title: Empirical entropy in context

abstract:
  We trace the history of empirical entropy, touching briefly on its relation
to Markov processes, normal numbers, Shannon entropy, the Chomsky hierarchy,
Kolmogorov complexity, Ziv-Lempel compression, de Bruijn sequences and
stochastic complexity.


title: A hyperbolic approach to exp_3(S^1)

abstract:
  In this paper we investigate a new geometric method of studying exp_k(S^1),
the set of all non-empty subsets of the circle of cardinality at most k. By
considering the circle as the boundary of the hyperbolic plane we are able to
use its group of isometries to determine explicitely the structure of its first
few configuration spaces. We then study how these configuration spaces fit
together in their union, exp_3(S^1), to reprove an old theorem of Bott as well
as to offer a new proof (following that of E. Shchepin) of the fact that the
embedding exp_1(S^1) into exp_3(S^1) is the trefoil knot.


title:
Correlation between $T_c$ and anisotropic scattering in
  Tl$_2$Ba$_2$CuO$_{6+\delta}$

abstract:
  Angle-dependent magnetoresistance measurements are used to determine the
isotropic and anisotropic components of the transport scattering rate in
overdoped Tl$_2$Ba$_2$CuO$_{6+\delta}$ for a range of $T_c$ values between 15K
and 35K. The size of the anisotropic scattering term is found to scale linearly
with $T_c$, establishing a link between the superconducting and normal state
physics. Comparison with results from angle resolved photoemission spectroscopy
indicates that the transport and quasiparticle lifetimes are distinct.


title: A version of the proof for Peres-Schlag's theorem on lacunary sequences

abstract:
  We present a proof of a multidimensional version of Peres-Schlag's theorem on
Diophantine approximations with lacunary sequences.


title:
Insulator to semiconductor transition and magnetic properties of the
  one-dimensional S = 1/2 system In_2VO_5

abstract:
  We report structural, magnetization, electrical resistivity and nuclear- and
electron spin resonance data of the complex transition metal oxide In_2VO_5 in
which structurally well-defined V-O chains are realized. An itinerant character
of the vanadium d-electrons and ferromagnetic correlations, revealed at high
temperatures, are contrasted with the insulating behavior and predominantly
antiferromagnetic exchange between the localized V^{4+} S = 1/2-magnetic
moments which develop below a certain characteristic temperature T* ~ 120 K.
Eventually the compound exhibits short-range magnetic order at $T_SRO ~ 20 K.
We attribute this crossover occurring around T* to the unusual anisotropic
thermal contraction of the lattice which changes significantly the overlap
integrals and the character of magnetic intra- and interchain interactions.


title:
Feasibility of acoustic neutrino detection in ice: First results from
  the South Pole Acoustic Test Setup (SPATS)

abstract:
  Astrophysical neutrinos in the EeV range (particularly those generated by the
interaction of cosmic rays with the cosmic microwave background) promise to be
a valuable tool to study astrophysics and particle physics at the highest
energies. Much could be learned from temporal, spectral, and angular
distributions of ~100 events, which could be collected by a detector with ~100
km^3 effective volume in a few years. Scaling the optical Cherenkov technique
to this scale is prohibitive. However, using the thick ice sheet available at
the South Pole, the radio and acoustic techniques promise to provide sufficient
sensitivity with sparse instrumentation. The best strategy may be a hybrid
approach combining all three techniques. A new array of acoustic transmitters
and sensors, the South Pole Acoustic Test Setup, was installed in three IceCube
holes in January 2007. The purpose of SPATS is to measure the attenuation
length, background noise, and sound speed for 10-100 kHz acoustic waves.
Favorable results would pave the way for a large hybrid array. SPATS is the
first array to study the possibility of acoustic neutrino detection in ice, the
medium expected to be best for the purpose. First results from SPATS are
presented.


title: The Product Space Conditions the Development of Nations

abstract:
  Economies grow by upgrading the type of products they produce and export. The
technology, capital, institutions and skills needed to make such new products
are more easily adapted from some products than others. We study the network of
relatedness between products, or product space, finding that most upscale
products are located in a densely connected core while lower income products
occupy a less connected periphery. We show that countries tend to move to goods
close to those they are currently specialized in, allowing nations located in
more connected parts of the product space to upgrade their exports basket more
quickly. Most countries can reach the core only if they jump over empirically
infrequent distances in the product space. This may help explain why poor
countries have trouble developing more competitive exports, failing to converge
to the income levels of rich countries.


title:
Spin dynamics in InAs-nanowire quantum-dots coupled to a transmission
  line

abstract:
  We study theoretically electron spins in nanowire quantum dots placed inside
a transmission line resonator. Because of the spin-orbit interaction, the spins
couple to the electric component of the resonator electromagnetic field and
enable coherent manipulation, storage, and read-out of quantum information in
an all-electrical fashion. Coupling between distant quantum-dot spins, in one
and the same or different nanowires, can be efficiently performed via the
resonator mode either in real time or through virtual processes. For the latter
case we derive an effective spin-entangling interaction and suggest means to
turn it on and off. We consider both transverse and longitudinal types of
nanowire quantum-dots and compare their manipulation timescales against the
spin relaxation times. For this, we evaluate the rates for spin relaxation
induced by the nanowire vibrations (phonons) and show that, as a result of
phonon confinement in the nanowire, this rate is a strongly varying function of
the spin operation frequency and thus can be drastically reduced compared to
lateral quantum dots in GaAs. Our scheme is a step forward to the formation of
hybrid structures where qubits of different nature can be integrated in a
single device.


title:
Spin Valve Effect in Self-exchange Biased Ferromagnetic
  Metal/Semiconductor Bilayers

abstract:
  We report magnetization and magetoresistance measurements in hybrid
ferromagnetic metal/semiconductor heterostructures comprised of MnAs/(Ga,Mn)As
bilayers. Our measurements show that the (metallic) MnAs and (semiconducting)
(Ga,Mn)As layers are exchange coupled, re- sulting in an exchange biasing of
the magnetically softer (Ga,Mn)As layer that weakens with layer thickness.
Magnetoresistance measurements in the current-perpendicular-to-the-plane
geometry show a spin valve effect in these self-exchange biased bilayers.
Similar measurements in MnAs/p- GaAs/(Ga,Mn)As trilayers show that the exchange
coupling diminishes with spatial separation between the layers.


title:
The neutrino emission due to plasmon decay and neutrino luminosity of
  white dwarfs

abstract:
  One of the effective mechanisms of neutrino energy losses in red giants,
presupernovae and in the cores of white dwarfs is the emission of
neutrino-antineutrino pairs in the process of plasmon decay. In this paper, we
numerically calculate the emissivity due to plasmon decay in a wide range of
temperatures (10^7-10^11) K and densities (200-10^14) g cm^-3. Numerical
results are approximated by convenient analytical expressions. We also
calculate and approximate by analytical expressions the neutrino luminosity of
white dwarfs due to plasmon decay, as a function of their mass and internal
temperature. This neutrino luminosity depends on the chemical composition of
white dwarfs only through the parameter mu_e (the net number of baryons per
electron) and is the dominant neutrino luminosity in all white dwarfs at the
neutrino cooling stage.


title: Search for flavor-changing-neutral-current D meson decays

abstract:
  We study the flavor-changing-neutral-current process c to u mu+ mu- using 1.3
fb^-1 of p p bar collisions at sqrt(s) = 1.96 TeV recorded by the D0 detector
operating at the Fermilab Tevatron Collider. We see clear indications of the
Ds+ and D+ to phi pi+ to mu+ mu- pi+ final states with significance greater
than four standard deviations above background for the D+ state. We search for
the continuum decay of D+ to pi+mu+mu- in the dimuon invariant mass spectrum
away from the phi resonance. We see no evidence of signal above background and
set a limit of B(D+ to pi+mu+mu-) < 3.9 x 10^-6 at the 90% C.L. This limit
places the most stringent constraint on new phenomena in the c to u mu+ mu-
transition.


title: Modulation of Negative Index Metamaterials in the Near-IR Range

abstract:
  Optical modulation of the effective refractive properties of a "fishnet"
metamaterial with a Ag/Si/Ag heterostructure is demonstrated in the near-IR
range and the associated fast dynamics of negative refractive index is studied
by pump-probe method. Photo excitation of the amorphous Si layer at visible
wavelength and corresponding modification of its optical parameters is found to
be responsible for the observed modulation of negative refractive index in
near-IR.


title: Non-uniform mixing of quantum walk on cycles

abstract:
  A classical lazy random walk on cycles is known to mix to the uniform
distribution. In contrast, we show that a continuous-time quantum walk on
cycles exhibit strong non-uniform mixing properties. Our results include the
following:
  - The instantaneous distribution of a quantum walk on most even-length cycles
is never uniform. - The average distribution of a quantum walk on any Abelian
circulant graph is never uniform. As a corollary, the average distribution of a
quantum walk on any standard circulant graph, such as the cycles, complete
graphs, and even hypercubes, is never uniform.


title: Time-dependent Dalitz Plot Analysis of B0 --> Ks pi+ pi-

abstract:
  We perform a time-dependent Dalitz plot analysis of $B^0 \to
K^0_{\scriptscriptstyle S}\pi^+\pi^-$ in order to extract the ${CP}$ violation
parameters of $f_0(980) K^0_{\scriptscriptstyle S}$ and $\rho^0(770)
K^0_{\scriptscriptstyle S}$ and direct ${CP}$-asymmetries of $K^{*+}(892)
\pi^-$. The results are obtained from a data sample of $(383\pm3)\times10^{6}$
$B \bar{B}$ decays, collected with the BaBar detector at the PEP2
asymmetric--energy $B$ factory at SLAC. The measured values of $2\beta_{\rm
eff}$ in $B^0$ decays to $f_0(980)K^0_{\scriptscriptstyle S}$ and $\rho^0(770)
K^0_{\scriptscriptstyle S}$ are $(89^{+22}_{-20} \pm 5 \pm 8)^\circ$ and $(37
^{+19}_{-17} \pm 5 \pm 6)^\circ$, respectively, where the first quoted
uncertainty is statistical, the second is systematic and the third is Dalitz
plot signal model uncertainty. We measure the significance of $2\beta_{\rm
eff}(f_0(980)K^0_{\scriptscriptstyle S})\neq 0$ to be $4.3 \sigma$. In decays
to $K^*(892) \pi$ we find $A_{{CP}} = -0.18 \pm 0.10 \pm 0.03 \pm 0.03$. The
measured phase difference between the decay amplitudes of $B^0 \to K^{*+}(892)
\pi^-$ and $\bar{B}^0 \to K^{*-}(892) \pi^+$ is $(-164 \pm 24 \pm 12 \pm
15)^\circ$. All results are preliminary.


