title: Cluster fans, stability conditions, and domains of semi-invariants

abstract:
  We show that the cone of finite stability conditions of a quiver Q without
oriented cycles has a fan covering given by (the dual of) the cluster fan of Q.
Along the way, we give new proofs of Schofield's results on perpendicular
categories. We also study domains of semi-invariants of quivers via quiver
exceptional sequences. In particular, we recover Igusa-Orr-Todorov-Weyman's
theorem on cluster complexes and domains of semi-invariants for Dynkin quivers.


title: The Chirality Of Life: From Phase Transitions To Astrobiology

abstract:
  The search for life elsewhere in the universe is a pivotal question in modern
science. However, to address whether life is common in the universe we must
first understand the likelihood of abiogenesis by studying the origin of life
on Earth. A key missing piece is the origin of biomolecular homochirality:
permeating almost every life-form on Earth is the presence of exclusively
levorotary amino acids and dextrorotary sugars. In this work we discuss recent
results suggesting that life's homochirality resulted from sequential chiral
symmetry breaking triggered by environmental events in a mechanism referred to
as punctuated chirality. Applying these arguments to other potentially
life-bearing platforms has significant implications for the search for
extraterrestrial life: we predict that a statistically representative sampling
of extraterrestrial stereochemistry will be racemic on average.


title:
Magnetic Fields and the Polarization of Astrophysical Maser Radiation: A
  Review

abstract:
  Basic aspects of the relationship between the magnetic field and polarized
maser radiation are described with the emphasis on interpreting the observed
spectra. Special attention is given to three issues--the limitations on the
applicability of the classic solutions of Goldreich, Keeley & Kwan (1973),
inferring the strength of the magnetic field from the circular polarization
when the Zeeman splitting is much less than the spectral linebreadth
(especially for SiO masers), and the significance of the absence of components
of the Zeeman triplet in the spectra of OH masers in regions of star formation.


title:
The Effective Spin Hamiltonian and Phase Separation Instability of the
  Almost Half-Filled Hubbard Model and Narrow-Band {\it S-f} Model

abstract:
  The effective spin Hamiltonian is constructed in the framework of the almost
half-filled Hubbard model on the Cayley tree by means of functional integral
technique with the use of static approximation. The system in the ground state
appears to be consisting of the ferromagnetic metallic domains and the
antiferromagnetic insulating one sprovided that the concentration of excess
electrons (or holes) does not exceed some critical value. The connection
between the Hubbard model and the {\it s-f} model is stated. Note added: This
posting is intended to show that the phase separation in strongly correlated
electronic systems was considered already in 1970-80's and is not a discovery
of latest manganites boom


title: Theory of Magnetic Order in $ Fe_{1+y}Te_{1-x}Se_x$

abstract:
  We develop a local spin model to explain the rich magnetic structures in the
iron-based superconductors $Fe_{1+y}Te_{1-x}Se_x$. We show that our model
exhibits both commensurate antiferromagnetic and incommensurate magnetic order
along the crystal a-axis. The transition from the commensurate to the
incommensurate phase is induced when the concentration of excess $Fe$ atoms is
larger than a critical value. Experimentally measurable spin-wave features are
calculated, and the mean-field phase diagram of the model is obtained. Our
model also suggests the existence of a large quantum critical region due to
strong spin frustration upon increasing $Se$ concentration.


title: Conductance asymmetry of graphene pn junction

abstract:
  We use the non-equilibrium Green function (NEGF) method in the ballistic
limit to provide a quantitative description of the conductance of graphene pn
junctions - an important building block for graphene electronics devices. In
this paper, recent experiments on graphene junctions are explained by a
ballistic transport model, but only if the finite junction transition width,
Dw, is accounted for. In particular, the experimentally observed anamolous
increase in the resistance asymmetry between nn and np junctions under low
source/drain charge density conditions is also quantitatively captured by our
model. In light of the requirement for sharp junctions in applications such as
electron focusing, we also examine the pn junction conductance in the regime
where Dw is small and find that wavefunction mismatch (so-called pseudo-spin)
plays a major role in sharp pn junctions.


title: Inhibition of DNA ejection from bacteriophage by Mg+2 counterions

abstract:
  The problem of inhibiting viral DNA ejection from bacteriophages by
multivalent counterions, specifically Mg$^{+2}$ counterions, is studied.
Experimentally, it is known that MgSO$_4$ salt has a strong and non-monotonic
effect on the amount of DNA ejected. There exists an optimal concentration at
which the minimum amount of DNA is ejected from the virus. At lower or higher
concentrations, more DNA is ejected from the capsid. We propose that this
phenomenon is the result of DNA overcharging by Mg$^{+2}$ multivalent
counterions. As Mg$^{+2}$ concentration increases from zero, the net charge of
DNA changes from negative to positive. The optimal inhibition corresponds to
the Mg$^{+2}$ concentration where DNA is neutral. At lower/higher
concentrations, DNA genome is charged. It prefers to be in solution to lower
its electrostatic self-energy, which consequently leads to an increase in DNA
ejection. By fitting our theory to available experimental data, the strength of
DNA$-$DNA short range attraction energies, mediated by Mg$^{+2}$, is found to
be $-$0.004 $k_BT$ per nucleotide base. This and other fitted parameters agree
well with known values from other experiments and computer simulations. The
parameters are also in aggreement qualitatively with values for tri- and
tetra-valent counterions.


title: Optimal sequential multiple hypothesis tests

abstract:
  This work deals with a general problem of testing multiple hypotheses about
the distribution of a discrete-time stochastic process. Both the Bayesian and
the conditional settings are considered. The structure of optimal sequential
tests is characterized.


title: Subspaces of 7 x 7 skew-symmetric matrices related to the group G_2

abstract:
  Let $K$ be a field of characteristic different from 2 and let $C$ be an
octonion algebra over $K$. We show that there is a seven-dimensional subspace
of $7\times 7$ skew-symmetric matrices over $K$ which is invariant under the
automorphism group of $C$. This subspace consists of elements of rank 6 when
$C$ is a division algebra, and elements of rank 4 and 6 when $C$ is a split
algebra. In the latter case, the automorphism group is the exceptional group
$G_2(K)$.


title:
Proposal for Optical Super-Focusing with a Metal-Dielectric Waveguide
  Array

abstract:
  In this paper, super-focusing using radiationless electromagnetic
interference is extended to the visible regime. It is shown that the
highest-order mode of a specifically designed metal-dielectric waveguide array
can provide the rapidly oscillating source field for radiationless
interference. Using finite-difference time-domain simulations, an example
structure is demonstrated. This structure provides focusing to 0.21 of the
optical wavelength at a distance of half the optical wavelength from the
source.


title: On Quadratic Fields Generated by Discriminants of Irreducible Trinomials

abstract:
  A. Mukhopadhyay, M. R. Murty and K. Srinivas (http://arxiv.org/abs/0808.0418)
have recently studied various arithmetic properties of the discriminant
$\Delta_n(a,b)$ of the trinomial $f_{n,a,b}(t) = t^n + at + b$, where $n \ge 5$
is a fixed integer. In particular, it is shown that, under the
$abc$-conjecture, for every $n \equiv 1 \pmod 4$, the quadratic fields
$\Q(\sqrt{\Delta_n(a,b)})$ are pairwise distinct for a positive proportion of
such discriminants with integers $a$ and $b$ such that $f_{n,a,b}$ is
irreducible over $\Q$ and $|\Delta_n(a,b)|\le X$, as $X\to \infty$. We use the
square-sieve and bounds of character sums to obtain a weaker but unconditional
version of this result.


title:
Distributed Algorithms for Computing Alternate Paths Avoiding Failed
  Nodes and Links

abstract:
  A recent study characterizing failures in computer networks shows that
transient single element (node/link) failures are the dominant failures in
large communication networks like the Internet. Thus, having the routing paths
globally recomputed on a failure does not pay off since the failed element
recovers fairly quickly, and the recomputed routing paths need to be discarded.
In this paper, we present the first distributed algorithm that computes the
alternate paths required by some "proactive recovery schemes" for handling
transient failures. Our algorithm computes paths that avoid a failed node, and
provides an alternate path to a particular destination from an upstream
neighbor of the failed node. With minor modifications, we can have the
algorithm compute alternate paths that avoid a failed link as well. To the best
of our knowledge all previous algorithms proposed for computing alternate paths
are centralized, and need complete information of the network graph as input to
the algorithm.


title:
Estimates from below of the Buffon noodle probability for undercooked
  noodles

abstract:
  Let $\Cant_n$ be the $n$-th generation in the construction of the middle-half
Cantor set. The Cartesian square $\K_n$ of $\Cant_n$ consists of $4^n$ squares
of side-length $4^{-n}$. The chance that a long needle thrown at random in the
unit square will meet $\K_n$ is essentially the average length of the
projections of $\K_n$, also known as the Favard length of $\K_n$. A result due
to Bateman and Volberg \cite{BV} shows that a lower estimate for this Favard
length is $c \frac{\log n}{n}$.
  We may bend the needle at each stage, giving us what we will call a noodle,
and ask whether the uniform lower estimate $c \frac{\log n}{n}$ still holds for
these so-called Buffon noodle probabilities. If so, we call the sequence of
noodles undercooked. We will define a few classes of noodles and prove that
they are undercooked. In particular, we are interested in the case when the
noodles are circular arcs of radius $r_n$. We will show that if $r_n \geq
4^{\frac{n}{5}}$, then the circular arcs are undercooked noodles.


title:
Seeing the magnetic monopole through the mirror of topological surface
  states

abstract:
  Existence of the magnetic monopole is compatible with the fundamental laws of
nature, however, this illusive particle has yet to be detected experimentally.
In this work, we show that an electric charge near the topological surface
state induces an image magnetic monopole charge due to the topological
magneto-electric effect. The magnetic field generated by the image magnetic
monopole can be experimentally measured, and the inverse square law of the
field dependence can be determined quantitatively. We propose that this effect
can be used to experimentally realize a gas of quantum particles carrying
fractional statistics, consisting of the bound states of the electric charge
and the image magnetic monopole charge.


