title: On Khintchine exponents and Lyapunov exponents of continued fractions

abstract:
  Assume that $x\in [0,1) $ admits its continued fraction expansion $x=[a_1(x),
a_2(x),...]$. The Khintchine exponent $\gamma(x)$ of $x$ is defined by
$\gamma(x):=\lim\limits_{n\to \infty}\frac{1}{n}\sum_{j=1}^n \log a_j(x)$ when
the limit exists. Khintchine spectrum $\dim E_\xi$ is fully studied, where $
E_{\xi}:=\{x\in [0,1):\gamma(x)=\xi\} (\xi \geq 0)$ and $\dim$ denotes the
Hausdorff dimension. In particular, we prove the remarkable fact that the
Khintchine spectrum $\dim E_{\xi}$, as function of $\xi \in [0, +\infty)$, is
neither concave nor convex. This is a new phenomenon from the usual point of
view of multifractal analysis. Fast Khintchine exponents defined by
$\gamma^{\phi}(x):=\lim\limits_{n\to\infty}\frac{1}{\phi(n)} \sum_{j=1}^n \log
a_j(x)$ are also studied, where $\phi (n)$ tends to the infinity faster than
$n$ does. Under some regular conditions on $\phi$, it is proved that the fast
Khintchine spectrum $\dim (\{x\in [0,1]: \gamma^{\phi}(x)= \xi \}) $ is a
constant function. Our method also works for other spectra like the Lyapunov
spectrum and the fast Lyapunov spectrum.


title:
Generic points in systems of specification and Banach valued Birkhoff
  ergodic average

abstract:
  We prove that systems satisfying the specification property are saturated in
the sense that the topological entropy of the set of generic points of any
invariant measure is equal to the measure-theoretic entropy of the measure. We
study Banach valued Birkhoff ergodic averages and obtain a variational
principle for its topological entropy spectrum. As application, we examine a
particular example concerning with the set of real numbers for which the
frequencies of occurrences in their dyadic expansions of infinitely many words
are prescribed. This relies on our explicit determination of a maximal entropy
measure.


title: Quotients of fake projective planes

abstract:
  Recently, Prasad and Yeung classified all possible fundamental groups of fake
projective planes. According to their result, many fake projective planes admit
a nontrivial group of automorphisms, and in that case it is isomorphic to
$\bbZ/3\bbZ$, $\bbZ/7\bbZ$, $7:3$, or $(\bbZ/3\bbZ)^2$, where $7:3$ is the
unique non-abelian group of order 21.
  Let $G$ be a group of automorphisms of a fake projective plane $X$. In this
paper we classify all possible structures of the quotient surface $X/G$ and its
minimal resolution.


title:
On a nonhierarchical version of the Generalized Random Energy Model. II.
  Ultrametricity

abstract:
  We study the Gibbs measure of the nonhierarchical versions of the Generalized
Random Energy Models introduced in previous work. We prove that the
ultrametricity holds only provided some nondegeneracy conditions on the
hamiltonian are met.


title:
On Cusick-Cheon's Conjecture About Balanced Boolean Functions in the
  Cosets of the Binary Reed-Muller Code

abstract:
  It is proved an amplification of Cusick-Cheon's conjecture on balanced
Boolean functions in the cosets of the binary Reed-Muller code RM(k,m) of order
k and length 2^m, in the cases where k = 1 or k >= (m-1)/2.


title: Quadrefringence of optical vortices in a uniaxial crystal

abstract:
  The splitting of a single optical vortex into four separate ones in a
singular beam is theoretically and experimentally described for the propagation
of light obliquely through a uniaxial crystal. Also we found the condition
under which the new-born vortices in each four individual beams propagate
independently without dislocation reactions and have different locations in all
beams for any crystal lengths.


title: Results from a search for the $0\nu\beta\beta$-decay of $^{130}Te$

abstract:
  A detailed description of the CUORICINO $^{130}Te$ neutrinoless double-beta
($\nbb$) decay experiment is given and recent results are reported. CUORICINO
is an array of 62 tellurium oxide ($TeO_{2}$) bolometers with an active mass of
40.7 kg. It is cooled to $\sim 8-10$ mK by a dilution refrigerator shielded
from environmental radioactivity and energetic neutrons. It is running in the
Laboratori Nazionali del Gran Sasso (LNGS) in Assergi, Italy. These data
represent an exposure of $11.83\textrm{kg}...\textrm{y}$ or 91 mole-years of
$^{130}Te$. No evidence for $\nbb$-decay was observed and a limit of
$T^{0\nu}_{1/2}(^{130}Te)\geq3.0\times10^{24}$ y (90% C.L.) is set. This
corresponds to an upper limit on the effective mass, $< m_{\nu}>$, between 0.19
and 0.68 eV when analyzed with the many published nuclear structure
calculations. In the context of these nuclear models, the values fall within
the range corresponding to the claim of evidence of $\nbb$-decay by H.V.
Klapdor-Kleingrothaus, \textit{et al.} The experiment continues to acquire
data.


title: Localization behavior of vibrational modes in granular packings

abstract:
  We study the localization of vibrational modes of frictionless granular
media. We introduce a new method, motivated by earlier work on non-Hermitian
quantum problems, which works well both in the localized regime where the
localization length $\xi$ is much less than the linear size $L$ and in the
regime $\xi$ grater or of order $L$ when modes are extended throughout our
finite system. Our very lowest frequency modes show "quasi-localized"
resonances away from the jamming point; the spatial extent of these regions
increases as the jamming point is approached, as expected theoretically.
Throughout the remaining frequency range, our data show no signature of the
nearness of the jamming point and collapse well when properly rescaled with the
system size. Using Random Matrix Theory we derive the scaling relation $\xi$ ~
$L^{d/2}$ for the regime $\xi$ >> $L$ in $d$ dimensions.


title:
Efficient implementation of GALS systems over commercial synchronous
  FPGAs: a new approach

abstract:
  The new vision presented is aimed to overcome the logic overhead issues that
previous works exhibit when applying GALS techniques to programmable logic
devices. The proposed new view relies in a 2-phase, bundled data parity based
protocol for data transfer and clock generation tasks. The ability of the
introduced methodology for smart real-time delay selection allows the
implementation of a variety of new methodologies for electromagnetic
interference mitigation and device environment changes adaptation.


title: Quantum graphs: an introduction and a brief survey

abstract:
  The purpose of this text is to set up a few basic notions concerning quantum
graphs, to indicate some areas addressed in the quantum graph research, and to
provide some pointers to the literature. The pointers in many cases are
secondary, i.e. they refer to other surveys.


title:
Fully Band Resolved Scattering Rate in MgB2 Revealed by Nonlinear Hall
  Effect and Magnetoresistance Measurements

abstract:
  We have measured the normal state temperature dependence of the Hall effect
and magnetoresistance in epitaxial MgB2 thin films with variable disorders
characterized by the residual resistance ratio RRR ranging from 4.0 to 33.3. A
strong nonlinearity of the Hall effect and magnetoresistance have been found in
clean samples, and they decrease gradually with the increase of disorders or
temperature. By fitting the data to the theoretical model based on the
Boltzmann equation and ab initio calculations for a four-band system, for the
first time, we derived the scattering rates of these four bands at different
temperatures and magnitude of disorders. Our method provides a unique way to
derive these important parameters in multiband systems.