title: Where are the degrees of freedom responsible for black hole entropy?

abstract:
  Considering the entanglement between quantum field degrees of freedom inside
and outside the horizon as a plausible source of black hole entropy, we address
the question: {\it where are the degrees of freedom that give rise to this
entropy located?} When the field is in ground state, the black hole area law is
obeyed and the degrees of freedom near the horizon contribute most to the
entropy. However, for excited state, or a superposition of ground state and
excited state, power-law corrections to the area law are obtained, and more
significant contributions from the degrees of freedom far from the horizon are
shown.


title:
Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical
  confinement

abstract:
  We report extensive simulations of the relaxation dynamics of a self-avoiding
polymer confined inside a cylindrical pore. In particular, we concentrate on
examining how confinement influences the scaling behavior of the global
relaxation time of the chain, t, with the chain length N and pore diameter D.
An earlier scaling analysis based on the de Gennes blob picture led to t ~
N^2D^(1/3). Our numerical effort that combines molecular dynamics and Monte
Carlo simulations, however, consistently produces different t-results for N up
to 2000. We argue that the previous scaling prediction is only asymptotically
valid in the limit N >> D^(5/3) >> 1, which is currently inaccessible to
computer simulations and, more interestingly, is also difficult to reach in
experiments. Our results are thus relevant for the interpretation of recent
experiments with DNA in nano- and micro-channels.


title:
Beaming Binaries - a New Observational Category of Photometric Binary
  Stars

abstract:
  The new photometric space-borne survey missions CoRoT and Kepler will be able
to detect minute flux variations in binary stars due to relativistic beaming
caused by the line-of-sight motion of their components. In all but very short
period binaries (P>10d), these variations will dominate over the ellipsoidal
and reflection periodic variability. Thus, CoRoT and Kepler will discover a new
observational class: photometric beaming binary stars. We examine this new
category and the information that the photometric variations can provide. The
variations that result from the observatory heliocentric velocity can be used
to extract some spectral information even for single stars.


title:
Distribution of the time at which the deviation of a Brownian motion is
  maximum before its first-passage time

abstract:
  We calculate analytically the probability density $P(t_m)$ of the time $t_m$
at which a continuous-time Brownian motion (with and without drift) attains its
maximum before passing through the origin for the first time. We also compute
the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the
driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim
t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In
presence of a drift towards the origin, $P(t_m)$ decays exponentially for large
$t_m$. The results from numerical simulations are in excellent agreement with
our analytical predictions.


title: Gain of Regularity for the KP-I Equation

abstract:
  In this paper we study the smoothness properties of solutions to the KP-I
equation. We show that the equation's dispersive nature leads to a gain in
regularity for the solution. In particular, if the initial data $\phi$
possesses certain regularity and sufficient decay as $x \to \infty$, then the
solution $u(t)$ will be smoother than $\phi$ for $0 < t \leq T$ where $T$ is
the existence time of the solution.


title:
Spitzer IRS Observations of the Galactic Center: Shocked Gas in the
  Radio Arc Bubble

abstract:
  We present Spitzer IRS spectra (R ~600, 10 - 38 micron) of 38 positions in
the Galactic Center (GC), all at the same Galactic longitude and spanning
plus/minus 0.3 degrees in latitude. Our positions include the Arches Cluster,
the Arched Filaments, regions near the Quintuplet Cluster, the ``Bubble'' lying
along the same line-of-sight as the molecular cloud G0.11-0.11, and the diffuse
interstellar gas along the line-of-sight at higher Galactic latitudes. From
measurements of the [O IV], [Ne II], [Ne III], [Si II], [S III], [S IV], [Fe
II], [Fe III], and H_2 S(0), S(1), and S(2) lines we determine the gas
excitation and ionic abundance ratios. The Ne/H and S/H abundance ratios are ~
1.6 times that of the Orion Nebula. The main source of excitation is
photoionization, with the Arches Cluster ionizing the Arched Filaments and the
Quintuplet Cluster ionizing the gas nearby and at lower Galactic latitudes
including the far side of the Bubble. In addition, strong shocks ionize gas to
O^{+3} and destroy dust grains, releasing iron into the gas phase (Fe/H ~ 1.3
times 10^{-6} in the Arched Filaments and Fe/H ~ 8.8 times 10^{-6} in the
Bubble). The shock effects are particularly noticeable in the center of the
Bubble, but O$^{+3}$ is present in all positions. We suggest that the shocks
are due to the winds from the Quintuplet Cluster Wolf-Rayet stars. On the other
hand, the H_2 line ratios can be explained with multi-component models of warm
molecular gas in photodissociation regions without the need for H_2 production
in shocks.


title: Internal Secular Evolution in Disk Galaxies: The Growth of Pseudobulges

abstract:
  Observational and theoretical evidence that internal, slow ("secular")
evolution reshapes galaxy disks is reviewed in Kormendy & Kennicutt (2004,
ARAA, 42, 603). This update has three aims. First, I emphasize that this
evolution is very general -- it is as fundamental to the evolution of galaxy
disks as (e.g.) core collapse is to globular clusters, as the production of hot
Jupiters is to the evolution of protoplanetary disks, and as evolution to red
giants containing proto-white-dwarfs is to stellar evolution. One consequence
for disk galaxies is the buildup of dense central components that get mistaken
for classical (i.e., merger-built) bulges but that were grown out of disk stars
and gas. We call these pseudobulges. Second, I review new results on
pseudobulge star formation and structure and on the distinction between boxy
and disky pseudobulges. Finally, I highlight how these results make a galaxy
formation problem more acute. How can hierarchical clustering produce so many
pure disk galaxies with no evidence for merger-built bulges?


title: Attribute Estimation and Testing Quasi-Symmetry

abstract:
  A Boolean function is symmetric if it is invariant under all permutations of
its arguments; it is quasi-symmetric if it is symmetric with respect to the
arguments on which it actually depends. We present a test that accepts every
quasi-symmetric function and, except with an error probability at most delta>0,
rejects every function that differs from every quasi-symmetric function on at
least a fraction epsilon>0 of the inputs. For a function of n arguments, the
test probes the function at O((n/epsilon)\log(n/delta)) inputs. Our
quasi-symmetry test acquires information concerning the arguments on which the
function actually depends. To do this, it employs a generalization of the
property testing paradigm that we call attribute estimation. Like property
testing, attribute estimation uses random sampling to obtain results that have
only "one-sided'' errors and that are close to accurate with high probability.


title: How common are long Gamma-Ray Bursts in the Local Universe?

abstract:
  The two closest Gamma-Ray Bursts so far detected (GRBs 980425 & 060218) were
both under-luminous, spectrally soft, long duration bursts with smooth,
single-peaked light curves. Only of the order of 100 GRBs have measured
redshifts, and there are, for example, 2704 GRBs in the BATSE catalogue alone.
It is therefore plausible that other nearby GRBs have been observed but not
identified as relatively nearby. Here we search for statistical correlations
between BATSE long duration GRBs and galaxy samples with recession velocities v
<= 11,000 km/s (z = 0.0367, ~ 155 Mpc) selected from two catalogues of nearby
galaxies. We also examine the correlations using burst sub-samples restricted
to those with properties similar to the two known nearby bursts. Our results
show correlation of the entire long GRB sample to remain consistent with zero
out to the highest radii considered whereas a sub-sample selected to be low
fluence, spectrally soft, with smooth single-peaked light curves (177 bursts)
demonstrates increased correlation with galaxies within ~ 155 Mpc. The measured
correlation (28% +/- 16% of the sample) suggests that BATSE observed between 2
and 9 long duration GRBs per year similar to, and from within similar distances
to GRBs 980425 and 060218. This implies an observed local rate density (to
BATSE limits) of 700 +/- 360 Gpc^{-3}yr^{-1} within 155 Mpc.


title: Quantum glass phases in the disordered Bose-Hubbard model

abstract:
  The phase diagram of the Bose-Hubbard model in the presence of off-diagonal
disorder is determined using Quantum Monte Carlo simulations. A sequence of
quantum glass phases intervene at the interface between the Mott insulating and
the Superfluid phases of the clean system. In addition to the standard Bose
glass phase, the coexistence of gapless and gapped regions close to the Mott
insulating phase leads to a novel Mott glass regime which is incompressible yet
gapless. Numerical evidence for the properties of these phases is given in
terms of global (compressibility, superfluid stiffness) and local
(compressibility, momentum distribution) observables.


title:
Morphological effects on surface plasmon polaritons at the planar
  interface of a metal and a columnar thin film The Planar Interface Of A Metal
  And A Columnar Thin Film

abstract:
  Surface plasmon polaritons (SPPs) at the interface of a columnar thin film
(CTF) and metal exist over a range of propagation directions relative to the
morphology of the CTF which depends on the tilt of the columns in the CTF. The
phase speed of the SPP wave varies mainly as a function of the tilt of the CTF
columns. Both the confinement of the SPP wave to the interface and the decay of
the SPP wave along the direction of propagation depend strongly on the
direction of propagation relative to the morphologically significant plane of
the CTF. The greater the columnar tilt in relation to the interface, the
shorter is the range of propagation. Because of its porosity and the ability to
engineer this biaxial dielectric material, the CTF-metal interface may be more
attractive than traditional methods of producing SPPs.


title: Computing arithmetic invariants for hyperbolic reflection groups

abstract:
  We describe a collection of computer scripts written in PARI/GP to compute,
for reflection groups determined by finite-volume polyhedra in $\mathbb{H}^3$,
the commensurability invariants known as the invariant trace field and
invariant quaternion algebra. Our scripts also allow one to determine
arithmeticity of such groups and the isomorphism class of the invariant
quaternion algebra by analyzing its ramification.
  We present many computed examples of these invariants. This is enough to show
that most of the groups that we consider are pairwise incommensurable. For
pairs of groups with identical invariants, not all is lost: when both groups
are arithmetic, having identical invariants guarantees commensurability. We
discover many ``unexpected'' commensurable pairs this way. We also present a
non-arithmetic pair with identical invariants for which we cannot determine
commensurability.