title:
NB-FEB: An Easy-to-Use and Scalable Universal Synchronization Primitive
  for Parallel Programming

abstract:
  This paper addresses the problem of universal synchronization primitives that
can support scalable thread synchronization for large-scale many-core
architectures. The universal synchronization primitives that have been deployed
widely in conventional architectures like CAS and LL/SC are expected to reach
their scalability limits in the evolution to many-core architectures with
thousands of cores. We introduce a non-blocking full/empty bit primitive, or
NB-FEB for short, as a promising synchronization primitive for parallel
programming on may-core architectures. We show that the NB-FEB primitive is
universal, scalable, feasible and convenient to use. NB-FEB, together with
registers, can solve the consensus problem for an arbitrary number of processes
(universality). NB-FEB is combinable, namely its memory requests to the same
memory location can be combined into only one memory request, which
consequently mitigates performance degradation due to synchronization "hot
spots" (scalability). Since NB-FEB is a variant of the original full/empty bit
that always returns a value instead of waiting for a conditional flag, it is as
feasible as the original full/empty bit, which has been implemented in many
computer systems (feasibility). The original full/empty bit is well-known as a
special-purpose primitive for fast producer-consumer synchronization and has
been used extensively in the specific domain of applications. In this paper, we
show that NB-FEB can be deployed easily as a general-purpose primitive. Using
NB-FEB, we construct a non-blocking software transactional memory system called
NBFEB-STM, which can be used to handle concurrent threads conveniently.
NBFEB-STM is space efficient: the space complexity of each object updated by
$N$ concurrent threads/transactions is $\Theta(N)$, the optimal.


title: Applying Practice to Theory

abstract:
  How can complexity theory and algorithms benefit from practical advances in
computing? We give a short overview of some prior work using practical
computing to attack problems in computational complexity and algorithms,
informally describe how linear program solvers may be used to help prove new
lower bounds for satisfiability, and suggest a research program for developing
new understanding in circuit complexity.


title: Vertex operators and sporadic groups

abstract:
  In the 1980's, the work of Frenkel, Lepowsky and Meurman, along with that of
Borcherds, culminated in the notion of vertex operator algebra, and an example
whose full symmetry group is the largest sporadic simple group: the Monster.
Thus it was shown that the vertex operators of mathematical physics play a role
in finite group theory. In this article we describe an extension of this
phenomenon by introducing the notion of enhanced vertex operator algebra, and
constructing examples that realize other sporadic simple groups, including one
that is not involved in the Monster.


title: Galaxy star formation in different environments

abstract:
  We use a semi-analytic model of galaxy formation to study signatures of
large-scale modulations in the star formation (SF) activity in galaxies. In
order to do this we carefully define local and global estimators of the density
around galaxies. The former are computed using a voronoi tessellation technique
and the latter are parameterised by the normalised distance to haloes and
voids, in terms of the virial and void radii, respectively. As a function of
local density, galaxies show a strong modulation in their SF, a result that is
in agreement with those from several authors. When taking subsamples of equal
local density at different large-scale environments, we find relevant global
effects whereby the fraction of red galaxies diminishes for galaxies in equal
local density environments farther away from clusters and closer to voids. In
general, the semianalytic simulation is in good agreement with the available
observational results, and offers the possibility to disentangle many of the
processes responsible for the variation of galaxy properties with the
environment; we find that the changes found in samples of galaxies with equal
local environment but different distances to haloes or voids come from the
variations in the underlying mass function of dark-matter haloes. There is an
additional possible effect coming from the host dark-matter halo ages,
indicating that halo assembly also plays a small but significant role
($1.14\sigma$) in shaping the properties of galaxies, and in particular, hints
at a possible spatial correlation in halo/stellar mass ages.


title: Virtual reshaping and invisibility in obstacle scattering

abstract:
  We consider reshaping a scattering obstacle virtually by using transformation
optics in acoustic and electromagnetic scattering. Among the general virtual
reshaping results, the virtual minification and virtual magnification are
particularly studied. Stability estimates are derived for scattering amplitude
in terms of the diameter of a small obstacle, which implies that the limiting
case for minification corresponds to a perfect cloaking, i.e., the obstacle is
invisible to detection.

categories: physics.optics math-ph math.AP math.MP physics.acc-ph


title:
Entanglement oscillation and survival induced by non-Markovian
  decoherence dynamics of entangled squeezed-state

abstract:
  We study the exact decoherence dynamics of the entangled squeezed state of
two single-mode optical fields interacting with two independent and
uncorrelated environments. We analyze in detail the non-Markovian effects on
the entanglement evolution of the initially entangled squeezed state for
different environmental correlation time scales. We find that the environments
have dual actions on the system: backaction and dissipation. In mparticular,
when the environmental correlation time scale is comparable to the time scale
for significant change in the system, the backaction would counteract the
dissipative effect. Interestingly, this results in the survival of some
residual entanglement in the final steady state.


title: Classification theorems for sumsets modulo a prime

abstract:
  Let $\Z/pZ$ be the finite field of prime order $p$ and $A$ be a subsequence
of $\Z/pZ$. We prove several classification results about the following
questions: (1) When can one represent zero as a sum of some elements of $A$ ?
(2) When can one represent every element of $\Z/pZ$ as a sum of some elements
of $A$ ? (3) When can one represent every element of $\Z/pZ$ as a sum of $l$
elements of $A$ ?


title: Squares in sumsets

abstract:
  A finite set $A$ of integers is square-sum-free if there is no subset of $A$
sums up to a square. In 1986, Erd\H os posed the problem of determining the
largest cardinality of a square-sum-free subset of $\{1, ..., n \}$. Answering
this question, we show that this maximum cardinality is of order
$n^{1/3+o(1)}$.


title: On two-point configurations in random set

abstract:
  We show that with high probability a random set of size $\Theta(n^{1-1/k})$
of $\{1,...,n\}$ contains two elements $a$ and $a+d^k$, where $d$ is a positive
integer. As a consequence, we prove an analogue of S\'ark\"ozy-F\"urstenberg's
theorem for random set.


title: RO(S^1)-graded TR-groups of F_p, Z and \ell

abstract:
  We give an algorithm for calculating the RO(S^1)-graded TR-groups of F_p,
completing the calculation started by the second author. We also calculate the
RO(S^1)-graded TR-groups of Z with mod p coefficients and of the Adams summand
\ell of connective complex K-theory with V(1)-coefficients. Some of these
calculations are used elsewhere to compute the algebraic K-theory of certain
Z-algebras.


title:
Collisionally inhomogeneous Bose-Einstein condensates in double-well
  potentials

abstract:
  In this work, we consider quasi-one-dimensional Bose-Einstein condensates
(BECs), with spatially varying collisional interactions, trapped in double well
potentials. In particular, we study a setup in which such a 'collisionally
inhomogeneous' BEC has the same (attractive-attractive or repulsive-repulsive)
or different (attractive-repulsive) type of interparticle interactions. Our
analysis is based on the continuation of the symmetric ground state and
anti-symmetric first excited state of the noninteracting (linear) limit into
their nonlinear counterparts. The collisional inhomogeneity produces a
saddle-node bifurcation scenario between two additional solution branches; as
the inhomogeneity becomes stronger, the turning point of the saddle-node tends
to infinity and eventually only the two original branches remain present, which
is completely different from the standard double-well phenomenology. Finally,
one of these branches changes its monotonicity as a function of the chemical
potential, a feature especially prominent, when the sign of the nonlinearity
changes between the two wells. Our theoretical predictions, are in excellent
agreement with the numerical results.


title: Hilbert series and obstructions to asymptotic semistability

abstract:
  Given a polarized manifold there are obstructions for asymptotic Chow
semistability described as integral invariants. One of them is an obstruction
to the existence for the first Chern class of the polarization to admit a
constant scalar curvature K\"ahler (cscK) metric. A natural question is whether
or not the other obstructions are linearly dependent on the obstruction to the
existence of a cscK metric. The purpose of this paper is to see that this is
not the case by exhibiting toric Fano threefolds in which these obstructions
span at least two dimension. To see this we show that on toric Fano manifolds
these obstructions are obtained as derivatives of the Hilbert series. This last
observation should be regarded as an extension of the volume minimization of
Martelli, Sparks and Yau.


title: Young Cool Stars Divided on the Issue of Rotation

abstract:
  We present the results of a combination of new stellar rotation periods and
extensive information about membership in the young open clusters M35 and M34.
The observations show that late-type members of both clusters divide into two
distinct groups, each with a different dependence of rotation on mass (color).
We discuss these new results in the context of existing rotation data for cool
stars in older clusters, with a focus on the dependence of rotation on mass and
age. We mention briefly tests of rotation as an "astronomical clock"
(gyrochronology), and our plans to use the Kepler space mission to push
observations of stellar rotation periods beyond the age of the Hyades and the
Sun.


title: Secrecy in Cooperative Relay Broadcast Channels

abstract:
  We investigate the effects of user cooperation on the secrecy of broadcast
channels by considering a cooperative relay broadcast channel. We show that
user cooperation can increase the achievable secrecy region. We propose an
achievable scheme that combines Marton's coding scheme for broadcast channels
and Cover and El Gamal's compress-and-forward scheme for relay channels. We
derive outer bounds for the rate-equivocation region using auxiliary random
variables for single-letterization. Finally, we consider a Gaussian channel and
show that both users can have positive secrecy rates, which is not possible for
scalar Gaussian broadcast channels without cooperation.


title: Curvatons and inhomogeneous scenarios with deviation from slow-roll

abstract:
  The spectral index is studied at the point where scalar fields deviate from
slow-roll during inflation. Considering the deviation that may cause a
significant difference to the time derivative of the Hubble parameter and also
to the terms in the evolution equation, we show how the deviation affects the
spectral index of the curvature perturbations. Considering conventional
inflation, curvatons and other inhomogeneous scenarios as mechanisms for
generating the cosmological perturbation, we examine whether the spectral index
induced by the deviation from the standard slow-roll can explain the spectral
index n-1>0 at k=0.002/Mpc while keeping n-1<0 at a smaller scale.


title: Modeling Social Annotation: a Bayesian Approach

abstract:
  Collaborative tagging systems, such as Delicious, CiteULike, and others,
allow users to annotate resources, e.g., Web pages or scientific papers, with
descriptive labels called tags. The social annotations contributed by thousands
of users, can potentially be used to infer categorical knowledge, classify
documents or recommend new relevant information. Traditional text inference
methods do not make best use of social annotation, since they do not take into
account variations in individual users' perspectives and vocabulary. In a
previous work, we introduced a simple probabilistic model that takes interests
of individual annotators into account in order to find hidden topics of
annotated resources. Unfortunately, that approach had one major shortcoming:
the number of topics and interests must be specified a priori. To address this
drawback, we extend the model to a fully Bayesian framework, which offers a way
to automatically estimate these numbers. In particular, the model allows the
number of interests and topics to change as suggested by the structure of the
data. We evaluate the proposed model in detail on the synthetic and real-world
data by comparing its performance to Latent Dirichlet Allocation on the topic
extraction task. For the latter evaluation, we apply the model to infer topics
of Web resources from social annotations obtained from Delicious in order to
discover new resources similar to a specified one. Our empirical results
demonstrate that the proposed model is a promising method for exploiting social
knowledge contained in user-generated annotations.