title: Automatic Verification of Correspondences for Security Protocols

abstract:
  We present a new technique for verifying correspondences in security
protocols. In particular, correspondences can be used to formalize
authentication. Our technique is fully automatic, it can handle an unbounded
number of sessions of the protocol, and it is efficient in practice. It
significantly extends a previous technique for the verification of secrecy. The
protocol is represented in an extension of the pi calculus with fairly
arbitrary cryptographic primitives. This protocol representation includes the
specification of the correspondence to be verified, but no other annotation.
This representation is then translated into an abstract representation by Horn
clauses, which is used to prove the desired correspondence. Our technique has
been proved correct and implemented. We have tested it on various protocols
from the literature. The experimental results show that these protocols can be
verified by our technique in less than 1 s.


title:
Free Field Construction of D-Branes in Rational Models of CFT and Gepner
  Models

abstract:
  This is a review article of my recent papers on free field construction of
D-branes in N = 2 superconformal minimal models and Gepner models.


title: Searching for the signatures of jet-ISM interactions in X-ray binaries

abstract:
  Jets from X-ray binaries are continuously injecting matter and energy into
the surrounding interstellar medium (ISM). However, there exist to date
relatively few cases where jet-ISM interactions have been directly observed. We
review the current examples, and go on to present new data on the proposed
hotspots of GRS1915+105, finding no concrete evidence for any association
between the hotspots and the central source, in agreement with previous
findings in the literature. We also present preliminary results on radio and
H-alpha searches for jet-ISM interactions around known X-ray binaries, and
discuss strategies for future searches.


title: On the functional properties of microRNA-mediated feed forward loops

abstract:
  Motivation: Recent studies of genomic-scale regulatory networks suggested
that a feed-forward loop (FFL) circuitry is a key component of many such
networks. This led to a study of the functional properties of different FFL
types, where the regulatory elements are transcription factors.
  Results: Here we investigate these properties when the mediating regulatory
element of the loop is a microRNA. We find that many of the FFL properties are
enhanced within this setup. We then proceed to identify all such FFLs in the D.
Melanogaster regulatory network. We observe that in FFLs rooted at the same
transcription factor there are significant correlations between the number of
predicted binding sites for the transcription factor and for the microRNA.
  Conclusions: Based on a modeling approach we suggest that these correlations
may be an outcome of the type of FFL preferred by the transcription factor.
This may help elucidate the type of regulation the TF confers.


title: Sketch-Based Estimation of Subpopulation-Weight

abstract:
  Summaries of massive data sets support approximate query processing over the
original data. A basic aggregate over a set of records is the weight of
subpopulations specified as a predicate over records' attributes. Bottom-k
sketches are a powerful summarization format of weighted items that includes
priority sampling and the classic weighted sampling without replacement. They
can be computed efficiently for many representations of the data including
distributed databases and data streams.
  We derive novel unbiased estimators and efficient confidence bounds for
subpopulation weight. Our estimators and bounds are tailored by distinguishing
between applications (such as data streams) where the total weight of the
sketched set can be computed by the summarization algorithm without a
significant use of additional resources, and applications (such as sketches of
network neighborhoods) where this is not the case.
  Our rigorous derivations are based on clever applications of the
Horvitz-Thompson estimator, and are complemented by efficient computational
methods. We demonstrate their benefit on a wide range of Pareto distributions.


title: On peak phenomena for non-commutative $H^\infty$

abstract:
  A non-commutative extension of Amar and Lederer's peak set result is given.
As its simple applications it is shown that any non-commutative
$H^\infty$-algebra $H^\infty(M,\tau)$ has unique predual,and moreover some
restriction in some of the results of Blecher and Labuschagne are removed,
making them hold in full generality.


title: Chiral symmetry and excited baryons

abstract:
  An approach to baryons in the framework of the microscopic Generalized
Nambu-Jona-Lasinio chiral potential quark model is considered and quite general
arguments are given in favor of effective restoration of chiral symmetry in
excited baryons.


title: Bifurcation and numerical study in an EHD convection problem

abstract:
  The linear eigenvalue problem governing the stability of the mechanical
equilibrium of the fluid in a electrohydrodynamic (EHD) convection problem is
investigated. The analytical study is one of bifurcation. This allows us to
regain the expression of the neutral surface in the classical case. The method
used in the numerical study is a Galerkin type spectral method based on
polynomials and it provides good results.


title: H\"ormander type pseudodifferential calculus on homogeneous groups

abstract:
  We produce, on general homogeneous groups, an analogue of the usual
H\"ormander pseudodifferential calculus on Euclidean space, at least as far as
products and adjoints are concerned. In contrast to earlier works, we do not
limit ourselves to analogues of classical symbols, nor to the Heisenberg group.
The key technique is to understand ``multipliers'' of any given order j, and
the operators of convolution with their inverse Fourier transforms, which we
here call convolution operators of order j. (Here a ``multiplier'' is an
analogue of a H\"ormander-type symbol a(x,\xi), which is independent of x.)
Specifically, we characterize the space of inverse Fourier transforms of
multipliers of any order j, and use this characterization to show that the
composition of convolution operators of order j_1 and j_2 is a convolution
operator of order j_1+j_2.


title: Galactic rotation curves and brane world models

abstract:
  In the present investigation flat rotational curves of the galaxies are
considered under the framework of brane-world models where the 4d effective
Einstein equation has extra terms which arise from the embedding of the 3-brane
in the $5d$ bulk. It has been shown here that these long range bulk
gravitational degrees of freedom can act as a mechanism to yield the observed
galactic rotation curves without the need for dark matter. The present model
has the advantage that the observed rotation curves result solely from
well-established non-local effects of gravitation, such as dark radiation and
dark pressure under a direct use of the condition of flat rotation curves and
does not invoke any exotic matter field.


title:
Unified Gauge Theories and Reduction of Couplings: from Finiteness to
  Fuzzy Extra Dimensions

abstract:
  Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories,
which can be made all-loop finite, both in the dimensionless (gauge and Yukawa
couplings) and dimensionful (soft supersymmetry breaking terms) sectors. This
remarkable property, based on the reduction of couplings at the quantum level,
provides a drastic reduction in the number of free parameters, which in turn
leads to an accurate prediction of the top quark mass in the dimensionless
sector, and predictions for the Higgs boson mass and the supersymmetric
spectrum in the dimensionful sector. Here we examine the predictions of two
such FUTs. Next we consider gauge theories defined in higher dimensions, where
the extra dimensions form a fuzzy space (a finite matrix manifold). We
reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein
modes. We then perform a generalized a la Forgacs-Manton dimensional reduction.
We emphasize some striking features emerging such as (i)the appearance of
non-Abelian gauge theories in four dimensions starting from an Abelian gauge
theory in higher dimensions, (ii) the fact that the spontaneous symmetry
breaking of the theory takes place entirely in the extra dimensions and (iii)
the renormalizability of the theory both in higher as well as in four
dimensions. Then reversing the above approach we present a renormalizable four
dimensional SU(N) gauge theory with a suitable multiplet of scalar fields,
which via spontaneous symmetry breaking dynamically develops extra dimensions
in the form of a fuzzy sphere $S^2_N$.


title: A Truncation Approach for Fast Computation of Distribution Functions

abstract:
  In this paper, we propose a general approach for improving the efficiency of
computing distribution functions. The idea is to truncate the domain of
summation or integration.