title:
Precision polarimetry with real-time mitigation of optical-window
  birefringence

abstract:
  Optical-window birefringence is frequently a major obstacle in experiments
measuring changes in the polarization state of light traversing a sample under
investigation. It can contribute a signal indistinguishable from that due to
the sample and complicate the analysis. Here, we explore a method to measure
and compensate for the birefringence of an optical window using the reflection
from the last optical surface before the sample. We demonstrate that this
arrangement can cancel out false signals due to the optical-window
birefringence-induced ellipticity drift to about 1%, for the values of total
ellipticity less than 0.25 rad.


title: 3D Spectroscopy and the Virtual Observatory

abstract:
  Integral field, or 3D, spectroscopy is the technique of obtaining spectral
information over a two-dimensional, hopefully contiguous, field of view. While
there is some form of astronomical 3D spectroscopy at all wavelengths, there
has been a rapid increase in interest in optical and near-infrared 3D
spectroscopy. This has resulted in the deployment of a large variety of
integral-field spectrographs on most of the large optical/infrared telescopes.
The amount of IFU data available in observatory archives is large and growing
rapidly. The complications of treating IFU data as both imaging and
spectroscopy make it a special challenge for the virtual observatory. This
article describes the various techniques of optical and near-infrared
spectroscopy and some of the general needs and issues related to the handling
of 3D data by the virtual observatory.


title: In-Medium Hadronic Interactions and the Nuclear Equation of State

abstract:
  Microscopic studies of nuclear matter under diverse conditions of density and
asymmetry are of great contemporary interest. Concerning terrestrial
applications, they relate to future experimental facilities that will make it
possible to study systems with extreme neutron-to-proton ratio. In this talk, I
will review recent efforts of my group aimed at exploring nuclear interactions
in the medium through the nuclear equation of state (EoS). The approach we take
is microscopic and relativistic, with the predicted EoS properties derived from
realistic nucleon-nucleon potentials. I will also discuss work in progress.
Most recently, we completed a DBHF calculation of the $\Lambda$ hyperon binding
energy in nuclear matter.


title: Detecting separable states via semidefinite programs

abstract:
  We introduce a new technique to detect separable states using semidefinite
programs. This approach provides a sufficient condition for separability of a
state that is based on the existence of a certain local linear map applied to a
known separable state. When a state is shown to be separable, a proof of this
fact is provided in the form of an explicit convex decomposition of the state
in terms of product states. All states in the interior of the set of separable
states can be detected in this way, except maybe for a set of measure zero.
Even though this technique is more suited for a numerical approach, a new
analytical criterion for separability can also be derived.


title:
On the Number of Facets of Three-Dimensional Dirichlet Stereohedra IV:
  Quarter Cubic Groups

abstract:
  In this paper we finish the intensive study of three-dimensional Dirichlet
stereohedra started by the second author and D. Bochis, who showed that they
cannot have more than 80 facets, except perhaps for crystallographic space
groups in the cubic system.
  Taking advantage of the recent, simpler classification of three-dimensional
crystallographic groups by Conway, Delgado-Friedrichs, Huson and Thurston, in a
previous paper we proved that Dirichlet stereohedra for any of the 27 "full"
cubic groups cannot have more than 25 facets. Here we study the remaining
"quarter" cubic groups. With a computer-assisted method, our main result is
that Dirichlet stereohedra for the 8 quarter groups, hence for all
three-dimensional crystallographic groups, cannot have more than 92 facets.


title:
From high temperature supercondutivity to quantum spin liquid: progress
  in strong correlation physics

abstract:
  This review gives a rather general discussion of high temperature
superconductors as an example of a strongly correlated material. The argument
is made that in view of the many examples of unconventional superconductors
discovered in the past twenty years, we should no longer be surprised that
superconductivity emerges as a highly competitive ground state in systems where
Coulomb repulsion plays a dominant role. The physics of the cuprates is
discussed, emphasizing the unusual pseudogap phase in the underdoped region. It
is argued that the resonating valence bond (RVB) picture, as formulated using
gauge theory with fermionic and bosonic matter fields, gives an adequate
physical understanding, even though many details are beyond the powers of
current calculational tools. The recent discovery of quantum oscillations in a
high magnetic field is discussed in this context. Meanwhile, the problem of the
quantum spin liquid (a spin system with antiferromagnetic coupling which
refuses to order even at zero temperature) is a somewhat simpler version of the
high $T_c$ problem where significant progress has been made recently. It is
understood that the existence of matter fields can lead to de-confinement of
the U(1) gauge theory in 2+1 dimensions, and novel new particles (called
fractionalized particles), such as fermionic spinons which carry spin ${1\over
2}$ and no charge, and gapless gauge bosons can emerge to create a new critical
state at low energies. We even have a couple of real materials where such a
scenario may be realized experimentally. The article ends with answers to
questions such as: what limits $T_c$ if pairing is driven by an electronic
energy scale? why is the high $T_c$ problem hard? why is there no consensus?
and why is the high $T_c$ problem important?


title:
A posteriori error estimates for finite element approximations of the
  Cahn-Hilliard equation and the Hele-Shaw flow

abstract:
  This paper develops a posteriori error estimates of residual type for
conforming and mixed finite element approximations of the fourth order
Cahn-Hilliard equation $u_t+\De\bigl(\eps \De u-\eps^{-1} f(u)\bigr)=0$. It is
shown that the {\it a posteriori} error bounds depends on $\eps^{-1}$ only in
some low polynomial order, instead of exponential order. Using these a
posteriori error estimates, we construct an adaptive algorithm for computing
the solution of the Cahn-Hilliard equation and its sharp interface limit, the
Hele-Shaw flow. Numerical experiments are presented to show the robustness and
effectiveness of the new error estimators and the proposed adaptive algorithm.


title: Pressure-induced Superconductivity in CaLi2

abstract:
  A search for superconductivity has been carried out on the hexagonal
polymorph of Laves-phase CaLi2, a compound for which Feng, Ashcroft, and
Hoffmann predict highly anomalous behavior under pressure. No superconductivity
is observed above 1.10 K at ambient pressure. However, high-pressure ac
susceptibility and electrical resistivity studies to 81 GPa reveal bulk
superconductivity in CaLi2 at temperatures as high as 13 K. The normal-state
resistivity shows a dramatic increase with pressure.


title: Optimal Control Theory for Continuous Variable Quantum Gates

abstract:
  We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.


title: Control Landscapes for Observable Preparation with Open Quantum Systems

abstract:
  A quantum control landscape is defined as the observable as a function(al) of
the system control variables. Such landscapes were introduced to provide a
basis to understand the increasing number of successful experiments controlling
quantum dynamics phenomena. This paper extends the concept to encompass the
broader context of the environment having an influence. For the case that the
open system dynamics are fully controllable, it is shown that the control
landscape for open systems can be lifted to the analysis of an equivalent
auxiliary landscape of a closed composite system that contains the
environmental interactions. This inherent connection can be analyzed to provide
relevant information about the topology of the original open system landscape.
Application to the optimization of an observable expectation value reveals the
same landscape simplicity observed in former studies on closed systems. In
particular, no false sub-optimal traps exist in the system control landscape
when seeking to optimize an observable, even in the presence of complex
environments. Moreover, a quantitative study of the control landscape of a
system interacting with a thermal environment shows that the enhanced
controllability attainable with open dynamics significantly broadens the range
of the achievable observable values over the control landscape.


title: Automorphisms of a polynomial ring which admit reductions of type I

abstract:
  Recently, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of
a polynomial ring. To solve the conjecture, they defined notions called
reductions of types I--IV for automorphisms of a polynomial ring. An
automorphism admitting a reduction of type I was first found by
Shestakov-Umirbaev. Using a computer, van den Essen--Makar-Limanov--Willems
gave a family of such automorphisms. In this paper, we present a new
construction of such automorphisms using locally nilpotent derivations. As a
consequence, we discover that there exists an automorphism admitting a
reduction of type I which satisfies some degree condition for each possible
value.


title:
Detection of an ancient principle and an elegant solution to the protein
  classification problem

abstract:
  This work is concerned with the development of a well-founded, theoretically
justified, and least complicated metric for the classification of proteins with
reference to enzymes. As the signature of an enzyme family, a catalytic domain
is easily fingerprinted. Given that the classification problem has so far
seemed intractable, a classification schema derived from the catalytic domain
would be satisfying. Here I show that there exists a natural ab initio if
nonobvious basis to theorize that the catalytic domain of an enzyme is uniquely
informative about its regulation. This annotates its function. Based on this
hypothesis, a method that correctly classifies potassium ion channels into
their respective subfamilies is described. To put the principle on firmer
ground, extra validation was sought and obtained through co-evolutionary
analyses. The co-evolutionary analyses reveal a departure from the notion that
potassium ion channel proteins are functionally modular. This finding is
discussed in light of the prevailing notion of domain. These studies establish
that significant co-evolution of the catalytic domain of a gene with its
conjoint domain is a specialized, necessary process following fusion and
swapping events in evolution. Instances of this discovery are likely to be
found pervasive in protein science.


title: Prospects for Charged Particle Astronomy

abstract:
  The likelihood of detecting individual discrete sources of cosmic rays
depends on the mean separation between sources. The analysis here derives the
minimum separation that makes it likely that the closest source is detectable.
For super-GZK energies, detection is signal limited and magnetic fields should
not matter. For sub-GZK energies, detection is background limited, and
intergalactic magnetic fields enter the analysis through one adjustable
parameter. Both super-GZK and sub-GZK results are presented for four different
types of sources: steady isotropic sources, steady jet sources, isotropic
bursts, and jet bursts.


title: Multi-quark potential from AdS/QCD

abstract:
  Heavy multi-quark potential in the SU(N) color group using hard-wall AdS/QCD
at both zero and finite temperature is studied. A Cornell-like potential is
obtained for baryons and other exotic configurations and compared with those in
the quenched lattice calculation in N=3 case. At the end we also discuss
possible improvements in the UV region of potential.


title: Maximum Likelihood Supertrees

abstract:
  We analyse a maximum-likelihood approach for combining phylogenetic trees
into a larger `supertree'. This is based on a simple exponential model of
phylogenetic error, which ensures that ML supertrees have a simple
combinatorial description (as a median tree, minimising a weighted sum of
distances to the input trees). We show that this approach to ML supertree
reconstruction is statistically consistent (it converges on the true species
supertree as more input trees are combined), in contrast to the widely-used MRP
method, which we show can be statistically inconsistent under the exponential
error model. We also show that this statistical consistency extends to an ML
approach for constructing species supertrees from gene trees. In this setting,
incomplete lineage sorting (due to coalescence rates of homologous genes being
lower than speciation rates) has been shown to lead to gene trees that are
frequently different from species trees, and this can confound efforts to
reconstruct the species phylogeny correctly.