title: Exact spin-cluster ground states in a mixed diamond chain

abstract:
  The mixed diamond chain is a frustrated Heisenberg chain composed of
successive diamond-shaped units with two kinds of spins of magnitudes S and S/2
(S: integer). Ratio $lambda$ of two exchange parameters controls the strength
of frustration. With varying $lambda$, the Haldane state and several spin
cluster states appear as the ground state. A spin cluster state is a tensor
product of exact local eigenstates of cluster spins. We prove that a spin
cluster state is the ground state in a finite interval of $lambda$. For S=1, we
numerically determine the total phase diagram consisting of five phases.


title: Emile Borel's difficult days in 1941

abstract:
  The German forces occupying Paris arrested Emile Borel and three other
members of the Acad\'emie des Sciences in October 1941 and released them about
five weeks later. Why? We examine some relevant German and French archives and
other sources and propose some hypotheses. In the process, we review how the
Occupation was structured and how it dealt with French higher education and
some French mathematicians.


title: 1-Saturating Sets, Caps and Round Sets in Binary Spaces

abstract:
  We show that, for a positive integer $r$, every minimal 1-saturating set in
${\rm PG}(r-1,2)$ of size at least ${11/36} 2^r+3$ is either a complete cap or
can be obtained from a complete cap $S$ by fixing some $s\in S$ and replacing
every point $s'\in S\setminus\{s\}$ by the third point on the line through $s$
and $s'$. Stated algebraically: if $G$ is an elementary abelian 2-group and a
set $A\subseteq G\setminus\{0\}$ with $|A|>{11/36} |G|+3$ satisfies $A\cup
2A=G$ and is minimal subject to this condition, then either $A$ is a maximal
sum-free set, or there are a maximal sum-free set $S\subseteq G$ and an element
$s\in S$ such that $A=\{s\}\cup\big(s+(S\setminus\{s\})\big)$. Since,
conversely, every set obtained in this way is a minimal 1-saturating set, and
the structure of large sum-free sets in an elementary 2-group is known, this
provides a complete description of large minimal 1-saturating sets.
  Our approach is based on characterizing those large sets $A$ in elementary
abelian 2-groups such that, for every proper subset $B$ of $A$, the sumset 2B
is a proper subset of 2A.


title:
Analytical Blowup Solutions to the 4-dimensional Pressureless
  Navier-Stokes-Poisson Equations with Density-dependent Viscosity

abstract:
  We study the 4-dimensional pressureless Navier--Stokes-Poisson equations with
density-dependent viscosity. The analytical solutions with arbitrary time
blowup, in radial symmetry, are constructed in this paper.


title:
Statistically Steady Turbulence in Soap Films: Direct Numerical
  Simulations with Ekman Friction

abstract:
  We present a detailed direct numerical simulation (DNS) designed to
investigate the combined effects of walls and Ekman friction on turbulence in
forced soap films. We concentrate on the forward-cascade regime and show how to
extract the isotropic parts of velocity and vorticity structure functions and
thence the ratios of multiscaling exponents. We find that velocity structure
functions display simple scaling whereas their vorticity counterparts show
multiscaling; and the probability distribution function of the Weiss parameter
$\Lambda$, which distinguishes between regions with centers and saddles, is in
quantitative agreement with experiments.


title:
Asymptotic dimension of proper CAT(0) spaces which are homeomorphic to
  the plane

abstract:
  In this paper, we investigate a proper CAT(0) space $(X,d)$ which is
homeomorphic to $R^2$ and we show that the asymptotic dimension $asdim (X,d)$
is equal to 2.


title:
Coarse-grained cellular automaton simulation of spherulite growth during
  polymer crystallization

abstract:
  The work introduces a 3D cellular automaton model for the spatial and
crystallographic prediction of spherulite growth phenomena in polymers at the
mesoscopic scale. The automaton is discrete in time, real space, and
orientation space. The kinetics is formulated according to the
Hoffman-Lauritzen secondary surface nucleation and growth theory for spherulite
expansion. It is used to calculate the switching probability of each grid point
as a function of its previous state and the state of the neighboring grid
points. The actual switching decision is made by evaluating the local switching
probability using a Monte Carlo step. The growth rule is scaled by the ratio of
the local and the maximum interface energies, the local and maximum occurring
Gibbs free energy of transformation, the local and maximum occurring
temperature, and by the spacing of the grid points. The use of experimental
input data provides a real time and space scale.


title: Characterization of Lee-Yang polynomials

abstract:
  The Lee-Yang circle theorem describes complex polynomials of degree $n$ in
$z$ with all their zeros on the unit circle $|z|=1$. These polynomials are
obtained by taking $z_1=...=z_n=z$ in certain multiaffine polynomials
$\Psi(z_1,...,z_n)$ which we call Lee-Yang polynomials (they do not vanish when
$|z_1|,...,|z_n|<1$ or $|z_1|,...,|z_n|>1$). We characterize the Lee-Yang
polynomials $\Psi$ in $n+1$ variables in terms of polynomials $\Phi$ in $n$
variables (those such that $\Phi(z_1,...,z_n)\ne0$ when $|z_1|,...,|z_n|<1$).
This characterization gives us a good understanding of Lee-Yang polynomials and
allows us to exhibit some new examples. In the physical situation where the
$\Psi$ are temperature dependent partition functions, we find that those $\Psi$
which are Lee-Yang polynomials for all temperatures are precisely the
polynomials with pair interactions originally considered by Lee and Yang.


title: From iterated tilted algebras to cluster-tilted algebras

abstract:
  In this paper the relationship between iterated tilted algebras and
cluster-tilted algebras and relation-extensions is studied. In the Dynkin case,
it is shown that the relationship is very strong and combinatorial.


title:
A Weighted Spike-Triggered Average of a Fluctuating Stimulus Yielding
  the Phase Response Curve

abstract:
  We demonstrate that the phase response curve (PRC) can be reconstructed using
a weighted spike-triggered average of an injected fluctuating input. The key
idea is to choose the weight to be proportional to the magnitude of the
fluctuation of the oscillatory period. Particularly, when a neuron exhibits
random switching behavior between two bursting modes, two corresponding PRCs
can be simultaneously reconstructed, even from the data of a single trial. This
method offers an efficient alternative to the experimental investigation of
oscillatory systems, without the need for detailed modeling.


title: Cohomology rings of almost-direct products of free groups

abstract:
  An almost-direct product of free groups is an iterated semidirect product of
finitely generated free groups in which the action of the constituent free
groups on the homology of one another is trivial. We determine the structure of
the cohomology ring of such a group. This is used to analyze the topological
complexity of the associated Eilenberg-Mac Lane space.


title: Resonance of basis-conjugating automorphism groups

abstract:
  We determine the structure of the first resonance variety of the cohomology
ring of the group of automorphisms of a finitely generated free group which act
by conjugation on a given basis.


title: Isotope effect and the role of phonon in the Fe-based superconductors

abstract:
  We studied the isotope effect of phonon in the Fe-based superconductors using
a phenomenological two band model for the sign-changing s-wave ($\pm$s-wave)
state. Within this mean-field model, we showed that the large isotope effect is
not inconsistent with the $\pm$s-wave pairing state and its high transition
temperature. In principle, a large phonon isotope coefficient $\alpha$ implies
a large phonon coupling constant. However, the asymmetric density of states
(DOS) between two bands substantially enhances the value of $\alpha$, so that a
moderate value of the phonon coupling constant ($\lambda_{\rm ph} \approx 0.4$)
can produce a very large value of $\alpha$ ($\approx 0.4$) as well as a high
transition temperature together with an antiferromagnet (AFM)-induced
interaction.


title:
Theoretical Limits on the Equation-of-State Parameter of Phantom
  Cosmology

abstract:
  We investigate the restrictions on the equation-of-state parameter of phantom
cosmology, due to the minimum quantum gravitational requirements. We find that
for all the examined $w_\Lambda(z)$-parametrizations and for arbitrary phantom
potentials and spatial curvature, the phantom equation-of-state parameter is
not restricted at all. This is in radical contrast with the quintessence
paradigm, and makes phantom cosmology more robust and capable of constituting
the underlying mechanism for dark energy.


title: Using synchronism of chaos for adaptive learning of network topology

abstract:
  In this paper we consider networks of dynamical systems that evolve in
synchrony and investigate how dynamical information from the synchronization
dynamics can be effectively used to learn the network topology, i.e., identify
the time evolution of the couplings between the network nodes. To this aim, we
present an adaptive strategy that, based on a potential that the network
systems seek to minimize in order to maintain synchronization, can be
successfully applied to identify the time evolution of the network from limited
information. This strategy takes advantage of the properties of synchronism of
chaos and of the presence of different communication delays over the network
links. As a motivating example we consider a network of sensors surveying an
area, in which information regarding the time evolution of the network
connections can be used, e.g., to detect changes taking place within the area.
We propose two different setups for our strategy. In the first one,
synchronization has to be achieved at each node (as well as the identification
of the couplings over the network links), based solely on a single scalar
signal representing a superposition of signals from the other nodes in the
network. In the second one, we incorporate an additional node, termed the
maestro, having the function of maintaining network synchronization. We will
see that when such an arrangement is realized, it will become possible to
effectively identify the time evolution of networks that are much larger than
would be possible in the absence of a maestro.


title:
Algorithmic Techniques for Several Optimization Problems Regarding
  Distributed Systems with Tree Topologies

abstract:
  As the development of distributed systems progresses, more and more
challenges arise and the need for developing optimized systems and for
optimizing existing systems from multiple perspectives becomes more stringent.
In this paper I present novel algorithmic techniques for solving several
optimization problems regarding distributed systems with tree topologies. I
address topics like: reliability improvement, partitioning, coloring, content
delivery, optimal matchings, as well as some tree counting aspects. Some of the
presented techniques are only of theoretical interest, while others can be used
in practical settings.


title: Schreier rewriting beyond the classical setting

abstract:
  Using actions of free monoids and free associative algebras, we establish
some Schreier-type formulas involving the ranks of actions and the ranks of
subactions in free actions or Grassmann-type relations for the ranks of
intersections of subactions of free actions. The coset action of the free group
is used to establish the generalization of the Schreier formula to the case of
subgroups of infinite index. We also study and apply large modules over free
associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V.,
Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008),
753 - 759.


title: Gravitational strings. Do we see one?

abstract:
  I present a class of objects called gravitational strings (GS) for their
similarity to the conventional cosmic strings: even though the former are just
singularities in flat spacetime, both varieties are equally "realistic", they
may play equally important cosmological r\^ole and their lensing properties are
akin. I argue that the enigmatic object CSL-1 is an evidence in favor of the
existence of GS.


title: Modern Theory of Nuclear Forces

abstract:
  Effective field theory allows for a systematic and model-independent
derivation of the forces between nucleons in harmony with the symmetries of
Quantum Chromodynamics. We review the foundations of this approach and discuss
its application for light nuclei at various resolution scales. The extension of
this approach to many-body systems is briefly sketched.