title: Selfdual strings and loop space Nahm equations

abstract:
  We give two independent arguments why the classical membrane fields should be
loops. The first argument comes from how we may construct selfdual strings in
the M5 brane from a loop space version of the Nahm equations. The second
argument is that there appears to be no infinite set of finite-dimensional Lie
algebras (such as $su(N)$ for any $N$) that satisfies the algebraic structure
of the membrane theory.


title: Spreadsheet Errors: What We Know. What We Think We Can Do

abstract:
  Fifteen years of research studies have concluded unanimously that spreadsheet
errors are both common and non-trivial. Now we must seek ways to reduce
spreadsheet errors. Several approaches have been suggested, some of which are
promising and others, while appealing because they are easy to do, are not
likely to be effective. To date, only one technique, cell-by-cell code
inspection, has been demonstrated to be effective. We need to conduct further
research to determine the degree to which other techniques can reduce
spreadsheet errors.


title:
Confidence Interval for the Mean of a Bounded Random Variable and Its
  Applications in Point Estimation

abstract:
  In this article, we derive an explicit formula for computing confidence
interval for the mean of a bounded random variable. Moreover, we have developed
multistage point estimation methods for estimating the mean value with
prescribed precision and confidence level based on the proposed confidence
interval.


title: Estimating Traffic Parameters with Rigorous Error Control

abstract:
  To perform a queuing analysis or design in a communications context, we need
to estimate the values of the input parameters, specifically the mean of the
arrival rate and service time. In this paper, we propose an approach for
estimating the arrival rate of Poisson processes and the average service time
for servers under the assumption that the service time is exponential. In
particular, we derive sample size (i.e., the number of i.i.d. observations)
required to obtain an estimate satisfying a pre-specified relative accuracy
with a given confidence level. A remarkable feature of this approach is that no
a priori information about the parameter is needed. In contrast to conventional
methods such as, standard error estimation and confidence interval
construction, which only provides post-experimental evaluations of the
estimate, this approach allows experimenters to rigorously control the error of
estimation.


title:
Mode identification for Balloon 090100001 using combined multicolour
  photometry and spectroscopy

abstract:
  In this paper, we show that method of mode identification using combined
multicolour photometry and spectroscopy can be successfully applied to the
pulsating subdwarf B star Balloon 090100001. The method constrains the
spherical degree, l.We confirm that the dominant mode is radial and we show
that for some other modes the method provides values of l consistent with the
observed rotationally split triplet. Moreover, we derive a radius variation of
1.7 per cent for the dominant mode. The identification opens the possibility
for constraining the internal structure of the star by means of seismic
methods.


title: Infinite class field towers

abstract:
  This paper studies infinite class field towers of number fields $K$ that are
ramified over $\Q$ only at one finite prime. In particular, we show the
existence of such towers for a general family of primes including $p=2$, 3 and
5.


title: Room-Temperature Superfluidity in Graphene Bilayers

abstract:
  Because graphene is an atomically two-dimensional gapless semiconductor with
nearly identical conduction and valence bands, graphene-based bilayers are
attractive candidates for high-temperature electron-hole pair condensation. We
present estimates which suggest that the Kosterlitz-Thouless temperatures of
these two-dimensional counterflow superfluids can approach room temperature.


title: Nuclear astrophysics from direct reactions

abstract:
  Accurate nuclear reaction rates are needed for primordial nucleosynthesis and
hydrostatic burning in stars. The relevant reactions are extremely difficult to
measure directly in the laboratory at the small astrophysical energies. In
recent years direct reactions have been developed and applied to extract
low-energy astrophysical S-factors. These methods require a combination of new
experimental techniques and theoretical efforts, which are the subject of this
presentation.


title: An electronic radiation of blackbody: Cosmic electron background

abstract:
  The Universe owns the electronic radiation of blackbody at temperature 2.725
K, which we call the cosmic electron background. We calculate its radiation
spectrum. The energy distribution of number density of electrons in the cosmic
electron background becomes zero as energy goes to both zero and infinity. It
has one maximum peak near the energy level of 10**(-23) J.


title: Swift UVOT Observations of Core-Collapse SNe

abstract:
  We review recent UV observations of core-collapse supernovae (SNe) with the
Swift Ultra-violet/Optical Telescope (UVOT) during its first two years.
Rest-frame UV photometry is useful for differentiating SN types by exploiting
the UV-optical spectral shape and more subtle UV features. This is useful for
the real-time classification of local and high-redshift SNe using only
photometry. Two remarkable SNe Ib/c were observed with UVOT -- SN2006jc was a
UV bright SN Ib. Swift observations of GRB060218/SN2006aj began shortly after
the explosion and show a UV-bright peak followed by a UV-faint SN bump. UV
observations are also useful for constraining the temperature and ionization
structure of SNe IIP. Rest-frame UV observations of all types are important for
understanding the extinction, temperature, and bolometric luminosity of SNe and
to interpret the observations of high redshift SNe observed at optical
wavelengths.


title:
Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule
  Decorations

abstract:
  We study a family of Hamiltonians of fermions hopping on a set of lattices in
the presence of a background gauge field. The lattices are constructed by
decorating the root lattices of various Lie algebras with their minuscule
representations. The Hamiltonians are, in momentum space, themselves elements
of the Lie algebras in these same representations. We describe various
interesting aspects of the spectra--which exhibit a family resemblance to the
Dirac spectrum, and in many cases are able to relate them to known facts about
the relevant Lie algebras. Interestingly, various realizable lattices such as
the kagom\'{e} and pyrochlore can be given this Lie algebraic interpretation
and the particular flux Hamiltonians arise as mean-field Hamiltonians for
spin-1/2 Heisenberg models on these lattices.


title:
The Aizenman-Sims-Starr and Guerra's schemes for the SK model with
  multidimensional spins

abstract:
  We prove upper and lower bounds on the free energy in the
Sherrington-Kirkpatrick model with multidimensional (e.g., Heisenberg) spins in
terms of the variational inequalities based on the corresponding Parisi
functional. We employ the comparison scheme of Aizenman, Sims and Starr and the
one of Guerra involving the generalised random energy model-inspired processes
and Ruelle's probability cascades. For this purpose an abstract quenched large
deviations principle of the Gaertner-Ellis type is obtained. Using the
properties of Ruelle's probability cascades and the Bolthausen-Sznitman
coalescent, we derive Talagrand's representation of the Guerra remainder term
for our model. We study the properties of the multidimensional Parisi
functional by establishing a link with a certain class of the non-linear
partial differential equations. Solving a problem posed by Talagrand, we show
the strict convexity of the local Parisi functional. We prove the Parisi
formula for the local free energy in the case of the multidimensional Gaussian
a priori distribution of spins using Talagrand's methodology of the a priori
estimates.


title: Fourier transforms of UD integrals

abstract:
  UD integrals published by N. Usyukina and A. Davydychev in 1992-1993 are
integrals corresponding to ladder-type Feynman diagrams. The results are UD
functions $\Phi^{(L)},$ where $L$ is the number of loops. They play an
important role in N=4 supersymmetic Yang-Mills theory. The integrals were
defined and calculated in the momentum space. In this paper the position space
representation of UD functions is investigated. We show that Fourier transforms
of UD functions are UD functions of space-time intervals but this
correspondence is indirect. For example, the Fourier transform of the second UD
integral is the second UD integral.