title: 1/f Flux Noise in Josephson Phase Qubits

abstract:
  We present a new method to measure 1/f noise in Josephson quantum bits
(qubits) that yields low-frequency spectra below 1Hz. Comparison of noise taken
at positive and negative bias of a phase qubit shows the dominant noise source
to be flux noise and not junction critical-current noise, with a magnitude
similar to that measured previously in other systems. Theoretical calculations
show that the level of flux noise is not compatible with the standard model of
noise from two-level state defects in the surface oxides of the films.


title: Forster signatures and qubits in optically driven quantum dot molecules

abstract:
  An interesting approach to achieve quantum gate operations in a solid state
device is to implement an optically driven quantum gate using two vertically
coupled self-assembled quantum dots, a quantum dot molecule (QDM). We present a
realistic model for exciton dynamics in InGaAs/GaAs QDMs under intense laser
excitation and applied electric fields. The dynamics is obtained by solutions
of the Lindblad master equation. A map of the dressed ground state as function
of laser energy and applied electric field exhibits rich structure that
includes excitonic anticrossings that permit the identification of the relevant
couplings. The optical signatures of the dipole-dipole Forster energy transfer
mechanism show as splittings of several (spatially) indirect excitonic lines.
Moreover, we construct a model for exciton qubit rotations by adiabatic
electric field cyclic sweeps into a Forster-tunneling regime which induces
level anticrossings. The proposed qubit exhibits Rabi oscillations among two
well defined exciton pairs as function of the residence time at the
anticrossing.


title: Baryogenesis by Quantum Gravity

abstract:
  A novel mechanism of baryogenesis is proposed on the basis of the phase
transition from the conformal invariant space-time to the Einstein space-time
in quantum gravity. Strong-coupling gravitational excitations with dynamical
mass about 10^17 GeV are generated at the transition. They eventually decay
into ordinary matters. As a realization of unparticle physics we show that the
low energy effective interactions between the gravitational potential
describing the excitation and the non-conserving matter currents by the axial
anomalies can explain matter asymmetry out of thermal equilibrium.


title:
Self-Trapping of Bose-Einstein Condensates in an Optical Lattice: the
  Effect of the System Dimension

abstract:
  In the present paper, we investigate the dynamics of a Bose-Einstein
condensates (BEC) loaded into an deep optical lattice of 1D, 2D and 3D, both
analytically and numerically. We focus on the self-trapping state and the
effect of the system dimension. Under the tight-binding approximation we obtain
an analytical criterion for the self-trapping state of BEC using time-dependent
variational method. The phase diagram for self-trapping, soliton, breather, or
diffusion of the BEC cloud is obtained accordingly and verified by directly
solving the discrete Gross-Pitaevskii equation (GPE) numerically. In
particular, we find that the criterion and the phase diagrams are modified
dramatically by the dimension of the lattices.


title:
Unitarily manipulating in time and space a Gaussian wave-packet motional
  state of a single atom in a quadratic potential field

abstract:
  The paper first discusses theoretically the off-resonance selective
excitation method that is dependent on the atomic internal states and used to
generate approximately a standard coherent state of harmonic oscillator. The
coherent average method then is proposed to construct the state-selective
trigger pulse. A state-selective trigger pulse can keep Gaussian shape
unchanged but change in an internal-state-dependent form the center-of-mass
position and/or momentum of an atomic Gaussian wave-packet motional state. A
Gaussian wave-packet state is one of the simplest wave-packet states that can
be easily manipulated and controlled in time and space. The paper also
investigates how to manipulate in time and space an atomic Gaussian wave-packet
motional state by a generalized quadratic potential field. A general quadratic
Hamiltonian can affect not only the center-of-mass position and momentum but
also the complex linewidth of a Gaussian wave-packet motional state while keep
Gaussian shape of the motional state unchanged. It is shown that generally
quadratic terms of a quadratic Hamiltonian can control directly the complex
linewidth, while linear terms of a quadratic Hamiltonian can affect only the
center-of-mass position and momentum of a Gaussian wave-packet motional state.


title: On The Solvability of Bilinear Equations in Finite Fields

abstract:
  We consider the equation $$ ab + cd = \lambda, \qquad a\in A, b \in B, c\in
C, d \in D, $$ over a finite field $F_q$ of $q$ elements, with variables from
arbitrary sets $ A, B, C, D \subseteq F_q$. The question of solvability of such
and more general equations has recently been considered by D. Hart and A.
Iosevich, who, in particular, proved that if $$ #A #B #C #D \gg q^3, $$ then
above equation has a solution for any $\lambda \in F_q^*$. Here we show that
using bounds of multiplicative character sums allows us to extend the class of
sets which satisfy this property.


title: On the possibility of a bimodal solar dynamo

abstract:
  A simple way to couple an interface dynamo model to a fast tachocline model
is presented, under the assumption that the dynamo saturation is due to a
quadratic process and that the effect of finite shear layer thickness on the
dynamo wave frequency is analoguous to the effect of finite water depth on
surface gravity waves. The model contains one free parameter which is fixed by
the requirement that a solution should reproduce the helioseismically
determined thickness of the tachocline. In this case it is found that, in
addition to this solution, another steady solution exists, characterized by a
four times thicker tachocline and 4-5 times weaker magnetic fields. It is
tempting to relate the existence of this second solution to the occurrence of
grand minima in solar activity.


title:
Classical Trajectory Perspective on Double Ionization Dynamics of
  Diatomic Molecules Irradiated by Ultrashort Intense Laser Pulses

abstract:
  In the present paper, we develop a semiclassical quasi-static model
accounting for molecular double ionization in an intense laser pulse. With this
model, we achieve insight into the dynamics of two highly-correlated valence
electrons under the combined influence of a two-center Coulomb potential and an
intense laser field, and reveal the significant influence of molecular
alignment on the ratio of double over single ion yield. Analysis on the
classical trajectories unveils sub-cycle dynamics of the molecular double
ionization. Many interesting features, such as the accumulation of emitted
electrons in the first and third quadrants of parallel momentum plane, the
regular pattern of correlated momentum with respect to the time delay between
closest collision and ionization moment, are revealed and successfully
explained by back analyzing the classical trajectories. Quantitative agreement
with experimental data over a wide range of laser intensities from tunneling to
over-the-barrier regime is presented.


title: Hard diffractive quarkonium hadroproduction at high energies

abstract:
  We present a study of heavy quarkonium production in hard diffractive process
by the Pomeron exchange for Tevatron and LHC energies. The numerical results
are computed using recent experimental determination of the diffractive parton
density functions in Pomeron and are corrected by unitarity corrections through
gap survival probability factor. We give predictions for single as well as
central diffractive ratios. These processes are sensitive to the gluon content
of the Pomeron at small Bjorken-x and may be particularly useful in studying
the small-x physics. They may also be a good place to test the different
available mechanisms for quarkonium production at hadron colliders.


title: Imaging the Radio Photospheres of Mira Variables

abstract:
  We have used the VLA at 43 GHz to image the radio continuum emission from o
Ceti, R Leo, and W Hya and to precisely locate their SiO maser emission with
respect to the star. The radio continuum emission region for all three stars
has a diameter close to 5.6 AU. These diameters are similar to those measured
at infrared wavelengths in bands containing strong molecular opacity and about
twice those measured in line-free regions of the infrared spectrum. Thus, the
radio photosphere and the infrared molecular layer appear to be coextensive.
The 43 GHz continuum emission is consistent with temperatures near 1600 K and
opacity from H-minus free-free interactions. While the continuum image of o
Ceti appears nearly circular, both R Leo and W Hya display significant
elongations. The SiO masers for all three stars show partial rings with
diameters close to 8 AU.


title:
Spectropolarimetry of R Coronae Borealis in 1998--2003: Discovery of
  Transient Polarization at Maximum Brightness

abstract:
  We present an extended optical spectropolarimetry of R CrB from 1998 January
to 2003 September. The polarization was almost constant in the phase of maximum
brightness, being consistent with past observations. We detected, however,
temporal changes of polarization ($\sim 0.5$ %) in 2001 March and August, which
were the first detection of large polarization variability in R CrB near
maximum brightness. The amplitude and the position angle of the `transient
polarization' were almost constant with wavelength in both two events. There
was a difference by about 20 degrees in the position angle between the two
events. Each event could be explained by light scattering due to short-lived
dust puff occasionally ejected off the line of sight. The flatness of the
polarization against the wavelength suggests that the scatterer is a mixture of
dust grains having various sizes. The rapid growth and fading of the transient
polarization favors the phenomenological model of dust formation near the
stellar photosphere (e.g., within two stellar radii) proposed for the time
evolution of brightness and chromospheric emission lines during deeply
declining periods, although the fading timescale can hardly be explained by a
simple dispersal of expanding dust puff with a velocity of $\sim 200-350$ km s
$^{-1}$. Higher expansion velocity or some mechanism to destroy the dust grains
should be needed.


title: A Short Study of Alexandroff Spaces

abstract:
  In this paper, we discuss the basic properties of Alexandroff spaces. Several
examples of Alexandroff spaces are given. We show how to construct new
Alexandroff spaces from given ones. Finally, two invariants for compact
Alexandroff spaces are defined and calculated for the given examples.


title:
Josephson vortex lattices with modulation perpendicular to an in-plane
  magnetic field in layered superconductor

abstract:
  In quasi low dimensional superconductors under {\it parallel} magnetic fields
applied along a conducting direction, vortex lattices with a modulation of
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type {\it perpendicular} to the field
may occur due to an enhanced paramagnetic depairing. As the strength of an
in-plane field is varied in a Q2D material, the Josephson vortex lattices
accompanied by nodal planes are formed in higher Landau level (LL) modes of the
superconducting (SC) order parameter and show field-induced structural
transitions. A change of orientation of nodal planes induced by these
transitions should be observed in transport measurements for an out-of-plane
current in real superconductors with point disorder effective on the SC layers.
Further, the $H_{c2}$-transition from this higher LL state to the normal phase
is of second order for moderately strong paramagnetic effects but, in the case
with a strong enough paramagnetic effect, becomes discontinuous as well as the
transition between this modulated state and an ordinary Abrikosov vortex
lattice in the lowest LL. Relevance of these results to recent observations in
organic superconductors suggesting the presence of an FFLO state are discussed.