title:
The Mass Function of Void Groups as a Probe of the Primordial
  non-Gaussianity

abstract:
  The primordial non-Gaussianity signal, if measured accurately, will allow us
to distinguish between different candidate models for the cosmic inflation.
Since the galaxy groups located in void regions are rare events, their
abundance may be a sensitive probe of the primordial non-Gaussianity. We
construct an analytic model for the mass function of void groups in the
framework of the extended Press-Schechter theory with non-Gaussian initial
conditions and investigate how it depends on the primordial non-Gaussianity
parameter. A feasibility study is conducted by fitting the analytic mass
function of void groups to the observational results from the galaxy group
catalog of the Sloan Digital Sky Survey Data Release 4 with adjusting the
primordial non-Gaussianity parameter.


title: Anomaly in the heat capacity of Kondo superconductors

abstract:
  Using numerical renormalization group we study thermodynamic properties of a
magnetic impurity described by the Anderson impurity model in a superconducting
host material described by the BCS Hamiltonian. When the Kondo temperature in
the normal state, T_K, is comparable to the critical temperature of the
superconducting transition, T_c, the magnetic doublet state may become
degenerate with the Kondo singlet state, leading to a ln3 peak in the
temperature dependence of the impurity contribution to the entropy. This
entropy increase translates into an anomalous feature in the heat capacity
which might have already been experimentally observed.


title: Conformal Supergravity Tree Amplitudes from Open Twistor String Theory

abstract:
  We display the vertex operators for all states in the conformal supergravity
sector of the twistor string, as outlined by Berkovits and Witten. These
include `dipole' states, which are pairs of supergravitons that do not
diagonalize the translation generators. We use canonical quantization of the
open string version of Berkovits, and compute N-point tree level scattering
amplitudes for gravitons, gluons and scalars. We reproduce the Berkovits-Witten
formula for maximal helicity violating (MHV) amplitudes (which they derived
using path integrals), and extend their results to the dipole pairs. We compare
these trees with those of Einstein gravity field theory.


title: On localization properties of Fourier transforms of hyperfunctions

abstract:
  In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized
function space $\mathcal U(R^k)$ which can be naturally interpreted as the
Fourier transform of the space of Sato's hyperfunctions on $R^k$. It was shown
that all Gelfand--Shilov spaces $S^{\prime 0}_\alpha(R^k)$ ($\alpha>1$) of
analytic functionals are canonically embedded in $\mathcal U(R^k)$. While the
usual definition of support of a generalized function is inapplicable to
elements of $S^{\prime 0}_\alpha(R^k)$ and $\mathcal U(R^k)$, their
localization properties can be consistently described using the concept of {\it
carrier cone} introduced by Soloviev [Lett. Math. Phys. 33 (1995) 49-59; Comm.
Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier
cones of elements of $S^{\prime 0}_\alpha(R^k)$ and $\mathcal U(R^k)$ is
studied. It is proved that an analytic functional $u\in S^{\prime
0}_\alpha(R^k)$ is carried by a cone $K\subset R^k$ if and only if its
canonical image in $\mathcal U(R^k)$ is carried by $K$.


title:
Improved "Position Squared" Readout of a Mechanical Resonator in an
  Optical Cavity Using Degenerate Optical Modes

abstract:
  Optomechanical devices in which a flexible SiN membrane is placed inside an
optical cavity allow for very high finesse and mechanical quality factor in a
single device. They also provide fundamentally new functionality: the cavity
detuning can be a quadratic function of membrane position. This enables a
measurement of "position squared" ($x^2$) and in principle a QND phonon number
readout of the membrane. However, the readout achieved using a single
transverse cavity mode is not sensitive enough to observe quantum jumps between
phonon Fock states.
  Here we demonstrate an $x^2$-sensitivity that is orders of magnitude stronger
using two transverse cavity modes that are nearly degenerate. We derive a
first-order perturbation theory to describe the interactions between
nearly-degenerate cavity modes and achieve good agreement with our measurements
using realistic parameters. We also demonstrate theoretically that the
$x^2$-coupling should be easily tunable over a wide range.


title:
Thermodynamics of ferromagnetic superconductors with spin-triplet
  electron pairing

abstract:
  We present a general thermodynamic theory that describes phases and phase
transitions of ferromagnetic superconductors with spin-triplet electron Cooper
pairing. The theory is based on extended Ginzburg-Landau expansion in powers of
superconducting and ferromagnetic order parameters. We propose a simple form
for the dependence of theory parameters on the pressure that allows correct
theoretical outline of the temperature-pressure phase diagram for which at low
temperatures a stable phase of coexistence of p-wave superconductivity and
itinerant ferromagnetism appears. We demonstrate that the theory is in an
agreement with the experimental data for some intermetallic compounds that are
experimentally proven to be itinerant ferromagnetic exhibiting spin-triplet
superconductivity. Some basic features of quantum phase transitions in such
systems are explained and clarified. We propose to group the spin-triplet
ferromagnetic superconductors in two different types of thermodynamic behavior,
on the basis of quantitative criterion deduced from the present theory and the
analysis of experimental data.

categories: cond-mat.supr-con cond-mat.stat-mech cond-mat.str-el physics.chem-ph


title: Quark Forces from Hadron Spectroscopy

abstract:
  We consider the implications of the most general two-body quark-quark
interaction Hamiltonian for the spin-flavor structure of the negative parity
L=1 excited baryons. Assuming the most general two-body quark interaction
Hamiltonian, we derive two correlations among the masses and mixing angles of
these states, which constrain the mixing angles, and can be used to test for
the presence of three-body quark interactions. We find that the pure
gluon-exchange model is disfavored by data, independently of any assumptions
about the hadronic wave functions.


title: Nonlocal-local multimode bifurcation in turbulence

abstract:
  It is shown that a mechanism of energy redistribution and dissipation by the
inertial waves can be effectively utilized in isotropic turbulence at small
Reynolds numbers (when the nonlocal interactions are the dominating ones). This
mechanism totally suppresses the local interactions (cascades) in isotropic
turbulence at the Taylor-scale based Reynolds number $R_{\lambda} < 10^2$. This
value of $R_{\lambda}$ (that can be considered as a bifurcation value at which
the local regime emerges from the nonlocal one in isotropic turbulence) is in
agreement with recent direct numerical simulations data. Applicability of this
approach to channel flows is also briefly discussed. A theory of multimode
bifurcations has been developed in order to explain anomalous (in comparison
with the Landau-Hopf bifurcations) properties of the nonlocal-local bifurcation
in isotropic turbulence.


title: Recent Progress on Tau Lepton Physics

abstract:
  Some important aspects of hadronic tau decays are reviewed: the determination
of alpha_s from the inclusive tau hadronic width, the measurement of |V_{us}|
through the Cabibbo-suppressed decays of the tau, and the theoretical
description of the tau -> nu_tau K pi spectrum. The present status of other
relevant electroweak topics, such as charged-current universality tests or
bounds on lepton-flavour violation, has been already summarized in a previous
review.


title: X-ray imaging of the dynamic magnetic vortex core deformation

abstract:
  Magnetic platelets with a vortex configuration are attracting considerable
attention. The discovery that excitation with small in-plane magnetic fields or
spin polarised currents can switch the polarisation of the vortex core did not
only open the possibility of using such systems in magnetic memories, but also
initiated the fundamental investigation of the core switching mechanism itself.
Micromagnetic models predict that the switching is mediated by a
vortex-antivortex pair, nucleated in a dynamically induced vortex core
deformation. In the same theoretical framework, a critical core velocity is
predicted, above which switching occurs. Although these models are extensively
studied and generally accepted, experimental support has been lacking until
now. In this work, we have used high-resolution time-resolved X-ray microscopy
to study the detailed dynamics in vortex structures. We could reveal the
dynamic vortex core deformation preceding the core switching. Also, the
threshold velocity could be measured, giving quantitative comparison with
micromagnetic models.


title: A Uniform Estimate for Fourier Restriction to Simple Curves

abstract:
  We prove a uniform Fourier extension-restriction estimate for a certain class
of curves in d-dimensional Euclidean space.


title: General Hormander and Mikhlin conditions for multipliers of Besov spaces

abstract:
  Here a new condition for the geometry of Banach spaces is introduced and the
operator--valued Fourier multiplier theorems in weighted Besov spaces are
obtained. Particularly, connections between the geometry of Banach spaces and
Hormander-Mikhlin conditions are established. As an application of main results
the regularity properties of degenerate elliptic differential operator
equations are investigated.


title: The orbit structure of the Gelfand-Zeitlin group on n x n matrices

abstract:
  In recent work (\cite{KW1},\cite{KW2}), Kostant and Wallach construct an
action of a simply connected Lie group $A\simeq \mathbb{C}^{{n\choose 2}}$ on
$gl(n)$ using a completely integrable system derived from the Poisson analogue
of the Gelfand-Zeitlin subalgebra of the enveloping algebra. In \cite{KW1}, the
authors show that $A$-orbits of dimension ${n\choose 2}$ form Lagrangian
submanifolds of regular adjoint orbits in $gl(n)$. They describe the orbit
structure of $A$ on a certain Zariski open subset of regular semisimple
elements. In this paper, we describe all $A$-orbits of dimension ${n\choose 2}$
and thus all polarizations of regular adjoint orbits obtained using
Gelfand-Zeitlin theory.


title:
Femtoscopically Probing the Freeze-out Configuration in Heavy Ion
  Collisions

abstract:
  Two-particle femtoscopy reveals the space-time substructure of the freeze-out
configuration from heavy ion collisions. Detailed fingerprints of bulk
collectivity are evident in space-momentum correlations, which have been
systematically measured as a function of particle type, three-momentum, and
collision conditions. A clear scenario, dominated by hydrodynamic-type flow
emerges. Reproducing the strength and features of the femtoscopic signals in
models involves important physical quantities like the Equation of State, as
well as less fundamental technical details. An interesting approximate
"factorization" in the measured systematics suggests that the overall physical
freeze-out scale is set by final state chemistry, but the kinematic
substructure is largely universal. Referring to previous results from hadron
and lepton collisions, we point to the importance of determining whether these
"universal" trends persist from the largest to the smallest systems. We review
theoretical expectations for heavy ion femtoscopy at the LHC, and point to
directions needing further theory and experimental work at RHIC and the LHC.