title:
Asymptotic Normality of the Additive Regression Components for
  Continuous Time Processes

abstract:
  In multivariate regression estimation, the rate of convergence depends on the
dimension of the regressor. This fact, known as the curse of the
dimensionality, motivated several works. The additive model, introduced by
Stone (10), offers an efficient response to this problem. In the setting of
continuous time processes, using the marginal integration method, we obtain the
quadratic convergence rate and the asymptotic normality of the components of
the additive model.


title: Leptogenesis in a perturbative SO(10) model

abstract:
  We consider a phenomenologically viable SO(10) grand unification model which
allows perturbative calculations up to the Planck scale or the string scale. We
use a set of Higgs superfields {10 + 16bar + 16 + 45}. In this framework, the
data fitting of the charged fermion mass matrices is re-examined. This model
can indeed reproduce the low-energy experimental data relating the charged
fermion masses and mixings. As for the neutrino sector, we take the neutrino
oscillation data as input data to construct right-handed Majorana neutrino mass
matrix and get a prediction for the physics related to the right-handed
neutrinos, e.g. the leptogenesis and for the proton decay. We propose two kinds
of phenomenologically viable model, quoted as Model 1 and Model 2. We show that
one of the models (Model 2) is consistent with all experimental constraints.


title: Moufang symmetry I. Generalized Lie and Maurer-Cartan equations

abstract:
  The continuous Moufang loops are characterized as the algebraic systems where
the associativity law is perturbed minimally. The minimal perturbation of
associativity is characterized by the first- order partial differential
equations, which in a natural way generalize the Lie and Maurer-Cartan
equations from the theory of Lie groups.


title: Reconciling Semiclassical and Bohmian Mechanics: I. Stationary states

abstract:
  The semiclassical method is characterized by finite forces and smooth,
well-behaved trajectories, but also by multivalued representational functions
that are ill-behaved at turning points. In contrast, quantum trajectory
methods--based on Bohmian mechanics (quantum hydrodynamics)--are characterized
by infinite forces and erratic trajectories near nodes, but also well-behaved,
single-valued representational functions. In this paper, we unify these two
approaches into a single method that captures the best features of both, and in
addition, satisfies the correspondence principle. Stationary eigenstates in one
degree of freedom are the primary focus, but more general applications are also
anticipated.


title: On Cobweb Posets and Discrete F-Boxes Tilings

abstract:
  F-boxes defined in [6] as hyper-boxes in N^{\infty} discrete space were
applied here for the geometric description of the cobweb posetes Hasse diagrams
tilings. The F-boxes edges sizes are taken to be values of terms of natural
numbers' valued sequence F. The problem of partitions of hyper-boxes
represented by graphs into blocks of special form is considered and these are
to be called F-tilings. The proof of such tilings' existence for certain
sub-family of admissible sequences F is delivered. The family of F-tilings
which we consider here includes among others F = Natural numbers, Fibonacci
numbers, Gaussian integers with their corresponding F-nomial (Binomial,
Fibonomial, Gaussian) coefficients. Extension of this tiling problem onto the
general case multi F-nomial coefficients is here proposed. Reformulation of the
present cobweb tiling problem into a clique problem of a graph specially
invented for that purpose - is proposed here too. To this end we illustrate the
area of our reconnaissance by means of the Venn type map of various cobweb
sequences families.


title:
Classification of electromagnetic fields in general relativity and its
  physical applications

abstract:
  The simplest electromagnetic fields' (general- as well as
special-relativistic) classification is formulated which is based on physically
motivated ideas. According to this classification these fields can belong to
three types (electric, magnetic and null), each of them being split in pure and
impure subtypes. Only pure null type field propagates with the fundamental
velocity $c$, all other fields have the propagation velocity less than that of
light. The reference-frame-based methods of elimination of alternative
three-fields (e.g., magnetic in the electric type case) are given for pure
subtypes; for pure null type the generalized Doppler effect takes place
instead. All three types of impure fields are shown to be {\bf E}-{\bf
B}-parallelizable. Thus such an elimination in pure non-null and
parallelization in all impure cases mean transformation to the reference frame
co-moving with the electromagnetic field in which the Poynting vector vanishes.
The methods we propose modernizing the Rainich--Misner--Wheeler approach, also
permit to construct new exact Einstein--Maxwell solutions from already known
seed solutions. As examples, the Kerr--Newman and Li\'enard--Wiechert solutions
are considered, three ``new'' types of rotating charged black holes (with the
same Kerr-Newman geometry) are presented, and new physical effects are
evaluated. PACS 2008 Numbers: 04.20-{\bf q}, 04.20.Ex, 04.40.Nr, 04.70.Bw


title:
Spreadsheet Development Methodologies using Resolver: Moving
  spreadsheets into the 21st Century

abstract:
  We intend to demonstrate the innate problems with existing spreadsheet
products and to show how to tackle these issues using a new type of spreadsheet
program called Resolver. It addresses the issues head-on and thereby moves the
1980's "VisiCalc paradigm" on to match the advances in computer languages and
user requirements. Continuous display of the spreadsheet grid and the
equivalent computer program, together with the ability to interact and add code
through either interface, provides a number of new methodologies for
spreadsheet development.


title: Fun Boy Three Were Wrong: it is what you do, not the way that you do it

abstract:
  I revisit some classic publications on modularity, to show what problems its
pioneers wanted to solve. These problems occur with spreadsheets too: to
recognise them may help us avoid them.


title: Concerning the Feasibility of Example-driven Modelling Techniques

abstract:
  We report on a series of experiments concerning the feasibility of example
driven modelling. The main aim was to establish experimentally within an
academic environment: the relationship between error and task complexity using
a) Traditional spreadsheet modelling; b) example driven techniques. We report
on the experimental design, sampling, research methods and the tasks set for
both control and treatment groups. Analysis of the completed tasks allows
comparison of several different variables. The experimental results compare the
performance indicators for the treatment and control groups by comparing
accuracy, experience, training, confidence measures, perceived difficulty and
perceived completeness. The various results are thoroughly tested for
statistical significance using: the Chi squared test, Fisher's exact test for
significance, Cochran's Q test and McNemar's test on difficulty.


title:
It Ain't What You View, But The Way That You View It: documenting
  spreadsheets with Excelsior, semantic wikis, and literate programming

abstract:
  I describe preliminary experiments in documenting Excelsior versions of
spreadsheets using semantic wikis and literate programming. The objective is to
create well-structured and comprehensive documentation, easy to use by those
unfamiliar with the spreadsheets documented. I discuss why so much
documentation is hard to use, and briefly explain semantic wikis and literate
programming; although parts of the paper are Excelsior-specific, these sections
may be of more general interest.


title:
An Empirical Study of End-User Behaviour in Spreadsheet Error Detection
  & Correction

abstract:
  Very little is known about the process by which end-user developers detect
and correct spreadsheet errors. Any research pertaining to the development of
spreadsheet testing methodologies or auditing tools would benefit from
information on how end-users perform the debugging process in practice.
Thirteen industry-based professionals and thirty-four accounting & finance
students took part in a current ongoing experiment designed to record and
analyse end-user behaviour in spreadsheet error detection and correction.
Professionals significantly outperformed students in correcting certain error
types. Time-based cell activity analysis showed that a strong correlation
exists between the percentage of cells inspected and the number of errors
corrected. The cell activity data was gathered through a purpose written VBA
Excel plug-in that records the time and detail of all cell selection and cell
change actions of individuals.