title:
Torus quotients of homogeneous spaces of the general linear group and
  the standard representation of certain symmetric groups

abstract:
  We give a stratification of the GIT quotient of the Grassmannian $G_{2,n}$
modulo the normaliser of a maximal torus of $SL_{n}(k)$ with respect to the
ample generator of the Picard group of $G_{2,n}$. We also prove that the flag
variety $GL_{n}(k)/B_{n}$ can be obtained as a GIT quotient of
$GL_{n+1}(k)/B_{n+1}$ modulo a maximal torus of $SL_{n+1}(k)$ for a suitable
choice of an ample line bundle on $GL_{n+1}(k)/B_{n+1}$.


title:
Constant flux relation for aggregation models with desorption and
  fragmentation

abstract:
  We study mass fluxes in aggregation models where mass transfer to large
scales by aggregation occurs alongside desorption or fragmentation. Two models
are considered. (1) A system of diffusing, aggregating particles with influx
and outflux of particles (in-out model) (2) A system of diffusing aggregating
particles with fragmentation (chipping model). Both these models can exist in
phases where probability distributions are power laws. In these power law
phases, we argue that the two point correlation function should have a certain
homogeneity exponent. These arguments are based on the exact constant flux
scaling valid for simple aggregation with input. Predictions are compared with
Monte Carlo simulations.


title:
The nanostructural origin of the ac conductance in dielectric granular
  metals: the case study of Co_20(ZrO_2)_80

abstract:
  We show which is the nanostructure required in granular Co20(ZrO2)80 thin
films to produce an ac response such as the one that is universally observed in
a very wide variety of dielectric materials. A bimodal size distribution of Co
particles yields randomly competing conductance channels which allow both
thermally assisted tunneling through small particles and capacitive conductance
among larger particles that are further apart. A model consisting on a simple
cubic random resistance-capacitor network describes quantitatively the
experimental results as functions of temperature and frequency, and enables the
determination of the microscopic parameters controlling the ac response of the
samples.


title: A model for exploring bird morphology

abstract:
  A simplified model of the bird skeleton along with elongation parameters for
the flight feathers is used to explore the diversity of bird shapes. Varying a
small number of parameters simulates a wide range of observed bird silhouettes.
The model may serve to examine developmental factors involved, help museum
curators develop computational approaches to bird morphometry and has
applications in computer generated illustration.


title: General entanglement-assisted quantum error-correcting codes

abstract:
  Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of
pre-existing entanglement between the sender and receiver to boost the rate of
transmission. It is possible to construct an EAQECC from any classical linear
code, unlike standard QECCs which can only be constructed from dual-containing
codes. Operator quantum error-correcting codes (OQECCs) allow certain errors to
be corrected (or prevented) passively, reducing the complexity of the
correction procedure. We combine these two extensions of standard quantum error
correction into a unified entanglement-assisted quantum error correction
formalism. This new scheme, which we call entanglement-assisted operator
quantum error correction (EAOQEC), is the most general and powerful quantum
error-correcting technique known, retaining the advantages of both
entanglement-assistance and passive correction. We present the formalism, show
the considerable freedom in constructing EAOQECCs from classical codes, and
demonstrate the construction with examples.


title: Spin-transfer torques in anti-ferromagnetic metals from first principles

abstract:
  In spite of the absence of a macroscopic magnetic moment, an anti-ferromagnet
is spin-polarized on an atomic scale. The electric current passing through a
conducting anti-ferromagnet is polarized as well, leading to spin-transfer
torques when the order parameter is textured, such as in anti-ferromagnetic
non-collinear spin valves and domain walls. We report a first principles study
on the electronic transport properties of anti-ferromagnetic systems. The
current-induced spin torques acting on the magnetic moments are comparable with
those in conventional ferromagnetic materials, leading to measurable angular
resistances and current-induced magnetization dynamics. In contrast to
ferromagnets, spin torques in anti-ferromagnets are very nonlocal. The torques
acting far away from the center of an anti-ferromagnetic domain wall should
facilitate current-induced domain wall motion.


title: Some Applications of Ricci Flow in Physics

abstract:
  I discuss certain applications of the Ricci flow in physics. I first review
how it arises in the renormalization group (RG) flow of a nonlinear sigma
model. I then review the concept of a Ricci soliton and recall how a soliton
was used to discuss the RG flow of mass in 2-dimensions. I then present recent
results obtained with Oliynyk on the flow of mass in higher dimensions. The
final section discusses one way in which Ricci flow may arise in general
relativity, particularly for static metrics.


title: Results and Frontiers in Lattice Baryon Spectroscopy

abstract:
  The Lattice Hadron Physics Collaboration (LHPC) baryon spectroscopy effort is
reviewed. To date the LHPC has performed exploratory Lattice QCD calculations
of the low-lying spectrum of Nucleon and Delta baryons. These calculations
demonstrate the effectiveness of our method by obtaining the masses of an
unprecedented number of excited states with definite quantum numbers. Future
work of the project is outlined.


title: Two-Fermion Bound States within the Bethe-Salpeter Approach

abstract:
  To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we
propose a novel method related to the use of hyperspherical harmonics. We
suggest an appropriate extension to form a new basis of spin-angular harmonics
that is suitable for a representation of the vertex functions. We present a
numerical algorithm to solve the Bethe-Salpeter equation and investigate in
detail the properties of the solution for the scalar, pseudoscalar and vector
meson exchange kernels including the stability of bound states. We also compare
our results to the non relativistic ones and to the results given by light
front dynamics.


title: The logistic equation and a critique of the theory of natural selection

abstract:
  Species coexistence is one of the central themes in modern ecology.
Coexistence is a prerequisite of biological diversity. However, the question
arises how biodiversity can be reconciled with the statement of competition
theory, which asserts that competing species cannot coexist. To solve this
problem natural selection theory is rejected because it contradicts kinetic
models of interacting populations. Biological evolution is presented as a
process equivalent to a chemical reaction. The main point is that interactions
occur between self-replicating units. Under these assumptions biodiversity is
possible if and only if species are identical with respect to the patterns of
energy flow in which individuals are involved.


title: Kondo lattice model at half-filling

abstract:
  The single- and two-channel Kondo lattice model consisting of localized spins
interacting antiferromagnetically with the itinerent electrons, are studied
using dynamical mean field theory. As an impurity solver for the effective
single impurity Anderson model we used the exact diagonalization (ED) method.
Using ED allowed us to perform calculations for low temperatures and couplings
of arbitrary large strength. Our results for the single-channel case confirm
and extend the recent investigations. In the two-channel case we find a
symmetry breaking phase transition with increasing coupling strength.


title: When do stepwise algorithms meet subset selection criteria?

abstract:
  Recent results in homotopy and solution paths demonstrate that certain
well-designed greedy algorithms, with a range of values of the algorithmic
parameter, can provide solution paths to a sequence of convex optimization
problems. On the other hand, in regression many existing criteria in subset
selection (including $C_p$, AIC, BIC, MDL, RIC, etc.) involve optimizing an
objective function that contains a counting measure. The two optimization
problems are formulated as (P1) and (P0) in the present paper. The latter is
generally combinatoric and has been proven to be NP-hard. We study the
conditions under which the two optimization problems have common solutions.
Hence, in these situations a stepwise algorithm can be used to solve the
seemingly unsolvable problem. Our main result is motivated by recent work in
sparse representation, while two others emerge from different angles: a direct
analysis of sufficiency and necessity and a condition on the mostly correlated
covariates. An extreme example connected with least angle regression is of
independent interest.


title: Local partial likelihood estimation in proportional hazards regression

abstract:
  Fan, Gijbels and King [Ann. Statist. 25 (1997) 1661--1690] considered the
estimation of the risk function $\psi (x)$ in the proportional hazards model.
Their proposed estimator is based on integrating the estimated derivative
function obtained through a local version of the partial likelihood. They
proved the large sample properties of the derivative function, but the large
sample properties of the estimator for the risk function itself were not
established. In this paper, we consider direct estimation of the relative risk
function $\psi (x_2)-\psi (x_1)$ for any location normalization point $x_1$.
The main novelty in our approach is that we select observations in shrinking
neighborhoods of both $x_1$ and $x_2$ when constructing a local version of the
partial likelihood, whereas Fan, Gijbels and King [Ann. Statist. 25 (1997)
1661--1690] only concentrated on a single neighborhood, resulting in the
cancellation of the risk function in the local likelihood function. The
asymptotic properties of our estimator are rigorously established and the
variance of the estimator is easily estimated. The idea behind our approach is
extended to estimate the differences between groups. A simulation study is
carried out.


title:
Mapping the distribution of luminous and dark matter in strong lensing
  galaxies

abstract:
  We present the distribution of luminous and dark matter in a set of strong
lensing (early-type) galaxies. By combining two independent techniques -
stellar population synthesis and gravitational lensing - we can compare the
baryonic and dark matter content in these galaxies within the regions that can
be probed using the images of the lensed background source. Two samples were
studied, extracted from the CASTLES and SLACS surveys. The former probes a
wider range of redshifts and allows us to explore the mass distribution out to
~5Re. The high resolution optical images of the latter (using HST/ACS) are used
to show a pixellated map of the ratio between total and baryonic matter. We
find dark matter to be absent in the cores of these galaxies, with an
increasing contribution at projected radii R>Re. The slopes are roughly
compatible with an isothermal slope (better interpreted as an adiabatically
contracted NFW profile), but a large scatter in the slope exists among
galaxies. There is a trend suggesting most massive galaxies have a higher
content of dark matter in the regions probed by this analysis.


title: Coupling, concentration inequalities and stochastic dynamics

abstract:
  In the context of interacting particle systems, we study the influence of the
action of the semigroup on the concentration property of Lipschitz functions.
As an application, this gives a new approach to estimate the relaxation speed
to equilibrium of interacting particle systems. We illustrate our approach in a
variety of examples for which we obtain several new results with short and
non-technical proofs. These examples include the symmetric and asymmetric
exclusion process and high-temperature spin-flip dynamics ("Glauber dynamics").
We also give a new proof of the Poincar\'e inequality, based on coupling, in
the context of one-dimensional Gibbs measures. In particular, we cover the case
of polynomially decaying potentials, where the log-Sobolev inequality does not
hold.