title:
Fermion pair production in QED and the backreaction problem in
  (1+1)-dimensional boost-invariant coordinates revisited

abstract:
  We study two different initial conditions for fermions for the problem of
pair production of fermions coupled to a classical electromagnetic field with
backreaction in \oneplusone boost-invariant coordinates. Both of these
conditions are consistent with fermions initially in a vacuum state. We present
results for the proper time evolution of the electric field $E$, the current,
the matter energy density, and the pressure as a function of the proper time
for these two cases. We also determine the interpolating number density as a
function of the proper time. We find that when we use a "first order adiabatic"
vacuum initial condition or a "free field" initial condition for the fermion
field, we obtain essentially similar behavior for physically measurable
quantities. The second method is computationally simpler, it is twice as fast
and involves half the storage required by the first method.


title: Holomorphic Engel Structures

abstract:
  Recently there has been renewed interest among differential geometers in the
theory of Engel structures. We introduce holomorphic analogues of these
structures, and pose the problem of classifying projective manifolds admitting
them. Besides providing the basic properties of these varieties, we present two
series of examples and characterize them by certain positivity conditions on
the Engel structure.


title:
Matrix approach to discrete fractional calculus II: partial fractional
  differential equations

abstract:
  A new method that enables easy and convenient discretization of partial
differential equations with derivatives of arbitrary real order (so-called
fractional derivatives) and delays is presented and illustrated on numerical
solution of various types of fractional diffusion equation. The suggested
method is the development of Podlubny's matrix approach (Fractional Calculus
and Applied Analysis, vol. 3, no. 4, 2000, 359--386). Four examples of
numerical solution of fractional diffusion equation with various combinations
of time/space fractional derivatives (integer/integer, fractional/integer,
integer/fractional, and fractional/fractional) with respect to time and to the
spatial variable are provided in order to illustrate how simple and general is
the suggested approach. The fifth example illustrates that the method can be
equally simply used for fractional differential equations with delays. A set of
MATLAB routines for the implementation of the method as well as sample code
used to solve the examples have been developed.

categories: math.NA cs.NA math-ph math.CA math.MP physics.comp-ph


title:
Photogalvanic effect and photoconductance in a quantum channel with a
  single short-range scatterer

abstract:
  The influence of electromagnetic radiation on the electron transport in a
quantum channel with a single short-range scatterer is investigated using a
generalized Landauer-Buttiker approach. We have shown that asymmetrical
position of the scatterer leads to appearance of the direct photocurrent in the
system. The dependence of the photocurrent on the electron chemical potential,
the position of the scatterer, and the frequency of the radiation is studied.
We have shown that the photocurrent and the photoconductance oscillate as
functions of the electron chemical potential. The nature of oscillations is
discussed.


title:
Spinor fields without Lorentz frames in curved spacetime using
  complexified quaternions

abstract:
  Using complexified quaternions, a formalism without Lorentz frames, and
therefore also without vierbeins, for dealing with tensor and spinor fields in
curved spacetime is presented. A local U(1) gauge symmetry, which, it is
speculated, might be related to electromagnetism, emerges naturally.


title:
Integrability of the symmetry reduced bosonic dynamics and soliton
  generating transformations in the low energy heterotic string effective
  theory

abstract:
  Integrable structure of the symmetry reduced dynamics of massless bosonic
sector of the heterotic string effective action is presented. For string
background equations that govern in the space-time of $D$ dimensions ($D\ge 4$)
the dynamics of interacting gravitational, dilaton, antisymmetric tensor and
any number $n\ge 0$ of Abelian vector gauge fields, all depending only on two
coordinates, we construct an \emph{equivalent} $(2 d+n)\times(2 d+n)$ matrix
spectral problem ($d=D-2$). This spectral problem provides the base for the
development of various solution constructing procedures (dressing
transformations, integral equation methods). For the case of the absence of
Abelian gauge fields, we present the soliton generating transformations of any
background with interacting gravitational, dilaton and the second rank
antisymmetric tensor fields. This new soliton generating procedure is available
for constructing of various types of field configurations including stationary
axisymmetric fields, interacting plane, cylindrical or some other types of
waves and cosmological solutions.


title: Discrimination of Unitary Transformations and Quantum Algorithms

abstract:
  Quantum algorithms are typically understood in terms of the evolution of a
multi-qubit quantum system under a prescribed sequence of unitary
transformations. The input to the algorithm prescribes some of the unitary
transformations in the sequence with others remaining fixed. For oracle query
algorithms, the input determines the oracle unitary transformation. Such
algorithms can be regarded as devices for discriminating amongst a set of
unitary transformations. The question arises: "Given a set of known oracle
unitary transformations, to what extent is it possible to discriminate amongst
them?" We investigate this for the Deutsch-Jozsa problem. The task of
discriminating amongst the admissible oracle unitary transformations results in
an exhaustive collection of algorithms which can solve the problem with
certainty.


title: On complex positive definite functions on Z_n vanishing on squares

abstract:
  We generalize the Sarkozy-Furstenberg theorem on squares in difference sets
of integers, and show that, given any positive definite function f:Z_N->C with
density at least r(N), where r(N)=O((\log N)^{-c}), there is a perfect square
s<=N/2 such that f(s) is non-zero. We do not rely on the usual analysis of the
dichotomy of randomness and periodicity of a set and iterative application of
the Hardy-Littlewood method. Instead, we find a bound for the van der Corput
property of the set of squares.


title:
Effect of pulse duration on the x-ray emission from Ar clusters in
  intense laser fields

abstract:
  We study experimentally and theoretically the production of characteristic Ka
x-rays during the interaction of intense infrared laser pulse with large
N~10^4-10^6 atoms/ argon clusters. We focus on the influence of laser intensity
and pulse length on both the total x-ray yields and the charge-state
distributions of the emitting cluster argon ions. An experimental optimization
of the x-ray yield based on the setup geometry is presented and the role of the
effective focal volume is investigated. Our theoretical model is based on a
mean-field Monte-Carlo simulation and allows identifying the effective heating
of a subensemble of electrons in strong fields as the origin of the observed
x-ray emission. Well-controlled experimental conditions allow a quantitative
bench marking of absolute x-ray yields as well as charge state distributions of
ions having a K-shell vacancy. The presence of an optimum pulse duration that
maximizes the x-ray yield at constant laser energy is found to be the result of
the competition between the single cluster dynamics and the number of clusters
participating in the emission.


title:
Analytic continuation of Dirichlet series with almost periodic
  coefficients

abstract:
  We prove that an ordinary Dirichlet series with coefficients a(n)=g(n b) has
an abscissa of convergence 0 if g is an odd 1-periodic, real-analytic function
and b is Diophantine. We also show that if g is odd and has bounded variation
and b is of bounded Diophantine type r>1, then the abscissa of convergence is
smaller or equal than 1-1/r. Using a polylogarithm expansion, we prove that if
g is odd and real analytic and b is Diophantine, then the ordinary Dirichlet
series has an analytic continuation to the entire complex plane.


title:
Computer Simulations of Pulsatile Human Blood Flow Through 3D-Models of
  the Human Aortic Arch, Vessels of Simple Geometry and a Bifurcated Artery:
  Investigation of Blood Viscosity and Turbulent Effects

abstract:
  We report computational results of blood flow through a model of the human
aortic arch and a vessel of actual diameter and length. On the top of the
aortic arch the branching of the %%three arteries are included: the subclavian
and jugular. A realistic pulsatile flow is used in all simulations.
Calculations for bifurcation type vessels are also carried out and presented.
Different mathematical methods for numerical solution of the fluid dynamics
equations have been considered. The non-Newtonian behaviour of the human blood
is investigated together with turbulence effects. A detailed time-dependent
mathematical convergence test has been carried out. The results of computer
simulations of the blood flow in vessels of three different geometries are
presented: for pressure, strain rate and velocity component distributions we
found significant disagreements between our results obtained with realistic
non-Newtonian treatment of human blood and the widely used method in the
literature: a simple Newtonian approximation. A significant increase of the
strain rate and, as a result, a wall shear stress distribution, is found in the
region of the aortic arch. Turbulent effects are found to be important,
particularly in the case of bifurcation vessels.


title:
Two-loop electroweak fermionic corrections to sin^2 theta_{eff}^{b
  anti-b}

abstract:
  We present the first calculation of the two-loop electroweak fermionic
correction to the flavour-dependent effective weak-mixing angle for bottom
quarks, sin^2 theta_{eff}^{b anti-b}. For the evaluation of the missing
two-loop vertex diagrams, two methods are employed, one based on a
semi-numerical Bernstein-Tkachov algorithm and the second on asymptotic
expansions in the large top-quark mass. A third method based on dispersion
relations is used for checking the basic loop integrals. We find that for small
Higgs-boson mass values, M_H ~ 100 GeV, the correction is sizable, of order
O(10^{-4}).


title: Configuration spaces of convex and embedded polygons in the plane

abstract:
  This paper studies the configuration spaces of linkages whose underlying
graph is a single cycle. Assume that the edge lengths are such that there are
no configurations in which all the edges lie along a line. The main results are
that, modulo translations and rotations, each component of the space of convex
configurations is homeomorphic to a closed Euclidean ball and each component of
the space of embedded configurations is homeomorphic to a Euclidean space. This
represents an elaboration on the topological information that follows from the
convexification theorem of Connelly, Demaine, and Rote.


title: The Physics Prospects for CLIC

abstract:
  Following a brief outline of the CLIC project, this talk summarizes some of
the principal motivations for an e+ e- collider with E_CM = 3 TeV. It is shown
by several examples that CLIC would represent a significant step beyond the LHC
and ILC in its capabilities for precision measurements at high energies. It
would make possible a complete study of a light Higgs boson, including rare
decay modes, and would provide a unique tool to study a heavy Higgs boson. CLIC
could also complete the studies of supersymmetric spectra, if sparticles are
relatively light, and discover any heavier sparticles. It would also enable
deeper probes of extra dimensions, new gauge bosons and excited quarks or
leptons. CLIC has unique value to add to experimental particle physics,
whatever the LHC discovers.


title:
Analogue of Newton-Puiseux series for non-holonomic D-modules and
  factoring

abstract:
  We introduce a concept of a fractional-derivatives series and prove that any
linear partial differential equation in two independent variables has a
fractional-derivatives series solution with coefficients from a differentially
closed field of zero characteristic. The obtained results are extended from a
single equation to $D$-modules having infinite-dimensional space of solutions
(i. e. non-holonomic $D$-modules). As applications we design algorithms for
treating first-order factors of a linear partial differential operator, in
particular for finding all (right or left) first-order factors.


title: Non-holonomic Ideals in the Plane and Absolute Factoring

abstract:
  We study {\it non-holonomic} overideals of a left differential ideal
$J\subset F[\partial_x, \partial_y]$ in two variables where $F$ is a
differentially closed field of characteristic zero. The main result states that
a principal ideal $J=< P>$ generated by an operator $P$ with a separable {\it
symbol} $symb(P)$, which is a homogeneous polynomial in two variables, has a
finite number of maximal non-holonomic overideals. This statement is extended
to non-holonomic ideals $J$ with a separable symbol. As an application we show
that in case of a second-order operator $P$ the ideal $<P>$ has an infinite
number of maximal non-holonomic overideals iff $P$ is essentially ordinary. In
case of a third-order operator $P$ we give few sufficient conditions on $<P>$
to have a finite number of maximal non-holonomic overideals.