title: Why Task-Based Training is Superior to Traditional Training Methods

abstract:
  The risks of spreadsheet use do not just come from the misuse of formulae. As
such, training needs to go beyond this technical aspect of spreadsheet use and
look at the spreadsheet in its full business context. While standard training
is by and large unable to do this, task-based training is perfectly suited to a
contextual approach to training.


title:
Establishing A Minimum Generic Skill Set For Risk Management Teaching In
  A Spreadsheet Training Course

abstract:
  Past research shows that spreadsheet models are prone to such a high
frequency of errors and data security implications that the risk management of
spreadsheet development and spreadsheet use is of great importance to both
industry and academia. The underlying rationale for this paper is that
spreadsheet training courses should specifically address risk management in the
development process both from a generic and a domain-specific viewpoint. This
research specifically focuses on one of these namely those generic issues of
risk management that should be present in a training course that attempts to
meet good-practice within industry. A pilot questionnaire was constructed
showing a possible minimum set of risk management issues and sent to academics
and industry practitioners for feedback. The findings from this pilot survey
will be used to refine the questionnaire for sending to a larger body of
possible respondents. It is expected these findings will form the basis of a
risk management teaching approach to be trialled in a number of selected
ongoing spreadsheet training courses.


title:
Formation and Detectability of Terrestrial Planets Around Alpha Centauri
  B

abstract:
  We simulate the formation of planetary systems around Alpha Centauri B. The
N-body accretionary evolution of a 1/r disk populated with 400-900 lunar-mass
protoplanets is followed for 200 Myr. All simulations lead to the formation of
multiple-planet systems with at least one planet in the 1-2 MEarth mass range
at 0.5-1.5 AU. We examine the detectability of our simulated planetary systems
by generating synthetic radial velocity observations including noise based on
the radial velocity residuals to the recently published three planet fit to the
nearby K0V star HD 69830. Using these synthetic observations, we find that we
can reliably detect a 1.8 MEarth planet in the habitable zone of Alpha Centauri
B after only three years of high cadence observations. We also find that the
planet is detectable even if the radial velocity precision is 3 m/s, as long as
the noise spectrum is white. Our results show that the greatest uncertainty in
our ability to detect rocky planets in the Alpha Centauri system is the unknown
magnitude of ultra-low frequency stellar noise.


title: Voice-controlled Debugging of Spreadsheets

abstract:
  Developments in Mobile Computing are putting pressure on the software
industry to research new modes of interaction that do not rely on the
traditional keyboard and mouse combination. Computer users suffering from
Repetitive Strain Injury also seek an alternative to keyboard and mouse devices
to reduce suffering in wrist and finger joints. Voice-control is an alternative
approach to spreadsheet development and debugging that has been researched and
used successfully in other domains. While voice-control technology for
spreadsheets is available its effectiveness has not been investigated. This
study is the first to compare the performance of a set of expert spreadsheet
developers that debugged a spreadsheet using voice-control technology and
another set that debugged the same spreadsheet using keyboard and mouse. The
study showed that voice, despite its advantages, proved to be slower and less
accurate. However, it also revealed ways in which the technology might be
improved to redress this imbalance.


title:
Perfect teleportation and superdense coding through an asymmetric five
  qubit state

abstract:
  We explicate an example of the so called Task oriented Maximally Entangled
states (TMES) in the context of teleportation and superdense coding. In
physical situation, this state can emerge from decoherence of more entangled
state or may be prepared for the purpose at hand, with less entanglement
resource. We find that a variant of the Brown state can be utilized for perfect
teleportation of single and two qubit states. In case of superdense coding, it
is observed that five cbits can be transmitted by sending only three qubits.


title: The waiting time for m mutations

abstract:
  We consider a model of a population of fixed size N in which each individual
gets replaced at rate one and each individual experiences a mutation at rate
\mu. We calculate the asymptotic distribution of the time that it takes before
there is an individual in the population with m mutations. Several different
behaviors are possible, depending on how \mu changes with N. These results have
applications to the problem of determining the waiting time for regulatory
sequences to appear and to models of cancer development.


title: A shallow-water theory for annular sections of Keplerian Disks

abstract:
  A scaling argument is presented that leads to a shallow water theory of
non-axisymmetric disturbances in annular sections of thin Keplerian disks. To
develop a theoretical construction that will aid in physically understanding
the relationship of known two-dimensional vortex dynamics to their
three-dimensional counterparts in Keplerian disks. Using asymptotic scaling
arguments varicose disturbances of a Keplerian disk are considered on radial
and vertical scales consistent with the height of the disk while the azimuthal
scales are the full $2\pi$ angular extent of the disk. The scalings lead to
dynamics which are radially geostrophic and vertically hydrostatic. It follows
that a potential vorticity quantity emerges and is shown to be conserved in a
Lagrangian sense. Uniform potential vorticity linear solutions are explored and
the theory is shown to contain an incarnation of the strato-rotational
instability under channel flow conditions. Linearized solutions of a single
defect on an infinite domain is developed and is shown to support a propagating
Rossby edgewave. Linear non-uniform potential vorticity solutions are also
developed and are shown to be similar in some respects to the dynamics of
strictly two-dimensional inviscid flows. Based on the framework of this theory,
arguments based on geophysical notions are presented to support the assertion
that the strato-rotational instability is in a generic class of
barotropic/baroclinic potential vorticity instabilities. Extensions of this
formalism are also proposed. The shallow water formulation achieved by the
asymptotic theory developed here opens a new approach to studying disk
dynamics.


title: Reconstruction of Random Colourings

abstract:
  Reconstruction problems have been studied in a number of contexts including
biology, information theory and and statistical physics. We consider the
reconstruction problem for random $k$-colourings on the $\Delta$-ary tree for
large $k$. Bhatnagar et. al. showed non-reconstruction when $\Delta \leq
\frac12 k\log k - o(k\log k)$ and reconstruction when $\Delta \geq k\log k +
o(k\log k)$. We tighten this result and show non-reconstruction when $\Delta
\leq k[\log k + \log \log k + 1 - \ln 2 -o(1)]$ and reconstruction when $\Delta
\geq k[\log k + \log \log k + 1+o(1)]$.


title:
Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type
  One

abstract:
  The quiver Hopf algebras are classified by means of ramification systems with
irreducible representations. This leads to the classification of Nichols
algebras over group algebras and pointed Hopf algebras of type one.


title: Fermi-edge problem in the presence of AC electric field

abstract:
  We study in this paper a non-equilibrium Fermi-edge problem where the system
under investigation is a single electron reservoir putting under an AC electric
field. We show that the electron Green's function and other correlation
functions in the problem can be solved and expressed exactly in terms of a
well-defined integral. The qualitative behaviors of the solution is studied and
compared with the situation where the impurity is coupled to more than one
reservoirs at different chemical potentials.