title: Estimating the number of classes

abstract:
  Estimating the unknown number of classes in a population has numerous
important applications. In a Poisson mixture model, the problem is reduced to
estimating the odds that a class is undetected in a sample. The discontinuity
of the odds prevents the existence of locally unbiased and informative
estimators and restricts confidence intervals to be one-sided. Confidence
intervals for the number of classes are also necessarily one-sided. A sequence
of lower bounds to the odds is developed and used to define pseudo maximum
likelihood estimators for the number of classes.


title: Gain of analyticity for semilinear Schroedinger equations

abstract:
  We discuss gain of analyticity phenomenon of solutions to the initial value
problem for semilinear Schroedinger equations with gauge invariant
nonlinearity. We prove that if the initial data decays exponentially, then the
solution becomes real-analytic in the space variable and a Gevrey function of
order 2 in the time variable except in the initial plane. Our proof is based on
the energy estimates developed in our previous work and on fine summation
formulae concerned with a matrix norm.


title: Strongly pseudoconvex domains as subvarieties of complex manifolds

abstract:
  In this paper (a sequel to B. Drinovec Drnovsek and F. Forstneric,
Holomorphic curves in complex spaces, Duke Math. J. 139 (2007), 203-253) we
obtain existence and approximation results for closed complex subvarieties that
are normalized by strongly pseudoconvex Stein domains. Our sufficient condition
for the existence of such subvarieties in a complex manifold is expressed in
terms of the Morse indices and the number of positive Levi eigenvalues of an
exhaustion function on the manifold. Examples show that our condition cannot be
weakened in general. Optimal results are obtained for subvarieties of this type
in complements of compact complex submanifolds with Griffiths positive normal
bundle; in the projective case these results generalize classical theorems of
Remmert, Bishop and Narasimhan concerning proper holomorphic maps and
embeddings to complex Euclidean spaces.


title:
Ordering from frustration in a strongly correlated one-dimensional
  system

abstract:
  We study a one-dimensional extended Hubbard model with longer-range Coulomb
interactions at quarter-filling in the strong coupling limit. We find two
different charge-ordered (CO) ground states as the strength of the longer range
interactions is varied. At lower energies, these CO states drive two different
spin-ordered ground states. A variety of response functions computed here bear
a remarkable resemblance to recent experimental observations for organic TMTSF
systems, and so we propose that these systems are proximate to a QCP associated
with T=0 charge order. For a ladder system relevant to $Sr_{14}Cu_{24}O_{41}$,
we find in-chain CO, rung-dimer, and orbital antiferromagnetic ordered phases
with varying interchain couplings and superconductivity with hole-doping. RPA
studies of many chains (ladders) coupled reveal a phase diagram with the
ordered phase extended to finite temperatures and a phase boundary ending at a
quantum critical point (QCP). Critical quantum fluctuations at the QCP are
found to enhance the transverse dispersion, leading to a dimensional crossover
and a T=0 decofinement transition.


title: Dynamics of \bar{K} and multi-\bar{K} nuclei

abstract:
  We report on self-consistent calculations of single-K^- nuclear states and
multi-Kbar nuclear states in 12C, 16O, 40Ca and 208Pb within the relativistic
mean-field (RMF) approach. Gradient terms motivated by the p-wave resonance
Sigma(1385) are found to play a secondary role for single-K^- nuclear systems
where the mean-field concept is acceptable. Significant contributions from the
Kbar N -> pi Lambda conversion mode, and from the nonmesonic Kbar NN -> YN
conversion modes which are assumed to follow a rho^2 density dependence, are
evaluated for the deep binding-energy range of over 100 MeV where the decay
channel Kbar N -> pi Sigma is closed. Altogether we obtain K^- total decay
widths of 50-100 MeV for binding energies exceeding 100 MeV in single-K^-
nuclei. Multi-Kbar nuclear calculations indicate that the binding energy per
Kbar meson saturates upon increasing the number of Kbar mesons embedded in the
nuclear medium. The nuclear and Kbar densities increase only moderately and are
close to saturation, with no indication of any kaon-condensation precursor.


title: Clathrate hydrates as a sink of noble gases in Titan's atmosphere

abstract:
  We use a statistical thermodynamic approach to determine the composition of
clathrate hydrates which may form from a multiple compound gas whose
composition is similar to that of Titan's atmosphere. Assuming that noble gases
are initially present in this gas phase, we calculate the ratios of xenon,
krypton and argon to species trapped in clathrate hydrates. We find that these
ratios calculated for xenon and krypton are several orders of magnitude higher
than in the coexisting gas at temperature and pressure conditions close to
those of Titan's present atmosphere at ground level. Furthermore we show that,
by contrast, argon is poorly trapped in these ices. This trapping mechanism
implies that the gas-phase is progressively depleted in xenon and krypton when
the coexisting clathrate hydrates form whereas the initial abundance of argon
remains almost constant. Our results are thus compatible with the deficiency of
Titan's atmosphere in xenon and krypton measured by the {\it Huygens} probe
during its descent on January 14, 2005. However, in order to interpret the
subsolar abundance of primordial Ar also revealed by {\it Huygens}, other
processes that occurred either during the formation of Titan or during its
evolution must be also invoked.


title:
From frustrated insulators to correlated anisotropic metals: charge
  ordering and quantum criticality in coupled chain systems

abstract:
  A recent study revealed the dynamics of the charge sector of a
one-dimensional quarter-filled electronic system with extended Hubbard
interactions to be that of an effective pseudospin transverse-field Ising model
(TFIM) in the strong coupling limit. With the twin motivations of studying the
co-existing charge and spin order found in strongly correlated chain systems
and the effects of inter-chain couplings, we investigate the phase diagram of
coupled effective (TFIM) systems. A bosonisation and RG analysis for a two-leg
TFIM ladder yields a rich phase diagram showing Wigner/Peierls charge order and
Neel/dimer spin order. In a broad parameter regime, the orbital
antiferromagnetic phase is found to be stable. An intermediate gapless phase of
finite width is found to lie in between two charge-ordered gapped phases.
Kosterlitz-Thouless transitions are found to lead from the gapless phase to
either of the charge-ordered phases. A detailed analysis is also carried out
for the dimensional crossover physics when many such pseudospin systems are
coupled to one another. Importantly, the analysis reveals the key role of
critical quantum fluctuations in driving the strong dispersion in the
transverse directions, as well as a T=0 deconfinement transition. Our work is
potentially relevant for a unified description of a class of strongly
correlated, quarter-filled chain and ladder systems.


title: Rational algebraic K-theory of topological K-theory

abstract:
  We show that after rationalization there is a homotopy fiber sequence BBU ->
K(ku) -> K(Z). We interpret this as a correspondence between the virtual
2-vector bundles over a space X and their associated anomaly bundles over the
free loop space LX. We also rationally compute K(KU) by using the localization
sequence, and K(MU) by a method that applies to all connective S-algebras.


title:
Dynamic elastic properties and magnetic susceptibility across the
  austenite-martensite transformation in site-disordered ferromagnetic Ni-Fe-Al
  alloy

abstract:
  Besides permitting an accurate determination of the
ferromagnetic-to-paramagnetic phase transition temperature and the
characteristic temperatures for the beginning and end of the growth of
martensite (austenite) phase at the expense of austenite (martensite) phase
while cooling (heating), the results of an extensive ac susceptibility, sound
velocity and internal friction investigation of the thermoelastic martensitic
transformation in melt-quenched (site-disordered) Ni55Fe20Al25 alloy provide a
clear experimental evidence for the following. Irreversible thermoelastic
changes (thermal hysteresis) occur in the austenite phase in the premartensitic
regime. In the heating cycle, the system retains the "memory" of the initiation
and subsequent growth of the martensitic phase (at the expense of the parent
austenite phase) that had taken place during the cooling cycle in the
austenite-martensite phase coexistence region. We report and discuss these
novel findings in this communication.


title: Normal Surface Theory in Link Diagrams

abstract:
  This paper has been withdrawn by the author, due to a significant error in
section 4.3.1.


abstract:
  The conditions for R-separation of variables for the conformally invariant
Laplace equation on an n-dimensional Riemannian manifold are determined and
compared with the conditions for the additive separation of the null geodesic
Hamilton-Jacobi equation. The case of 3-dimensions is examined in detail and it
is proven that on any conformally flat manifold the two equations separate in
the same coordinates.


title:
Constraining Dark Energy From Splitting Angle Statistic of Strong
  Gravitational Lenses

abstract:
  Utilizing the CLASS statistical sample, we investigate the constraint of the
splitting angle statistic of strong gravitational lenses(SGL) on the
equation-of-state parameter $w=p/\rho$ of the dark energy in the flat cold dark
matter cosmology. Through the comoving number density of dark halos described
by Press-Schechter theory, dark energy affects the efficiency with which
dark-matter concentrations produce strong lensing signals. The constraints on
both constant $w$ and time-varying $w(z)=w_0+w_az/(1+z)$ from the SGL splitting
angle statistic are consistently obtained by adopting a two model combined
mechanism of dark halo density profile matched at the mass scale $M_c$. Our
main observations are: (a) the resulting model parameter $M_c$ is found to be
$M_c \sim 1.4$ for both constant $w$ and time-varying $w(z)$, which is larger
than $M_c \sim 1$ obtained in literatures; (b) the fitting results for the
constant $w$ are found to be $w =-0.89^{+0.49}_{-0.26}$ and $w
=-0.94^{+0.57}_{-0.16}$ for the source redshift distributions of the Gaussian
models $g(z_s)$ and $g^c(z_s)$ respectively, which are consistent with the
$\Lambda \rm CDM$ at 95% C.L; (c) the time-varying $w(z)$ is found to be for
$\sigma_8 = 0.74$: $(M_c; w_0, w_a)=(1.36; -0.92, -1.31)$ and $(M_c; w_0,
w_a)=(1.38; -0.89, -1.21)$ for $g(z_s)$ and $g^c(z_s)$ respectively.


title: Matching with shift for one-dimensional Gibbs measures

abstract:
  We consider matching with shifts for Gibbsian sequences. We prove that the
maximal overlap behaves as $c\log n$, where $c$ is explicitly identified in
terms of the thermodynamic quantities (pressure) of the underlying potential.
Our approach is based on the analysis of the first and second moment of the
number of overlaps of a given size. We treat both the case of equal sequences
(and nonzero shifts) and independent sequences.