title: A Thermodynamic Classification of Real Numbers

abstract:
  A new classification scheme for real numbers is given, motivated by ideas
from statistical mechanics in general and work of Knauf and of Fiala and Kleban
in particular. Critical for this classification of a real number will be the
Diophantine properties of its continued fraction expansion.


title:
Three-Dimensional Simulations of Tidally Disrupted Solar-Type Stars and
  the Observational Signatures of Shock Breakout

abstract:
  We describe a three-dimensional simulation of a $1 M_{\odot}$ solar-type star
approaching a $10^{6} M_{\odot}$ black hole on a parabolic orbit with a
pericenter distance well within the tidal radius. While falling towards the
black hole, the star is not only stretched along the orbital direction but even
more severely compressed at right angles to the orbit. The overbearing degree
of compression achieved shortly after pericenter leads to the production of
strong shocks which largely homogenize the temperature profile of the star,
resulting in surface temperatures comparable to the initial temperature of the
star's core. This phenomenon, which precedes the fallback accretion phase,
gives rise to a unique double-peaked X-ray signature that, if detected, may be
one of the few observable diagnostics of how stars behave under the influence
of strong gravitational fields. If $\sim 10^{6} M_{\odot}$ black holes were
prevalent in small or even dwarf galaxies, the nearest of such flares may be
detectable by EXIST from no further away than the Virgo Cluster.


title: The Rees-Suschkewitsch Theorem for simple topological semigroups

abstract:
  We detect topological semigroups that are topological paragroups, i.e., are
isomorphic to a Rees product of a topological group over topological spaces
with a continuous sandwich function. We prove that a simple topological
semigroup $S$ is a topological paragroup if one of the following conditions is
satisfied: (1) $S$ is completely simple and the maximal subgroups of $S$ are
topological groups, (2) $S$ contains an idempotent and the square $S\times S$
is countably compact or pseudocompact, (3) $S$ is sequentially compact or each
power of $S$ is countably compact. The last item generalizes an old Wallace's
result saying that each simple compact topological semigroup is a topological
paragroup.


title: Quantum Gravity, CPT symmetry and Entangled States

abstract:
  There may unique ("smoking-gun") signatures of the breakdown of CPT symmetry,
induced in some models of Quantum Gravity entailing decoherence for quantum
matter. Such effects can be observed in entangled states of neutral mesons via
modifications of the respective Einstein-Podolsky-Rosen (EPR) correlators
("omega"-effect). In the talk I discuss experimental signatures and bounds of
the omega-effect in Phi- and B-factories, and argue that the effect might be
falsifiable at the next generation facilities.


title:
Construction of universal Thom-Whitney-a stratifications, their
  functoriality and Sard-type Theorem for singular varieties

abstract:
  {\bf Construction.} For a dominating polynomial mapping {$F: K^n\to K^l$}
with an isolated critical value at 0 ($K$ an algebraically closed field of
characteristic zero) we construct a closed {\it bundle} $G_F \subset T^{*}K^n
$. We restrict $ G_F $ over the critical points $Sing(F)$ of $ F$ in $
F^{-1}(0)$ and partition $Sing(F)$ into {\it 'quasistrata'} of points with the
fibers of $G_F$ of constant dimension. It turns out that T-W-a (Thom and
Whitney-a) stratifications 'near' $F^{-1}(0)$ exist iff the fibers of bundle
$G_F$ are orthogonal to the tangent spaces at the smooth points of the
quasistrata (e. g. when $ l=1$). Also, the latter are the orthogonal
complements over an irreducible component $ S $ of a quasistratum only if $S $
is {\bf universal} for the class of {T-W-a} stratifications, meaning that for
any $\{S_j'\}_j $ in the class, $ \Sing (F) = \cup_j S'_j $, there is a
component $S' $ of an $ S_j' $ with $S\cap S'$ being open and dense in both $S
$ and $ S' $.
  {\bf Results.} We prove that T-W-a stratifications with only universal strata
exist iff all fibers of $G_F$ are the orthogonal complements to the respective
tangent spaces to the quasistrata, and then the partition of $\Sing(F)$ by the
latter yields the coarsest {\it universal T-W-a stratification}.
  The key ingredient is our version of {\bf Sard-type Theorem for singular
spaces} in which a singular point is considered to be noncritical iff
nonsingular points nearby are 'uniformly noncritical' (e. g. for a dominating
map $ F: X \to Z $ meaning that the sum of the absolute values of the $l\times
l$ minors of the Jacobian matrix of $ F $, where $ l = \dim (Z) $, not only
does not vanish but, moreover, is separated from zero by a positive constant).


title:
Localized linear polynomial operators and quadrature formulas on the
  sphere

abstract:
  The purpose of this paper is to construct universal, auto--adaptive,
localized, linear, polynomial (-valued) operators based on scattered data on
the (hyper--)sphere $\SS^q$ ($q\ge 2$). The approximation and localization
properties of our operators are studied theoretically in deterministic as well
as probabilistic settings. Numerical experiments are presented to demonstrate
their superiority over traditional least squares and discrete Fourier
projection polynomial approximations. An essential ingredient in our
construction is the construction of quadrature formulas based on scattered
data, exact for integrating spherical polynomials of (moderately) high degree.
Our formulas are based on scattered sites; i.e., in contrast to such well known
formulas as Driscoll--Healy formulas, we need not choose the location of the
sites in any particular manner. While the previous attempts to construct such
formulas have yielded formulas exact for spherical polynomials of degree at
most 18, we are able to construct formulas exact for spherical polynomials of
degree 178.


title:
Emergence of Animals from Heat Engines. Part 1. Before the Snowball
  Earths

abstract:
  Previous studies modelled the origin of life and the emergence of
photosynthesis on the early Earth-i.e. the origin of plants-in terms of
biological heat engines that worked on thermal cycling caused by suspension in
convecting water. In this new series of studies, heat engines using a more
complex mechanism for thermal cycling are invoked to explain the origin of
animals as well. Biological exploitation of the thermal gradient above a
submarine hydrothermal vent is hypothesized, where a relaxation oscillation in
the length of a protein 'thermotether' would have yielded the thermal cycling
required for thermosynthesis. Such a thermal transition driven movement is not
impeded by the low Reynolds number of a small scale. In the model the
thermotether together with the protein export apparatus evolved into a
'flagellar proton pump' that turned into today's bacterial flagellar motor
after the acquisition of the proton-pumping respiratory chain. The flagellar
pump resembles Feynman's ratchet, and the 'flagellar computer' that implements
chemotaxis a Turing machine: the stator would have functioned as Turing's paper
tape and the stator's proton-transferring subunits with their variable
conformation as the symbols on the tape. The existence of a cellular control
centre in the cilium of the eukaryotic cell is proposed that would have evolved
from the prokaryotic flagellar computer.


title: On the Geroch-Traschen class of metrics

abstract:
  We compare two approaches to Semi-Riemannian metrics of low regularity. The
maximally "reasonable" distributional setting of Geroch and Traschen is shown
to be consistently contained in the more general setting of nonlinear
distributional geometry in the sense of Colombeau.


title:
Merging and splitting of clusters in the electromagnetic calorimeter of
  the KLOE detector

abstract:
  The work was carried out in the framework of the KLOE collaboration studying
the decays of the phi meson produced in the DAFNE accelerator in the collisions
of electron and positron. The main aim of this thesis was investigation of the
influence of the merging and splitting of clusters in decays with the high
multiplicity of gamma quanta, which are at most biased by these effects. For
this aim we implemented the full geometry and realistic material composition of
the barrel electromagnetic calorimeter in FLUKA package. The prepared Monte
Carlo based simulation program permits to achieve a fast generation of the
detector response separately for each interested reaction. The program was used
to study the reconstruction efficiency with the KLOE clustering algorithm as a
function of the photocathode quantum efficiency. It was also used to
investigate merging and splitting probabilities as a function of the quantum
efficiency. The conducted studies indicated that the increase of quantum
efficiency does not improve significantly the identification of clusters. The
influence of these effects was estimated for eta meson decays into 3 neutral
pions and K_short meson into 2 neutral pions.


title:
Dirichlet Forms on Laakso and Barlow-Evans Fractals of Arbitrary
  Dimension

abstract:
  In this paper we explore two constructions of the same family of metric
measure spaces. The first construction was introduced by Laakso in 2000 where
he used it as an example that Poincar\'e inequalities can hold on spaces of
arbitrary Hausdorff dimension. This was proved using minimal generalized upper
gradients. Following Cheeger's work these upper gradients can be used to define
a Sobolev space. We show that this leads to a Dirichlet form. The second
construction was introduced by Barlow and Evans in 2004 as a way of producing
exotic spaces along with Markov processes from simpler spaces and processes. We
show that for the correct base process in the Barlow Evans construction that
this Markov process corresponds to the Dirichlet form derived from the minimal
generalized upper gradients.


title:
Comparison of Resonant Inelastic X-Ray Scattering Spectra and Dielectric
  Loss Functions in Copper Oxides

abstract:
  We report empirical comparisons of Cu K-edge indirect resonant inelastic
x-ray scattering (RIXS) spectra, taken at the Brillouin zone center, with
optical dielectric loss functions measured in a number of copper oxides. The
RIXS data are obtained for Bi$_2$CuO$_4$, CuGeO$_3$, Sr$_2$Cu$_3$O$_4$Cl$_2$,
La$_2$CuO$_4$, and Sr$_2$CuO$_2$Cl$_2$, and analyzed by considering both
incident and scattered photon resonances. An incident-energy-independent
response function is then extracted. The dielectric loss functions, measured
with spectroscopic ellipsometry, agree well with this RIXS response, especially
in Bi$_2$CuO$_4$ and CuGeO$_3$.


title: A $\Gamma$-matrix generalization of the Kitaev model

abstract:
  We extend the Kitaev model defined for the Pauli-matrices to the Clifford
algebra of $\Gamma$-matrices, taking the $4 \times 4$ representation as an
example. On a decorated square lattice, the ground state spontaneously breaks
time-reversal symmetry and exhibits a topological phase transition. The
topologically non-trivial phase carries gapless chiral edge modes along the
sample boundary. On the 3D diamond lattice, the ground states can exhibit
gapless 3D Dirac cone-like excitations and gapped topological insulating
states. Generalizations to even higher rank $\Gamma$-matrices are also
discussed.