title: On capacity of wireless ad hoc networks with MIMO MMSE receivers

abstract:
  Widely adopted at home, business places, and hot spots, wireless ad-hoc
networks are expected to provide broadband services parallel to their wired
counterparts in near future. To address this need, MIMO techniques, which are
capable of offering several-fold increase in capacity, hold significant
promise. Most previous work on capacity analysis of ad-hoc networks is based on
an implicit assumption that each node has only one antenna. Core to the
analysis therein is the characterization of a geometric area, referred to as
the exclusion region, which quantizes the amount of spatial resource occupied
by a link. When multiple antennas are deployed at each node, however, multiple
links can transmit in the vicinity of each other simultaneously, as
interference can now be suppressed by spatial signal processing. As such, a
link no longer exclusively occupies a geometric area, making the concept of
"exclusion region" not applicable any more. In this paper, we investigate
link-layer throughput capacity of MIMO ad-hoc networks. In contrast to previous
work, the amount of spatial resource occupied by each link is characterized by
the actual interference it imposes on other links. To calculate the link-layer
capacity, we first derive the probability distribution of post-detection SINR
at a receiver. The result is then used to calculate the number of active links
and the corresponding data rates that can be sustained within an area. Our
analysis will serve as a guideline for the design of medium access protocols
for MIMO ad-hoc networks. To the best of knowledge, this paper is the first
attempt to characterize the capacity of MIMO ad-hoc networks by considering the
actual PHY-layer signal and interference model.


title: Efficient Counting and Asymptotics of $k$-noncrossing tangled-diagrams

abstract:
  In this paper we enumerate $k$-noncrossing tangled-diagrams. A
tangled-diagram is a labeled graph whose vertices are $1,...,n$ have degree
$\le 2$, and are arranged in increasing order in a horizontal line. Its arcs
are drawn in the upper halfplane with a particular notion of crossings and
nestings. Our main result is the asymptotic formula for the number of
$k$-noncrossing tangled-diagrams $T_{k}(n) \sim c_k n^{-((k-1)^2+(k-1)/2)}
(4(k-1)^2+2(k-1)+1)^n$ for some $c_k>0$.


title: The RDF Virtual Machine

abstract:
  The Resource Description Framework (RDF) is a semantic network data model
that is used to create machine-understandable descriptions of the world and is
the basis of the Semantic Web. This article discusses the application of RDF to
the representation of computer software and virtual computing machines. The
Semantic Web is posited as not only a web of data, but also as a web of
programs and processes.


title: New scenario for transition to slow 3D turbulence

abstract:
  Analytical non-perturbative study of the three-dimensional nonlinear
stochastic partial differential equation with additive thermal noise, analogous
to that proposed by V.N. Nikolaevskii [1]-[5]to describe longitudinal seismic
waves, is presented. The equation has a threshold of short-wave instability and
symmetry, providing long wave dynamics. New mechanism of quantum chaos
generating in nonlinear dynamical systems with infinite number of degrees of
freedom is proposed. The hypothesis is said, that physical turbulence could be
identified with quantum chaos of considered type. It is shown that the additive
thermal noise destabilizes dramatically the ground state of the Nikolaevskii
system thus causing it to make a direct transition from a spatially uniform to
a turbulent state.


title: Waves in the solar photosphere

abstract:
  The solar photosphere is a partially ionized medium with collisions between
electrons, various metallic ions and neutral hydrogen playing an important role
in the momentum and energy transport in the medium. Furthermore, the number of
neutral hydrogen atom could be as large as $10^{4}$ times the number of plasma
particles in the lower photosphere. The non-ideal MHD effects, namely Ohm,
Ambipolar and Hall diffusion can play an important role in the photosphere. We
demonstrate that Hall is an important non-ideal MHD effect in the solar
photosphere and show that Hall effect can significantly affect the excitation
and propagation of the waves in the medium. We also demonstrate that the
non-ideal Hall dominated inhomogeneous medium can become parametrically
unstable, and it could have important ramification for the photosphere and
chromosphere of the sun. The analysis hints at the possibility of solar
photosphere becoming parametrically unstable against the linear fluctuations.


title:
Gaussian Interference Networks: Sum Capacity in the Low Interference
  Regime and New Outer Bounds on the Capacity Region

abstract:
  Establishing the capacity region of a Gaussian interference network is an
open problem in information theory. Recent progress on this problem has led to
the characterization of the capacity region of a general two user Gaussian
interference channel within one bit. In this paper, we develop new, improved
outer bounds on the capacity region. Using these bounds, we show that treating
interference as noise achieves the sum capacity of the two user Gaussian
interference channel in a low interference regime, where the interference
parameters are below certain thresholds. We then generalize our techniques and
results to Gaussian interference networks with more than two users. In
particular, we demonstrate that the total interference threshold, below which
treating interference as noise achieves the sum capacity, increases with the
number of users.


title:
Quantized meson fields in and out of equilibrium. I : Kinetics of meson
  condensate and quasi-particle excitations

abstract:
  We formulate a kinetic theory of self-interacting meson fields with an aim to
describe the freezeout stage of the space-time evolution of matter in
ultrarelativistic nuclear collisions. Kinetic equations are obtained from the
Heisenberg equation of motion for a single component real scalar quantum field
taking the mean field approximation for the non-linear interaction. The mesonic
mean field obeys the classical non-linear Klein-Gordon equation with a
modification due to the coupling to mesonic quasi-particle excitations which
are expressed in terms of the Wigner functions of the quantum fluctuations of
the meson field, namely the statistical average of the bilinear forms of the
meson creation and annihilation operators. In the long wavelength limit, the
equations of motion of the diagonal components of the Wigner functions take a
form of Vlasov equation with a particle source and sink which arises due to the
non-vanishing off-diagonal components of the Wigner function expressing
coherent pair-creation and pair-annihilation process in the presence of
non-uniform condensate. We show that in the static homogeneous system, these
kinetic equations reduce to the well-known gap equation in the Hartree
approximation, and hence they may be considered as a generalization of the
Hartree approximation method to non-equilibrium systems. As an application of
these kinetic equations, we compute the dispersion relations of the collective
mesonic excitations in the system near equilibrium.


title:
Mapping properties of fundamental operators in harmonic analysis related
  to Bessel operators

abstract:
  We prove sharp power-weighted strong type, weak type and restricted weak type
inequalities for the heat and Poisson integral maximal operators, Riesz
transform and a Littlewood-Paley type square function, emerging naturally in
the harmonic analysis related to Bessel operators.


title:
Vibrational detection and control of spin in mixed-valence molecular
  transistors

abstract:
  We investigate electron transport through a mixed-valence molecular complex
in which an excess electron can tunnel between hetero-valent transition metal
ions, each having a fixed localized spin. We show that in this class of
molecules the interplay of the spins and the vibrational breathing modes of the
ionic ligand-shells allows the total molecular spin to be detected as well as
controlled by nonequilibrium transport. Due to a spin-dependent pseudo
Jahn-Teller effect electronic transitions with different spin values can be
distinguished by their vibronic conductance side peaks, without using an
external magnetic field. Conversely, we show that the spin state of the entire
molecule can also be controlled via the nonequilibrium quantized molecular
vibrations due to a vibration-induced spin-blockade.


title:
Coulomb interactions in single, charged self-assembled quantum dots:
  radiative lifetime and recombination energy

abstract:
  We present results on the charge dependence of the radiative recombination
lifetime, Tau, and the emission energy of excitons confined to single
self-assembled InGaAs quantum dots. There are significant dot-to-dot
fluctuations in the lifetimes for a particular emission energy. To reach
general conclusions, we present the statistical behavior by analyzing data
recorded on a large number of individual quantum dots. Exciton charge is
controlled with extremely high fidelity through an n-type field effect
structure, providing access to the neutral exciton (X0), the biexciton (2X0)
and the positively (X1+) and negatively (X1-) charged excitons. We find
significant differences in the recombination lifetime of each exciton such
that, on average, Tau(X1-) / Tau(X0) = 1.25, Tau(X1+) / Tau(X0) = 1.58 and
Tau(2X0) / Tau(X0) = 0.65. We attribute the change in lifetime to significant
changes in the single particle hole wave function on charging the dot, an
effect more pronounced on charging X0 with a single hole than with a single
electron. We verify this interpretation by recasting the experimental data on
exciton energies in terms of Coulomb energies. We show directly that the
electron-hole Coulomb energy is charge dependent, reducing in value by 5-10% in
the presence of an additional electron, and that the electron-electron and
hole-hole Coulomb energies are almost equal.