title: An approximate theory for substructure propagation in clusters

abstract:
  The existence of dark matter can be proved in an astrophysical context by the
discovery of a system in which the observed baryons and the inferred dark
matter are spatially segregated, such as the bullet cluster (1E0657-558). The
full descriptions of the dark matter halo and X-ray gas substructure motions
are necessary to forecast the location of the dark halo from X-ray maps, which
can be confirmed by the detection of a galaxy concentration or by gravitational
lensing. We present an analytical hydrodynamic model to determine the distance
between the X-ray and dark-matter components and the Mach number of the merger
shock. An approximate solution is given for the problem of the substructure
propagation in merging clusters. A new method to predict the position of a dark
matter halo in clusters, where there is a separation between the X-ray gas and
the dark halo, is proposed and applied to the clusters 1E0657-558 and Abell
1763.


title:
Thompson's renormalization group method applied to QCD at high energy
  scale

abstract:
  We use a renormalization group method to treat QCD-vacuum behavior specially
closer to the regime of asymptotic freedom. QCD-vacuum behaves effectively like
a "paramagnetic system" of a classical theory in the sense that virtual color
charges (gluons) emerges in it as a spin effect of a paramagnetic material when
a magnetic field aligns their microscopic magnetic dipoles. Due to that strong
classical analogy with the paramagnetism of Landau's theory,we will be able to
use a certain Landau effective action without temperature and phase transition
for just representing QCD-vacuum behavior at higher energies as being
magnetization of a paramagnetic material in the presence of a magnetic field
$H$. This reasoning will allow us to apply Thompson's approach to such an
action in order to extract an "effective susceptibility" ($\chi>0$) of
QCD-vacuum. It depends on logarithmic of energy scale $u$ to investigate
hadronic matter. Consequently we are able to get an ``effective magnetic
permeability" ($\mu>1$) of such a "paramagnetic vacuum". Actually,as QCD-vacuum
must obey Lorentz invariance,the attainment of $\mu>1$ must simply require that
the "effective electrical permissivity" is $\epsilon<1$ in such a way that
$\mu\epsilon=1$ ($c^2=1$). This leads to the anti-screening effect where the
asymptotic freedom takes place. We will also be able to extend our
investigation to include both the diamagnetic fermionic properties of
QED-vacuum (screening) and the paramagnetic bosonic properties of QCD-vacuum
(anti-screening) into the same formalism by obtaining a $\beta$-function at 1
loop,where both the bosonic and fermionic contributions are considered.


title:
Room-temperature magnetocaloric effect in La0.7Sr0.3Mn1-xM'xO3 (M'=Al,
  Ti)

abstract:
  Magnetic entropy and adiabatic temperature changes in and above the
room-temperature region has been measured for La0.7Sr0.3Mn1-xM'xO3 (M' = Al,
Ti) by means of magnetization and heat capacity measurements in magnetic fields
up to 6 T. The magnetocaloric effect becomes largest at the ferromagnetic
ordering temperature Tc that is tuned to ~300 K by the substitution of Al or Ti
for Mn. While the substitution of Al for Mn drastically reduces the entropy
change, it extends considerably the working temperature span and improves the
relative cooling power. The magnetocaloric effect seems to be only lightly
affected by Ti substitution. Although manganites have been considered potential
for magnetic refrigerants, the magnetocaloric effect in these materials is
limited due to the existence of short-range ferromagnetic correlations above
Tc.


title: Photogalvanic effects in HgTe quantum wells

abstract:
  We report on the observation of the terahertz radiation induced circular
(CPGE) and linear (LPGE) photogalvanic effects in HgTe quantum wells. The
current response is well described by the phenomenological theory of CPGE and
LPGE.


title:
Future Directions of Research in Geometry: A Summary of the Panel
  Discussion at the 2007 Midwest Geometry Conference

abstract:
  The 2007 Midwest Geometry Conference included a panel discussion devoted to
open problems and the general direction of future research in fields related to
the main themes of the conference. This paper summarizes the comments made
during the panel discussion.


title: Control of laser wake field acceleration by plasma density profile

abstract:
  We show that both the maximum energy gain and the accelerated beam quality
can be efficiently controlled by the plasma density profile. Choosing a proper
density gradient one can uplift the dephasing limitation. When a periodic wake
field is exploited, the phase synchronism between the bunch of relativistic
particles and the plasma wave can be maintained over extended distances due to
the plasma density gradient. Putting electrons into the $n-$th wake period
behind the driving laser pulse, the maximum energy gain is increased by the
factor $2\pi n$ over that in the case of uniform plasma. The acceleration is
limited then by laser depletion rather than by dephasing. Further, we show that
the natural energy spread of the particle bunch acquired at the acceleration
stage can be effectively removed by a matched deceleration stage, where a
larger plasma density is used.


title: Gravitational stability in the disk of M51

abstract:
  Star formation laws, like i.e. the Schmidt law relating star formation rate
and total gas density, have been studied in several spiral galaxies but the
underlying physics are not yet well understood. M51, as a nearby face-on, grand
design spiral galaxy studied in many line transitions, is an ideal target to
study the connection between physical conditions of the gas and star formation
activity. In this contribution we combine molecular, atomic, total gas and
stellar surface densities and study the gravitational stability of the gas
(Schuster et al.2007, Hitschfeld et al. in prep.). From our IRAM-30m 12 CO2-1
map and complementary HI-, Radio Continuum- and ACS-HST B-band-data we derive
maps of the total gas density and the stellar surface density to study the
gravitational stability of the gas via the Toomre Q parameter.


title: Provenance as Dependency Analysis

abstract:
  Provenance is information recording the source, derivation, or history of
some information. Provenance tracking has been studied in a variety of
settings; however, although many design points have been explored, the
mathematical or semantic foundations of data provenance have received
comparatively little attention. In this paper, we argue that dependency
analysis techniques familiar from program analysis and program slicing provide
a formal foundation for forms of provenance that are intended to show how (part
of) the output of a query depends on (parts of) its input. We introduce a
semantic characterization of such dependency provenance, show that this form of
provenance is not computable, and provide dynamic and static approximation
techniques.


title:
A geometric analysis of the Maxwell field in a vicinity of a multipole
  particle and new special functions

abstract:
  A method of solving Maxwell equations in a vicinity of a multipole particle
(moving along an arbitrary trajectory) is proposed. The method is based on a
geometric construction of a trajectory-adapted coordinate system, which
simplifies considerably the equations. The solution is given in terms of a
series, where a new family of special functions arises in a natural way.
Singular behaviour of the field near to the particle may be analyzed this way
up to an arbitrary order. Application to the self-interaction problems in
classical electrodynamics is discussed.


title:
Cyclotron resonance photoconductivity of a two-dimensional electron gas
  in HgTe quantum wells

abstract:
  Far-infrared cyclotron resonance photoconductivity (CRP) is investigated in
HgTe quantum wells (QWs) of various widths grown on (013) oriented GaAs
substrates. It is shown that CRP is caused by the heating of two-dimensional
electron gas (2DEG). From the resonance magnetic field strength effective
masses and their dependence on the carrier concentration is obtained. We found
that the effective mass in each sample slightly increases from the value
(0.0260 \pm 0.0005)m_0 at N_s = 2.2x10^11 cm^(-2) to (0.0335 \pm 0.0005)m_0 at
N_s = 9.6x10^11 cm^(-2). Compared to determination of effective masses by the
temperature dependence of magnitudes of the Shubnikov-de Haas (SdH)
oscillations used so far in this material our measurements demonstrate that the
CRP provides a more accurate (about few percents) tool. Combining optical
methods with transport measurements we found that the transport time
substantially exceeds the cyclotron resonance lifetime as well as the quantum
lifetime which is the shortest.


title: Link-space formalism for network analysis

abstract:
  We introduce the link-space formalism for analyzing network models with
degree-degree correlations. The formalism is based on a statistical description
of the fraction of links l_{i,j} connecting nodes of degrees i and j. To
demonstrate its use, we apply the framework to some pedagogical network models,
namely, random-attachment, Barabasi-Albert preferential attachment and the
classical Erdos and Renyi random graph. For these three models the link-space
matrix can be solved analytically. We apply the formalism to a simple
one-parameter growing network model whose numerical solution exemplifies the
effect of degree-degree correlations for the resulting degree distribution. We
also employ the formalism to derive the degree distributions of two very simple
network decay models, more specifically, that of random link deletion and
random node deletion. The formalism allows detailed analysis of the
correlations within networks and we also employ it to derive the form of a
perfectly non-assortative network for arbitrary degree distribution.


title: Likelihood based inference for monotone response models

abstract:
  The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio
statistic in a family of problems involving pointwise nonparametric estimation
of a monotone function is studied. This class of problems differs radically
from the usual parametric or semiparametric situations in that the MLE of the
monotone function at a point converges to the truth at rate $n^{1/3}$ (slower
than the usual $\sqrt{n}$ rate) with a non-Gaussian limit distribution. A
framework for likelihood based estimation of monotone functions is developed
and limit theorems describing the behavior of the MLEs and the likelihood ratio
statistic are established. In particular, the likelihood ratio statistic is
found to be asymptotically pivotal with a limit distribution that is no longer
$\chi^2$ but can be explicitly characterized in terms of a functional of
Brownian motion. Applications of the main results are presented and potential
extensions discussed.


title: The S2N2 metallicity calibrator and the abundance gradient of M 33

abstract:
  We introduce the log(Ha/[SII]6717+6731) vs. log(Ha/[NII]6583) (S2N2)
diagnostic diagram as metallicity and ionisation parameter indicator for HII
regions in external galaxies. The location of HII regions in the S2N2 diagram
was studied both empirically and theoretically. We found that, for a wide range
of metallicities, the S2N2 diagram gives single valued results in the
metallicity-ionisation parameter plane. We demonstrate that the S2N2 diagram is
a powerful tool to estimate metallicities of high-redshift (z ~ 2) HII
galaxies. Finally, we derive the metallicity for 76 HII regions in M33 from the
S2N2 diagram and calculate an O/H abundance gradient for this galaxy of -0.05
(+-0.01) dex kpc^-1.