title: Mid- to Far-IR Emission and Star Formation in Early-Type Galaxies

abstract:
  Many early-type galaxies have been detected at wavelengths of 24 to 160
micron, but the emission is usually dominated by heating from an AGN or from
the evolved stellar population. Here we present Spitzer MIPS observations of a
sample of elliptical and lenticular galaxies that are rich in cold molecular
gas, and we investigate whether the MIR to FIR emission could be associated
with star formation activity. The 24 micron images show a rich variety of
structures, including nuclear point sources, rings, disks, and smooth extended
emission. Comparisons to matched-resolution CO and radio continuum images
suggest that the bulk of the 24 micron emission can be traced to star formation
with some notable exceptions. The 24 micron luminosities of the CO-rich
galaxies are typically a factor of 15 larger than what would be expected from
the dust associated with their evolved stars. In addition, FIR/radio flux
density ratios are consistent with star formation. We conclude that the star
formation rates in z=0 elliptical and lenticular galaxies, as inferred by other
authors from UV and optical data, are roughly consistent with the molecular gas
abundances and that the molecular gas is usually unstable to star formation
activity.


title:
Testing the Possible Intrinsic Origin of the Excess of Very Strong MgII
  Absorbers Along GRB Lines-of-Sight

abstract:
  The startling discovery of Prochter et al. (2006) that the frequency of very
strong (W_r(2796)>1 A) MgII absorbers along gamma-ray burst (GRB) lines of
sight ([dN/dz]_{GRB} = 0.90) is more than three times the frequency along
quasar lines of sight ([dN/dz]_{QSO} = 0.24), over similar redshift ranges, has
yet to be understood. We reconsider the possibility that the excess of very
strong MgII absorbers toward GRBs is intrinsic either to the GRBs themselves or
to their immediate environment, and associated with bulk outflows with
velocities as large as v_{max} ~ 0.3c. In order to examine this hypothesis, we
accumulate a sample of 27 W_r(2796) > 1 A absorption systems found toward 81
quasars, and compare their properties to those of 9 W_r(2796)>1 A absorption
systems found toward 6 GRBs; all systems have been observed at high spectral
resolution (R = 45,000) using the Ultraviolet and Visual Echelle Spectrograph
on the Very Large Telescope. We make multiple comparisons of the absorber
properties across the two populations, testing for differences in metallicity,
ionization state, abundance patterns, dust abundance, kinematics, and phase
structure. We find no significant differences between the two absorber
populations using any of these metrics, implying that, if the excess absorbers
toward GRB lines of sight are indeed intrinsic, they must be produced in a
process which has strong similarities to the processes yielding strong MgII
systems in association with intervening galaxies. Although this may seem a
priori unlikely, given the high outflow velocities required for any intrinsic
model, we note that the same conclusion was reached, recently, with respect to
the narrow absorption line systems seen in some quasars.


title: Magnetic field effects on neutrino production in microquasars

abstract:
  We investigate the effects of magnetic fields on neutrino production in
microquasars. We calculate the steady particle distributions for the pions and
muons generated in p-gamma and p-p interactions in the jet taking the effects
of all energy losses into account. The obtained neutrino emission is
significantly modified due to the synchrotron losses suffered by secondary
pions and muons. The estimates made for neutrino fluxes arriving on the Earth
imply that detection of high-energy neutrinos from the vicinity of the compact
object can be difficult. However, in the case of windy microquasars, the
interaction of energetic protons in the jet with matter of dense clumps of the
wind could produce detectable neutrinos. This is because the pions and muons at
larger distances from the compact object will not be affected by synchrotron
losses.


title: Asymptotic behaviour of variation of pure polarized TERP structures

abstract:
  The purpose of this paper is twofold. One is to give a survey of our study on
the reductions of harmonic bundles, and the other is to explain a simple
application in the study of TERP structure. In particular, we investigate the
asymptotic behaviour of the "new supersymmetric index" for variation of pure
polarized TERP structures.


title: The Figure Eight Knot Group is Conjugacy Separable

abstract:
  We prove that torsion free subgroups of PGL(2,C) (abstractly) commensurable
with the Euclidean Bianchi groups are conjugacy separable. As a consequence we
deduce the result stated in the title.


title:
Tuning magnetic frustration on the diamond lattice of the A-site
  magnetic spinels CoAl$_{2-x}$Ga$_x$O$_4$: Lattice expansion and site disorder

abstract:
  The spinels CoB$_2$O$_4$ with magnetic Co$^{2+}$ ions on the diamond lattice
A site can be frustrated because of competing near-neighbor ($J_1$) and
next-near neighbor ($J_2$) interactions. Here we describe attempts to tune the
relative strengths of these interactions by substitution on the non-magnetic
B-site. The system we employ is CoAl$_{2-x}$Ga$_x$O$_4$, where Al is
systematically replaced by the larger Ga, ostensibly on the B site. As
expected, Ga substitution expands the lattice, resulting in Co atoms on the
A-site being pushed further from one other and thereby weakening magnetic
interactions. In addition, Ga distributes between the B and the A site in a
concentration dependent manner displacing an increasing amount of Co from the A
site with increasing $x$. This increased inversion, which is confirmed by
neutron diffraction studies carried out at room temperature, affects magnetic
ordering very significantly, and changes the nature of the ground state.
Modeling of the magnetic coupling illustrates the complexity that arises from
the cation site disorder.


title: Light bound states of heavy fermions

abstract:
  In the Standard Model, a group of heavy fermions, e.g. top quarks, can
collectively strongly affect the Higgs field and create relatively long-lived
bound states. If there exist new generations of fermions with masses beyond 1
TeV, strong binding of several of them can make them lighter than even a single
heavy fermion. Using the mean field approximation we find multi-fermion states
with masses M ~ 5 v N^{1/2} ~ 1.2 N^{1/2} TeV, with N=2,3... being the total
number of heavy fermions bound together, and v=246 GeV the Higgs VEV. The
experimental search for multi-fermions within the range of energies 2-3 Tev
would either discover them, or suggest absence of new Standard Model fermions
with larger masses. Possible implications related to multi-top states and
baryonic asymmetry of the Universe are discussed.


title: Tunneling Time in the Landau-Zener Model

abstract:
  We give a general definition for the tunneling time in the Landau-Zener
model. This definition allows us to compute numerically the Landau-Zener
tunneling time at any sweeping rate without ambiguity. We have also obtained
analytical results in both the adiabatic limit and the sudden limit. Whenever
applicable, our results are compared to previous results and they are in good
agreement.


title:
Quantum mechanical potentials related to the prime numbers and Riemann
  zeros

abstract:
  Prime numbers are the building blocks of our arithmetic, however, their
distribution still poses fundamental questions. Bernhard Riemann showed that
the distribution of primes could be given explicitly if one knew the
distribution of the non-trivial zeros of the Riemann $\zeta(s)$ function.
According to the Hilbert-P{\'o}lya conjecture there exists a Hermitean operator
of which the eigenvalues coincide with the real part of the non-trivial zeros
of $\zeta(s)$. This idea encourages physicists to examine the properties of
such possible operators, and they have found interesting connections between
the distribution of zeros and the distribution of energy eigenvalues of quantum
systems. We apply the Mar{\v{c}}henko approach to construct potentials with
energy eigenvalues equal to the prime numbers and to the zeros of the
$\zeta(s)$ function. We demonstrate the multifractal nature of these potentials
by measuring the R{\'e}nyi dimension of their graphs. Our results offer hope
for further analytical progress.


title:
On elements of order p^s in the plane Cremona group over a field of
  characteristic p

abstract:
  We show that the plane Cremona group over a field of characteristic p > 0
does not contain elements of order of power of p larger than 2 and it does not
contain elements of order p^2 unless p =2. Also we describe conjugacy classes
of elements of order 4.


title:
Anisotropic magnetic diffuse scattering in an easy-plane type
  antiferromagnet ErNi$_{2}$Ge$_{2}$

abstract:
  We report on neutron scattering studies of a rare earth intermetallic
compound ErNi$_{2}$Ge$_{2}$. Polarized neutron scattering experiments revealed
that the magnetic ordered moment ${\bm m}$ lies in ab-plane. Taking account of
a lack of the third higher harmonic reflection, ErNi$_{2}$Ge$_{2}$ is
considered to have a helical magnetic structure. The magnetic scattering
profiles along the $[100]^{\ast}$- and the $[110]^{\ast}$-directions are well
described by the sum of Gaussian and modified-Lorentzian terms, even far below
$T_{\scriptsize N}$, indicating that short-range orders coexist with a
long-range order. Interestingly, the modified-Lorentzian-type diffuse
scattering is not present in the profiles along the $[001]^{\ast}$-direction.
The anisotropy of the diffuse scattering suggests that the short-range-order
consists of one dimensional long-range helices along the c-axis.


title: A self-interacting partially directed walk subject to a force

abstract:
  We consider a directed walk model of a homopolymer (in two dimensions) which
is self-interacting and can undergo a collapse transition, subject to an
applied tensile force. We review and interpret all the results already in the
literature concerning the case where this force is in the preferred direction
of the walk. We consider the force extension curves at different temperatures
as well as the critical-force temperature curve. We demonstrate that this model
can be analysed rigorously for all key quantities of interest even when there
may not be explicit expressions for these quantities available. We show which
of the techniques available can be extended to the full model, where the force
has components in the preferred direction and the direction perpendicular to
this. Whilst the solution of the generating function is available, its analysis
is far more complicated and not all the rigorous techniques are available.
However, many results can be extracted including the location of the critical
point which gives the general critical-force temperature curve. Lastly, we
generalise the model to a three-dimensional analogue and show that several key
properties can be analysed if the force is restricted to the plane of preferred
directions.


title:
Thermodynamic potential of a mechanical constitutive model for two-phase
  band flow

abstract:
  Starting from a simple mechanical constitutive model (the non-local diffusive
Johnson-Segalman model; DJS model), we provide a rigorous theoretical
explanation as to why a unique value of the stress plateau of a highly sheared
viscoelastic fluid is stably realized. The present analysis is based on a
reduction theory of the degrees of freedom of the model equation in the
neighborhood of a critical point, which leads to a time-evolution equation that
is equivalent to those for first-order phase transitions.


title:
The Observation of Percolation-Induced 2D Metal-Insulator Transition in
  a Si MOSFET

abstract:
  By analyzing the temperature ($T$) and density ($n$) dependence of the
measured conductivity ($\sigma$) of 2D electrons in the low density
($\sim10^{11}$cm$^{-2}$) and temperature (0.02 - 10 K) regime of high-mobility
(1.0 and 1.5 $\times 10^4$ cm$^2$/Vs) Si MOSFETs, we establish that the
putative 2D metal-insulator transition is a density-inhomogeneity driven
percolation transition where the density-dependent conductivity vanishes as
$\sigma (n) \propto (n - n_p)^p$, with the exponent $p \sim 1.2$ being
consistent with a percolation transition. The `metallic' behavior of $\sigma
(T)$ for $n > n_p$ is shown to be well-described by a semi-classical Boltzmann
theory, and we observe the standard weak localization-induced negative
magnetoresistance behavior, as expected in a normal Fermi liquid, in the
metallic phase.


