grayish brown over time. Conidiophores were single or fasciculate, straight or knee curved, gray-brown with regular septa, branched or unbranched, and 12.5 to 90.0 × 2.0 to 5.0 μm. Conidia were oval, obclavate, or obpyriform, brown or dark brown, surface smooth or spinulose with short columnar beaks, and 20.0 to 42.0 × 7.5 to 14.5 μm with three to eight transverse septa and zero to three longitudinal or oblique septa. The sporulation pattern appeared in bush branches. According to the morphology, the pathogen was identified as Alternaria alternata (Fr:Fr.) Keissler (2,3). The internal transcribed spacer (ITS) region of rDNA was amplified using the primers ITS1/ITS4 and the ITS sequence was 99% identical to A. alternata (GenBank Accession No. FJ228163). Pathogenicity tests were performed on detached, asymptomatic fruit. Six fruit were inoculated by placing a PDA plug containing mycelia on the upper surface of the fruit. Another six fruit received sterile PDA plugs. Fruit were cultured in petri dishes with a 12-h photoperiod at 25°C and 90% relative humidity. Black spot symptoms were observed on inoculated fruit but not control fruit after 5 days. The pathogen was reisolated from inoculated fruit and confirmed to be A. alternata. The pathogenicity test was repeated once. A. alternata has a broad host range, but to our knowledge, this is the first report of A. alternata infecting cherries in China.

References: (1) Z. D. Fang. Research Methods of Plant Disease, 124, 1998. (2) E. G. Simmons. Alternaria themes and variations. Mycotaxon 37: 79, 1990. (3) T. Y. Zhang et al. Fungi Notes–Genera Alternaria in China, 16:32, 2003.
Rhizoctonia solani Anastomosis Group 3 is Predominant in Potato Tubers in Poland
Authors: Woodhall J. W. , Lutomirska B. , Peters J. C. , Wharton P. S.
Published: June 2012

Rhizoctonia solani is a species complex of 13 related but genetically distinct anastomosis groups (AGs). In potato, R. solani can infect the stems, stolons, and roots, resulting in quantitative losses. It can also cause qualitative losses through blemishes occurring on progeny tubers, such as black scurf and elephant hide (corky cracking). Knowledge of the AG in local populations is important because they differ in host range, fungicide sensitivity, and disease severity (2). To determine the AGs present in Poland, 54 tuber samples displaying typical R. solani symptoms were taken from six different fields in 2011. The fields were representative of five different administrative regions of Poland and from at least 10 different varieties. Rhizoctonia was isolated from tubers by placing symptomatic material on to tap water agar amended with streptomycin and penicillin and after 2 to 3 days Rhizoctonia colonies were identified and hyphal tips of these transferred to potato dextrose agar. Rhizoctonia was successfully isolated from 48 tubers displaying black scurf and two tubers displaying elephant hide symptoms. DNA was extracted from Rhizoctonia cultures using a Wizard Food kit (Promega) and the AG was determined using specific real-time PCR assays (1). All Rhizoctonia isolates were determined to be AG3 and this was confirmed for 10 selected isolates by observing hyphal fusion with a known AG3 tester isolate (Rs08) as described previously (3). Pairings were also conducted amongst the 10 Polish isolates, C2 reactions were typically observed indicating numerous vegetative compatible groups are present. This study shows that AG3 is likely to be the predominant AG in potato tubers in Poland. This is similar to other studies in Europe, which have all determined that AG3 accounts for at least 92% of isolates from potato (2,3). AG2-1, 4, and 5 have also been found in tubers worldwide and climate and certain crop rotations can influence the presence of these other AGs in potato tubers (2). However, climate and crop rotations in Poland are similar to other parts of Europe so the predominance of AG3 is expected. AG3 was also isolated from elephant hide symptoms; however, it was more frequently isolated from sclerotia. The ability of AG3 to prolifically produce sclerotia and thereby survive on seed tubers may explain its predominance in potato crops (4). Therefore, studies focusing on the management of Rhizoctonia potato disease in Poland should consider AG3 in the first instance.