title: A simple proof of the matrix-valued Fej\'er-Riesz theorem

abstract: A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case


title: A nonparametric approach to the estimation of lengths and surface areas

abstract:
  The Minkowski content $L_0(G)$ of a body $G\subset{\mathbb{R}}^d$ represents
the boundary length (for $d=2$) or the surface area (for $d=3$) of $G$. A
method for estimating $L_0(G)$ is proposed. It relies on a nonparametric
estimator based on the information provided by a random sample (taken on a
rectangle containing $G$) in which we are able to identify whether every point
is inside or outside $G$. Some theoretical properties concerning strong
consistency, $L_1$-error and convergence rates are obtained. A practical
application to a problem of image analysis in cardiology is discussed in some
detail. A brief simulation study is provided.


title: The Phase Structure of Higher-Dimensional Black Rings and Black Holes

abstract:
  We construct an approximate solution for an asymptotically flat, neutral,
thin rotating black ring in any dimension D>=5 by matching the near-horizon
solution for a bent boosted black string, to a linearized gravity solution away
from the horizon. The rotating black ring solution has a regular horizon of
topology S^1 x S^{D-3} and incorporates the balancing condition of the ring as
a zero-tension condition. For D=5 our method reproduces the thin ring limit of
the exact black ring solution. For D>=6 we show that the black ring has a
higher entropy than the Myers-Perry black hole in the ultra-spinning regime. By
exploiting the correspondence between ultra-spinning black holes and black
membranes on a two-torus, we take steps towards qualitatively completing the
phase diagram of rotating blackfolds with a single angular momentum. We are led
to propose a connection between MP black holes and black rings, and between MP
black holes and black Saturns, through merger transitions involving two kinds
of `pinched' black holes. More generally, the analogy suggests an infinite
number of pinched black holes of spherical topology leading to a complicated
pattern of connections and mergers between phases.


title: Local rigidity in quaternionic hyperbolic space

abstract:
  In this note, we study deformations of quaternionic hyperbolic lattices in
larger quaternionic hyperbolic spaces and prove local rigidity results. On the
other hand, surface groups are shown to be more flexible in quaternionic
hyperbolic plane than in complex hyperbolic plane.


title: Nuclear condensation and the equation of state of nuclear matter

abstract:
  The isothermal compression of a dilute nucleonic gas invoking cluster degrees
of freedom is studied in an equilibrium statistical model; this clusterized
system is found to be more stable than the pure nucleonic system. The equation
of state (EoS) of this matter shows features qualitatively very similar to the
one obtained from pure nucleonic gas. In the isothermal compression process,
there is a sudden enhancement of clusterization at a transition density
rendering features analogous to the gas-liquid phase transition in normal
dilute nucleonic matter. Different observables like the caloric curves, heat
capacity, isospin distillation, etc. are studied in both the models. Possible
changes in the observables due to recently indicated medium modifications in
the symmetry energy are also investigated.


title: Monte Carlo likelihood inference for missing data models

abstract:
  We describe a Monte Carlo method to approximate the maximum likelihood
estimate (MLE), when there are missing data and the observed data likelihood is
not available in closed form. This method uses simulated missing data that are
independent and identically distributed and independent of the observed data.
Our Monte Carlo approximation to the MLE is a consistent and asymptotically
normal estimate of the minimizer $\theta^*$ of the Kullback--Leibler
information, as both Monte Carlo and observed data sample sizes go to infinity
simultaneously. Plug-in estimates of the asymptotic variance are provided for
constructing confidence regions for $\theta^*$. We give Logit--Normal
generalized linear mixed model examples, calculated using an R package.


title: On combinatorial model categories

abstract:
  Combinatorial model categories were introduced by J. H. Smith as model
categories which are locally presentable and cofibrantly generated. He has not
published his results yet but proofs of some of them were presented by T. Beke
or D. Dugger. We are contributing to this endeavour by proving that weak
equivalences in a combinatorial model category form an accessible category. We
also present some new results about weak equivalences and cofibrations in
combinatorial model categories.


title: Monodromy of a Class of Logarithmic Connections on an Elliptic Curve

abstract:
  The logarithmic connections studied in the paper are direct images of regular
connections on line bundles over genus-2 double covers of the elliptic curve.
We give an explicit parametrization of all such connections, determine their
monodromy, differential Galois group and the underlying rank-2 vector bundle.
The latter is described in terms of elementary transforms. The question of its
(semi)-stability is addressed.


title: Stochastic Variational Integrators

abstract:
  This paper presents a continuous and discrete Lagrangian theory for
stochastic Hamiltonian systems on manifolds. The main result is to derive
stochastic governing equations for such systems from a critical point of a
stochastic action. Using this result the paper derives Langevin-type equations
for constrained mechanical systems and implements a stochastic analog of
Lagrangian reduction. These are easy consequences of the fact that the
stochastic action is intrinsically defined. Stochastic variational integrators
(SVIs) are developed using a discretized stochastic variational principle. The
paper shows that the discrete flow of an SVI is a.s. symplectic and in the
presence of symmetry a.s. momentum-map preserving. A first-order mean-square
convergent SVI for mechanical systems on Lie groups is introduced. As an
application of the theory, SVIs are exhibited for multiple, randomly forced and
torqued rigid-bodies interacting via a potential.


title:
Comparison between Second Variation of Area and Second Variation of
  Energy of a Minimal Surface

abstract:
  The conformal parameterisation of a minimal surface is harmonic. Therefore, a
minimal surface is a critical point of both the energy functional and the area
functional. In this paper, we compare the Morse index of a minimal surface as a
critical point of the area functional with its Morse index as a critical point
of the energy functional. The difference between these indices is at most the
real dimension of Teichmuller space. This comparison allows us to obtain
surprisingly good upper bounds on the index of minimal surfaces of finite total
curvature in Euclidean space of any dimension. We also bound the index of a
minimal surface in an arbitrary Riemannian manifold by the area and genus of
the surface, and the dimension and geometry of the ambient manifold.


title: Reconsidering Relativistic Causality

abstract:
  I discuss the idea of relativistic causality, i.e. the requirement that
causal processes or signals can propagate only within the light-cone. After
briefly locating this requirement in the philosophy of causation, my main aim
is to draw philosophers' attention to the fact that it is subtle, indeed
problematic, in relativistic quantum physics: there are scenarios in which it
seems to fail.
  I consign to an Appendix two such scenarios, which are familiar to
philosophers of physics: the pilot-wave approach, and the Newton-Wigner
representation. I instead stress two unfamiliar scenarios: the
Drummond-Hathrell and Scharnhorst effects. These effects also illustrate a
general moral in the philosophy of geometry: that the mathematical structures,
especially the metric tensor, that represent geometry get their geometric
significance by dint of detailed physical arguments.


title: Primitive Divisors of some Lehmer-Pierce Sequences

abstract:
  We study the primitive divisors of the terms of $(\Delta_n)_{n \geq 1}$,
where $\Delta_n=N_{K/ \mathbb{Q}}(u^n-1)$ for $K$ a real quadratic field, and
$u>1$ a unit element of its ring of integers. The methods used allow us to find
the terms of the sequence that do not have a primitive prime divisor.


title: The global isoperimetric methodology applied to Kneser's Theorem

abstract:
  We give in the present work a new methodology that allows to give
isoperimetric proofs, for Kneser's Theorem and
  Kemperman's structure Theory and most sophisticated results of this type. As
an illustration we present a new proof of Kneser's Theorem.


title: Stochastic Einstein Locality Revisited

abstract:
  I discuss various formulations of stochastic Einstein locality (SEL), which
is a version of the idea of relativistic causality, i.e. the idea that
influences propagate at most as fast as light. SEL is similar to Reichenbach's
Principle of the Common Cause (PCC), and Bell's Local Causality.
  My main aim is to discuss formulations of SEL for a fixed background
spacetime. I previously argued that SEL is violated by the outcome dependence
shown by Bell correlations, both in quantum mechanics and in quantum field
theory. Here I re-assess those verdicts in the light of some recent literature
which argues that outcome dependence does not violate the PCC. I argue that the
verdicts about SEL still stand.
  Finally, I briefly discuss how to formulate relativistic causality if there
is no fixed background spacetime.


title: Focusing waves in unknown media by modified time reversal iteration

abstract:
  We study the wave equation in a bounded domain or on a compact Riemannian
manifold with boundary. Assume that we are given the hyperbolic
Neumann-to-Dirichlet map on the boundary corresponding to physical boundary
measurements. We consider how to focus waves, that is, how to find Neumann
boundary values so that at a given time the corresponding wave converges to a
delta distribution $\delta_y$ while the time derivative of the wave converges
to zero. Such boundary value are generated by an iterative sequence of
measurements. In each iteration step we apply time reversal and other simple
operators to measured data and compute boundary values for the next iteration
step. The key feature of the algorithm is that it does not require knowledge of
the coefficients in the wave equation, that is, the material parameters inside
the media. However, we assume that the point $y$ where the wave focuses is
known in travel time coordinates.


title:
Fermionic vacuum polarization in higher-dimensional global monopole
  spacetime

abstract:
  In this paper we analyse the vacuum polarization effects associated with a
massless fermionic field in a higher-dimensional global monopole spacetime in
the "braneworld" scenario. In this context we admit that the our Universe, the
bulk, is represented by a flat $(n-1)-$dimensional brane having a global
monopole in a extra transverse three dimensional submanifold. We explicitly
calculate the renormalized vacuum average of the energy-momentum tensor,
$<T_A^B(x)>_{Ren.}$, admitting the global monopole as being a point-like
object. We observe that this quantity depends crucially on the value of $n$,
and we provide explicit expressions to it for specific values attributed to
$n$.


title:
Connection between ordinary multinomials, generalized Fibonacci numbers,
  partial Bell partition polynomials and convolution powers of discrete uniform
  distribution

abstract:
  Using an explicit computable expression of ordinary multinomials, we
establish three remarkable connections, with the q-generalized Fibonacci
sequence, the exponential partial Bell partition polynomials and the density of
convolution powers of the discrete uniform distribution. Identities and various
combinatorial relations are derived.


title:
Superfluid properties of a Bose-Einstein condensate in an optical
  lattice confined in a cavity

abstract:
  We study the effect of a one dimensional optical lattice in a cavity field
with quantum properties on the superfluid dynamics of a Bose-Einstein
condensate(BEC). In the cavity the influence of atomic backaction and the
external driving pump become important and strongly modify the optical
potential. Due to the strong coupling between the condensate wavefunction and
the cavity modes, the cavity light field develops a band structure. This study
reveals that the pump and the cavity emerges as a new handle to control the
superfluid properties of the BEC.