title: Inter-Quark Potentials in Baryons and Multi-Quark Systems in QCD

abstract:
  We perform the first studies of various inter-quark potentials in SU(3)$_{\rm
c}$ lattice QCD. From the accurate lattice calculation for more than 300
different patterns of three-quark (3Q) systems, we find that the static 3Q
potential $V_{\rm 3Q}$ is well described by Y-Ansatz, i.e., the Coulomb plus
Y-type linear potential. Quark confinement mechanism in baryons is also
investigated in maximally-Abelian projected QCD. We next study the multi-quark
potentials $V_{n{\rm Q}}$ ($n$=4,5) in SU(3)$_{\rm c}$ lattice QCD, and find
that they are well described by the one-gluon-exchange Coulomb plus multi-Y
type linear potential, which supports the flux-tube picture even for the
multi-quarks. Finally, we study the heavy-heavy-light quark (QQq) potential
both in lattice QCD and in a lattice-QCD-based quark model.


title: Noise induced decoherence in quantum dots

abstract: This paper has been withdrawn by the author and replaced by arXiv:0809.4751


title:
Analytical solution of the equations describing interstitial migration
  of impurity atoms

abstract:
  An analytical solution of the equations describing impurity diffusion due to
the migration of nonequilibrium impurity interstitial atoms was obtained for
the case of the Robin boundary condition on the surface of a semiconductor. The
solution obtained can be useful for verification of approximate numerical
solutions, for simulation of a number of processes of interstitial diffusion,
and for modeling impurity diffusion in doped layers with the decananometer
thickness because in these layers a disequilibrium between immobile
substitutionally dissolved impurity atoms, migrating self-interstitials, and
migrating interstitial impurity atoms can take place. To illustrate the latter
cases, a model of nitrogen diffusion in gallium arsenide was developed and
simulation of nitrogen redistribution from a doped epi-layer during thermal
annealing of GaAs substrate was done. The calculated impurity concentration
profile agrees well with experimental data. The fitting to the experimental
profiles allowed us to derive the values of the parameters that describe
interstitial impurity diffusion.


title:
Controlling subluminal to superluminal behavior of group velocity in an
  f-deformed Bose-Einstein condensate beyond the rotating wave approximation

abstract:
  In this paper, we investigate tunable control of the group velocity of a weak
probe field propagating through an f-deformed Bose-Einstein condensate of
three-level atoms beyond the rotating wave approximation. For this purpose, we
use an f- deformed generalization of an effective two-level quantum model of
the three-level configuration without the rotating wave approximation in which
the Gardiners phonon operators for Bose-Einstein condensate are deformed by an
operator- valued function,f(n), of the particle- number operator n .
Corrections produced by the counter- rotating terms appear in the first order
as an intensity- dependent detuning and in the second order as an intensity-
dependent atom-field coupling. We consider the collisions between the atoms as
a special kind of f- deformation where the collision rate k is regarded as the
deformation parameter. We demonstrate the enhanced effect of subluminal and
superluminal propagation based on electromagnetically induced transparency and
electromagnetically induced absorption, respectively. In particular, we find
that (i) the absorptive and dispersive properties of the deformed condensate
can be controlled effectively in the absence of the rotating wave approximation
by changing the deformation parameter k, the total number of atoms N and the
counter- rotating terms parameter, (ii) by increasing the values of k, 1/N and
the counter- rotating terms parameter, the group velocity of the probe pulse
changes, from subluminal to superluminal and (iii) beyond the rotating wave
approximation, the subluminal and superluminal behaviors of the probe field are
enhanced.


abstract:
  Aims. A simplified model of jet power from active galactic nuclei is proposed
in which the relationship between jet power and disk luminosity is discussed by
combining disk accretion with two mechanisms of extracting energy magnetically
from a black hole accretion disk, i.e., the Blandford-Payne (BP) and the
Blandford-Znajek (BZ) processes.
  Methods. By including the BP process into the conservation laws of mass,
angular momentum and energy, we derive the expressions of the BP power and disk
luminosity, and the jet power is regarded as the sum of the BZ and BP powers.
  Results. We find that the disk radiation flux and luminosity decrease because
a fraction of the accretion energy is channelled into the outflow/jet in the BP
process. It is found that the dominant cooling mode of the accretion disk is
determined mainly by how the poloidal magnetic field decreases with the
cylindrical radius of the jet. By using the parameter space we found, which
consists of the black hole spin and the self-similar index of the configuration
of the poloidal magnetic field frozen in the disk, we were able to compare the
relative importance of the following quantities related to the jet production:
(1) the BP power versus the disk luminosity, (2) the BP power versus the BZ
power, and (3) the jet power versus the disk luminosity. In addition, we fit
the jet power and broad-line region luminosity of 11 flat-spectrum radio
quasars (FSRQs) and 17 steep-spectrum radio quasars (SSRQs) based on our model.


title:
Quasi-nearly subharmonicity and separately quasi-nearly subharmonic
  functions

abstract:
  Wiegerinck has shown that a separately subharmonic function need not be
subharmonic. Improving previous results of Lelong, of Avanissian, of Arsove and
of us, Armitage and Gardiner gave an almost sharp integrability condition which
ensures a separately subharmonic function to be subharmonic. Completing now our
recent counterparts to the cited results of Lelong, Avanissian and Arsove for
so called quasi-nearly subharmonic functions, we present a counterpart to the
cited result of Armitage and Gardiner for separately quasi-nearly subharmonic
functions. This counterpart enables us to slightly improve Armitage's and
Gardiner's original result, too. The method we use is a rather straightforward
and technical, but still by no means easy, modification of Armitage's and
Gardiner's argument combined with an old argument of Domar.


title:
Simulations of the Nonlinear Helmholtz Equation: Arrest of Beam
  Collapse, Nonparaxial Solitons, and Counter-Propagating Beams

abstract:
  We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that
collapse in the simpler NLS model. Thereby, we provide the first ever numerical
evidence that nonparaxiality and backscattering can arrest the collapse. We
also solve the (1+1)D NLH and show that solitons with radius of only half the
wavelength can propagate over forty diffraction lengths with no distortions. In
both cases we calculate the backscattered field, which has not been done
previously. Finally, we compute the dynamics of counter-propagating solitons
using the NLH model, which is more comprehensive than the previously used
coupled NLS model.


title: Feynman diagrams and minimal models for operadic algebras

abstract:
  We construct an explicit minimal model for an algebra over the
cobar-construction of a differential graded operad. The structure maps of this
minimal model are expressed in terms of sums over decorated trees. We introduce
the appropriate notion of a homotopy equivalence of operadic algebras and show
that our minimal model is homotopy equivalent to the original algebra. All this
generalizes and gives a conceptual explanation of well-known results for
A-infinity algebras. Further, we show that these results carry over to the case
of algebras over modular operads; the sums over trees get replaced by sums over
general Feynman graphs. As a by-product of our work we prove gauge-independence
of Kontsevich's `dual construction' producing graph cohomology classes from
contractible differential graded Frobenius algebras.