title: Some examples of lifting problems from quotient algebras

abstract:
  We consider three lifting questions: Given a $C\sp{*}$-algebra $I$, if there
is a unital $C\sp{*}$-algebra $A$ contains $I$ as an ideal, is every unitary
from $A/I$ lifted to a unitary in $A$? is every unitary from $A/I$ lifted to an
extremal partial isometry? is every extremal partial isometry from $A/I$ lifted
to an extremal partial isometry? We show several constructions of $I$ which
serve as working examples or counter-examples for above questions.


title: Fractal properties of quantum spacetime

abstract:
  We show that in general a spacetime having a quantum group symmetry has also
a scale dependent fractal dimension which deviates from its classical value at
short scales, a phenomenon that resembles what observed in some approaches to
quantum gravity. In particular we analyze the cases of a quantum sphere and of
$\k$-Minkowski, the latter being relevant in the context of quantum gravity.


title:
Theoretical backgrounds of nonlinear THz spectroscopy of semiconductor
  superlattices

abstract:
  We consider terahertz absorption and gain in a single miniband of
semiconductor superlattice subject to a bichromatic electric field in the most
general case of commensurate frequencies of the probe and pump fields. Using an
exact solution of Boltzmann transport equation, we show that in the
small-signal limit the formulas for absorption always contain two distinct
terms related to the parametric and incoherent interactions of miniband
electrons with the alternating pump field. It provides a theoretical background
for a control of THz gain without switching to the negative differential
conductivity state. For pedagogical reasons we present derivations of formulas
in detail.


title: The Origin of the 24-micron Excess in Red Galaxies

abstract:
  Observations with the Spitzer Space Telescope have revealed a population of
red-sequence galaxies with a significant excess in their 24-micron emission
compared to what is expected from an old stellar population. We identify 900
red galaxies with 0.15<z<0.3 from the AGN and Galaxy Evolution Survey (AGES)
selected from the NOAO Deep Wide-Field Survey Bootes field. Using Spitzer/MIPS,
we classify 89 (~10%) with 24-micron infrared excess (f24>0.3 mJy). We
determine the prevalence of AGN and star-formation activity in all the AGES
galaxies using optical line diagnostics and mid-IR color-color criteria. Using
the IRAC color-color diagram from the IRAC Shallow Survey, we find that 64% of
the 24-micron excess red galaxies are likely to have strong PAH emission
features in the 8-micron IRAC band. This fraction is significantly larger than
the 5% of red galaxies with f24<0.3 mJy that are estimated to have strong PAH
emission, suggesting that the infrared emission is largely due to
star-formation processes. Only 15% of the 24-micron excess red galaxies have
optical line diagnostics characteristic of star-formation (64% are classified
as AGN and 21% are unclassifiable). The difference between the optical and
infrared results suggest that both AGN and star-formation activity is occurring
simultaneously in many of the 24-micron excess red galaxies. These results
should serve as a warning to studies that exclusively use optical line
diagnostics to determine the dominant emission mechanism in the infrared and
other bands. We find that ~40% of the 24-micron excess red galaxies are edge-on
spiral galaxies with high optical extinctions. The remaining sources are likely
to be red galaxies whose 24-micron emission comes from a combination of
obscured AGN and star-formation activity.


title:
Polynomial Representation of E6 and Its Combinatorial and PDE
  Implications

abstract:
  In this paper, we use partial differential equations to find the
decomposition of the polynomial algebra over the basic irreducible module of E6
into a sum of irreducible submodules. It turns out that the cubic polynomial
invariant corresponding to the Dicksons' invariant trilinear form is the unique
fundamental invariant. Moreover, we obtain a combinatorial identity saying that
the dimensions of certain irreducible modules of E6 are correlated by the
binomial coefficients of twenty-six. Furthermore, we find all the polynomial
solutions for the invariant differential operator corresponding to the Dickson
trilinear form in terms of the irreducible submodules.


title: Cascade Baryon Spectrum from Lattice QCD

abstract:
  A comprehensive study of the cascade baryon spectrum using lattice QCD
affords the prospect of predicting the masses of states not yet discovered
experimentally, and determining the spin and parity of those states for which
the quantum numbers are not yet known. The study of the cascades, containing
two strange quarks, is particularly attractive for lattice QCD in that the
chiral effects are reduced compared to states composed only of u/d quarks, and
the states are typically narrow. We report preliminary results for the cascade
spectrum obtained by using anisotropic N_f = 2 Wilson lattices with temporal
lattice spacing inverse 5.56 GeV.


title: Fermions on atom chips

abstract:
  We review our recent and ongoing work with Fermi gases on an atom chip. After
reviewing some statistical and thermodynamic properties of the ideal,
non-interacting Fermi gas, and a brief description of our atom chip and its
capabilities, we discuss our experimental approach to producing a potassium-40
degenerate Fermi gas (DFG) using sympathetic cooling by a rubidium-87
Bose-Einstein condensate on an atom chip. In doing so, we describe the factors
affecting the loading efficiency of the atom chip microtrap. This is followed
by a discussion of species selectivity in radio frequency manipulation of the
Bose-Fermi mixture, which we explore in the context of sympathetic evaporative
cooling and radio-frequency dressed adiabatic double-well potentials. Next, we
describe the incorporation of a crossed-beam dipole trap into the atom chip
setup, in which we generate and manipulate strongly interacting spin mixtures
of potassium-40. Finally, we conclude with a brief discussion of future
research directions with DFGs and atom chips.


title:
Studies on multiplication effect of noises of PPDs, and a proposal of a
  new structure to improve the performance

abstract:
  Pixelated Photon Detectors (PPDs) are the most promising semiconductor
photodetectors in recent years. One of the issues with the PPD is its high
noise rate. As well as random noise, PPD also exhibits so called after-pulsing
and optical crosstalk, and these limit the applicable range of its gain as well
as its size. By accurately measuring each of these causes of noises
independently, we quantitatively evaluated how the performance of the present
device is limited by multiplication effect of these noises. With this result
and the pulsing mechanism of PPD, we propose a new structure of PPD which could
have high gain with low noise.


title: Supernova Remnants in the AKARI IRC Survey of the Large Magellanic Cloud

abstract:
  We present the near- to mid-infared study of supernova remnants (SNRs) using
the AKARI IRC Survey of the Large Magellanic Cloud (LMC). The LMC survey
observed about a 10 square degree area of the LMC in five bands centered at 3,
7, 11, 15, and 24 \micron using the Infrared Camera (IRC) aboard AKARI. The
number of SNRs in the survey area is 21, which is about a half of the known LMC
SNRs. We systematically examined the AKARI images and identified eight SNRs
with distinguishable infrared emission. All of them were detected at $\gtrsim
10$ \micron and some at 3 and 7 \micron, too. We present their AKARI images and
fluxes. In the 11/15 \micron versus 15/24 \micron color-color diagram, the SNRs
appear to be aligned along a modified blackbody curve, representing thermal
emission from dust at temperatures between 90 and 190 K. There is a good
correlation between the 24 \micron and X-ray fluxes of the SNRs. It was also
found that there is a good correlation between the 24 \micron and radio fluxes
even if there is no direct physical connection between them. We considered the
origin of the detected mid-infrared emission in individual SNRs. We conclude
that the mid-infrared emissions in five SNRs that show morphologies similar to
the X-rays are dominated by thermal emission from hot dust heated by X-ray
emitting plasma. Their 15/24 \micron color temperatures are generally higher
than the Spitzer 24/70 \micron color temperatures, which suggests that a
single-temperature dust model cannot describe the full spectral energy
distribution (SED) of the SNRs. It also implies that our understanding of the
full SED is essential for estimating the dust destruction rate of grains by SNR
shocks.


title: Intrinsically triple-linked graphs in RP^3

abstract:
  Flapan--Naimi--Pommersheim showed that every spatial embedding of $K_{10}$,
the complete graph on ten vertices, contains a non-split three-component link;
that is, $K_{10}$ is intrinsically triple-linked in $\mathbb{R}^3$. The work of
Bowlin--Foisy and Flapan--Foisy--Naimi--Pommersheim extended the list of known
intrinsically triple-linked graphs in $\mathbb{R}^3$ to include several other
families of graphs. In this paper, we will show that while some of these graphs
can be embedded 3-linklessly in $\mathbb{R}P^3$, $K_{10}$ is intrinsically
triple-linked in $\mathbb{R}P^3$.


title: Projections of structure functions in a spin-one hadrons

abstract:
  There exist new polarized structure functions in a spin-one hadron. In deep
inelastic electron scattering from a spin-one hadron, there are eight structure
functions F_1, F_2, g_1, g_2, b_1, b_2, b_3, and b_4. We derive projections to
these eight functions from the hadron tensor W^{mu nu} by combinations of the
hadron momentum and its polarization vectors.


title: Lattice study of flavor SU(3) breaking in hyperon beta decay

abstract:
  We present a quenched lattice calculation of all six form factors: vector
[f_1(q^2)], weak magnetism [f_2(q^2)], induced scalar [f_3(q^2)], axial-vector
[g_1(q^2)], weak electricity [g_2(q^2)] and induce pseudoscalar [g_3(q^2)] form
factors in hyperon semileptonic decay Xi^0 -> Sigma^{+} l nu using domain wall
fermions. The q^2 dependences of all form factors in the relatively low q^2
region are examined in order to evaluate their values at zero momentum
transfer. The Xi^0 -> Sigma^+ transition is highly sensitive to flavor SU(3)
breaking since this decay corresponds to the direct analogue of neutron beta
decay under the exchange of the down quark with the strange quark. The pattern
of flavor SU(3) breaking effects in the hyperon beta decay is easily exposed in
a comparison to results for neutron beta decay. We measure SU(3)-breaking
corrections to f_1(0), f_2(0)/f_1(0) and g_1(0)/f_1(0). A sign of the leading
order corrections, of which the size is less than a few %, on f_1(0) is likely
negative, while f_2(0)/f_1(0) and g_1(0)/f_1(0) receive positive corrections of
order 16% and 5% respectively. The observed patterns of the deviation from the
values in the exact SU(3) limit does not support some of model estimates. We
show that there are nonzero second-class form factors in the Xi^0 -> Sigma^+
decay, measuring f_3(0)/f_1(0)=0.14(10) and g_2(0)/g_1(0)=0.68(18), which are
comparable to the size of first-order SU(3) breaking. It is also found that the
SU(3) breaking effect on g_3(0)/g_1(0) agree with the prediction of the
generalized pion-pole dominance.