References: (1) G. E. Budge et al. Plant Pathol. 58:1071, 2009. (2) L. Tsror. J. Phytopathol. 158:649, 2010. (3) J. W. Woodhall et al. Plant Pathol. 56:286, 2007. (4) J. W. Woodhall et al. Plant Pathol. 57:5, 2008.
An Optimized Duplex Real-Time PCR Tool for Sensitive Detection of the Quarantine Oomycete Plasmopara halstedii in Sunflower Seeds
Authors: Ioos Renaud , Fourrier Céline , Wilson Véronique , Webb Kathryn , Schereffer Jean-Luc , de Labrouhe Denis Tourvieille
Published: June 2012

Plasmopara halstedii, the causal agent of downy mildew of sunflower, is an oomycete listed as a quarantine pathogen. This obligate parasite resides in a quiescent state in seeds of sunflower and can be spread from seed production areas to areas of crop production by international seed trade. To prevent the spread or the introduction of potentially new genotypes or fungicide-tolerant strains, an efficient method to detect P. halstedii in sunflower seed is required. This work reports the optimization of a real-time detection tool that targets the pathogen within sunflower seeds, and provides statistically validated data for that tool. The tool proved to be specific and inclusive, based on computer simulation and in vitro assessments, and could detect as few as 45 copies of target DNA. A fully optimized DNA extraction protocol was also developed starting from a sample of 1,000 sunflower seeds, and enabled the detection of <1 infected seed/1,000 seeds. To ensure reliability of the results, a set of controls was used systematically during the assays, including a plant-specific probe used in a duplex quantitative polymerase chain reaction that enabled the assessment of the quality of each DNA extract.
Grapevine Phenolic Compounds in Xylem Sap and Tissues Are Significantly Altered During Infection byXylella fastidiosa
Authors: Wallis Christopher M. , Chen Jianchi
Published: June 2012

Pierce's disease of grapevine (PD), caused by the bacterial pathogen Xylella fastidiosa, remains a serious problem for grape production in California and elsewhere. This research examined induction of phenolic compounds in grapevines (‘Thompson Seedless’) infected with X. fastidiosa over a 6-month period. Two months postinoculation with X. fastidiosa, catechin, digalloylquinic acid, and astringin were found at greater levels in xylem sap; multiple catechins, procyanidins, and stilbenoids were found at greater levels in xylem tissues; and precursors to lignin and condensed tannins were found at greater levels in xylem cell walls. However, such large-scale inductions of phenolic compounds were not observed 4 months after inoculation. Six months after inoculation, infected plants had significantly reduced phenolic levels in xylem sap and tissues when compared with control plants, including lowered levels of lignin and condensed tannins. At 6 months, PD symptoms were severe in infected plants and most photosynthetic tissue was abscised. These results suggest that, even though grapevine hosts may initially respond to X. fastidiosa infections with increased production of phenolic compounds, ultimately, PD causes grapevines to enter a state of decline whereby diseased hosts no longer have the resources to support secondary metabolite production, including defense-associated phenolic compounds.
Cool running: locomotor performance at low body temperature in mammals
Authors: Rojas A. Daniella , Körtner Gerhard , Geiser Fritz
Published: June 2012

Mammalian torpor saves enormous amounts of energy, but a widely assumed cost of torpor is immobility and therefore vulnerability to predators. Contrary to this assumption, some small marsupial mammals in the wild move while torpid at low body temperatures to basking sites, thereby minimizing energy expenditure during arousal. Hence, we quantified how mammalian locomotor performance is affected by body temperature. The three small marsupial species tested, known to use torpor and basking in the wild, could move while torpid at body temperatures as low as 14.8–17.9°C. Speed was a sigmoid function of body temperature, but body temperature effects on running speed were greater than those in an ectothermic lizard used for comparison. We provide the first quantitative data of movement at low body temperature in mammals, which have survival implications for wild heterothermic mammals, as directional movement at low body temperature permits both basking and predator avoidance.
Live-bearing manta ray: how the embryo acquires oxygen without placenta and umbilical cord
Authors: Tomita Taketeru , Toda Minoru , Ueda Keiichi , Uchida Senzo , Nakaya Kazuhiro
Published: June 2012

We conducted an ultrasonographic experiment on a pregnant manta ray,
Manta alfredi
(Chondrichthyes, Batoidea). This study showed how the embryo of the live-bearing elasmobranchs respires in the body of the female. In the embryonic stage, the manta ray embryo takes in uterine fluid by buccal-pumping. After birth, the manta ray shifts its respiratory mode from buccal-pumping to ram-ventilation. The rapid reduction of the spiracle size in the young manta ray may reflect this shift of respiratory mode.

Unlike mammals or some carcharhinid sharks that acquire oxygen through a placenta and umbilical cord, the manta ray embryo does not have a direct connection with the mother. Thus, the manta ray embryo obtains oxygen by buccal-pumping of the uterine fluid, in the same way that the embryos of egg-laying species obtain oxygen from the water in the egg case. This finding extends our understanding of the diversity of embryonic respiratory systems in live-bearing vertebrates.