title: Fragmentation of Spinning Branes

abstract:
  The near-horizon geometries of the spinning D3-, M2- and M5-branes are
examined by the probes immersed in a co-rotating frame. It is found that the
geometries become unstable at critical values of the spin angular velocity by
emitting the branes. We show that this instability corresponds to the
metastability of the black hole systems and different from the known (local)
thermodynamic instability. For the D3 case, the instability found here is in
complete agreement with the known metastability of the N=4 super-Yang-Mills
theory with R-symmetry chemical potentials.


title:
Dynamics of the Solar Magnetic Network. II. Heating the Magnetized
  Chromosphere

abstract:
  We consider recent observations of the chromospheric network, and argue that
the bright network grains observed in the Ca II H & K lines are heated by an as
yet unidentified quasi-steady process. We propose that the heating is caused by
dissipation of short-period magnetoacoustic waves in magnetic flux tubes
(periods less than 100 s). Magnetohydrodynamic (MHD) models of such waves are
presented. We consider wave generation in the network due to two separate
processes: (a) by transverse motions at the base of the flux tube; and (b) by
the absorption of acoustic waves generated in the ambient medium. We find that
the former mechanism leads to an efficient heating of the chromosphere by slow
magnetoacoustic waves propagating along magnetic field lines. This heating is
produced by shock waves with a horizontal size of a few hundred kilometers. In
contrast, acoustic waves excited in the ambient medium are converted into
transverse fast modes that travel rapidly through the flux tube and do not form
shocks, unless the acoustic sources are located within 100 km from the tube
axis. We conclude that the magnetic network may be heated by magnetoacoustic
waves that are generated in or near the flux tubes.


title: Semiclassical bosonic D-brane boundary states in curved spacetime

abstract:
  We give a simple method to calculate the semiclassical $D$-brane boundary
states of the bosonic string propagating in an arbitrary curved spacetime in a
perturbative approach in which the metric $g_{AB}$ and the constant
antisymmetric Kalb-Ramond field $b_{AB}$ form the general background which is
treated exactly. As an important particular case, it is shown that at the first
order perturbation theory there are $D$-brane coherent states in the
$d$-dimensional {\em AdS} spacetime if certain conditions are fulfilled by the
boundary projectors.


title:
Coherent presentations of structure monoids and the Higman-Thompson
  groups

abstract:
  Structure monoids and groups are algebraic invariants of equational
varieties. We show how to construct presentations of these objects from
coherent categorifications of equational varieties, generalising several
results of Dehornoy. We subsequently realise the higher Thompson groups
$F_{n,1}$ and the Higman-Thompson groups $G_{n,1}$ as structure groups. We go
on to obtain presentations of these groups via coherent categorifications of
the varieties of higher-order associativity and of higher-order associativity
and commutativity, respectively. These categorifications generalise Mac Lane's
pentagon and hexagon conditions for coherently associative and commutative
bifunctors.


title:
Maximum vertex occupation time and inert fugitive: recontamination does
  help

abstract:
  Given a simple graph $G$, we consider the node search problem with inert
fugitive. We are interested in minimizing the maximum vertex occupation time,
i.e. the maximum number of steps in which a vertex is occupied by a searcher
during a search of $G$. We prove that a search program which does not allow a
recontamination may not find an optimal solution to this problem, and the
difference between the maximum vertex occupation time computed by a monotone
search program and a program without such restriction may be arbitrarily large.


title: The Complexity of Node Blocking for Dags

abstract:
  We consider the following modification of annihilation game called node
blocking. Given a directed graph, each vertex can be occupied by at most one
token. There are two types of tokens, each player can move his type of tokens.
The players alternate their moves and the current player $i$ selects one token
of type $i$ and moves the token along a directed edge to an unoccupied vertex.
If a player cannot make a move then he loses. We consider the problem of
determining the complexity of the game: given an arbitrary configuration of
tokens in a directed acyclic graph, does the current player has a winning
strategy? We prove that the problem is PSPACE-complete.


title: On the locality of the Pr\"ufer code

abstract:
  The Pr\"ufer code is a bijection between trees on the vertex set $[n]$ and
strings on the set $[n]$ of length $n-2$ (Pr\"ufer strings of order $n$). In
this paper we examine the `locality' properties of the Pr\"ufer code, i.e. the
effect of changing an element of the Pr\"ufer string on the structure of the
corresponding tree. Our measure for the distance between two trees $T,T^*$ is
$\Delta(T,T^*)=n-1-| E(T)\cap E(T^*)|$. We randomly mutate the $\mu$th element
of the Pr\"ufer string of the tree $T$, changing it to the tree $T^*$, and we
asymptotically estimate the probability that this results in a change of $\ell$
edges, i.e. $P(\Delta=\ell | \mu).$ We find that P(\Delta=\ell | \mu)$ is on
the order of $ n^{-1/3+o(1)}$ for any integer $\ell>1,$ and that $P(\Delta=1 |
\mu)=(1-\mu/n)^2+o(1).$ This result implies that the probability of a `perfect'
mutation in the Pr\"ufer code (one for which $\Delta(T,T^*)=1$) is $1/3.$


title: Properties of ideal Gaussian glass-forming systems

abstract:
  We introduce the ideal Gaussian glass-forming system as a model to describe
the thermodynamics and dynamics of supercooled liquids on a local scale in
terms of the properties of the potential energy landscape (PEL). The first
ingredient is the Gaussian distribution of inherent structures, the second a
specific relation between energy and mobility. This model is compatible with
general considerations as well as with several computer simulations on atomic
computer glass-formers. Important observables such as diffusion constants,
structural relaxation times and kinetic as well as thermodynamic fragilities
can be calculated analytically. In this way it becomes possible to identify a
relevant PEL parameter determining the kinetic fragility. Several experimental
observations can be reproduced. The remaining discrepancies to the experiment
can be qualitatively traced back to the difference between small and large
systems.


title:
Can the dynamics of an atomic glass-forming system be described as a
  continuous time random walk?

abstract:
  We show that the dynamics of supercooled liquids, analyzed from computer
simulations of the binary mixture Lennard-Jones system, can be described in
terms of a continuous time random walk (CTRW). The required discretization
comes from mapping the dynamics on transitions between metabasins. This
comparison involves verifying the conditions of the CTRW as well as a
quantitative test of the predictions. In particular it is possible to express
the wave vector-dependence of the relaxation time as well as the degree of
non-exponentiality in terms of the first three moments of the waiting time
distribution.


title: Moufang symmetry II. Moufang-Mal'tsev pairs and triality

abstract:
  A concept of the Moufang-Malt'tsev pair is elaborated. This concept is based
on the generalized Maurer-Cartan equations of a local analytic Moufang loop.
Triality can be seen as a fundamental property of such pairs. Based on
triality, the Yamagutian is constructed. Properties of the Yamagutian are
studied.


title: On integrability of the Yang-Baxter $\si$-model

abstract:
  We prove the integrability of the Yang-Baxter $\si$-model which is the
Poisson-Lie deformation of the principal chiral model. We find also an explicit
one-to-one map transforming every solution of the principal chiral model into a
solution of the deformed model. With the help of this map, the standard
procedure of the dressing of the principal chiral solutions can be directly
transferred into the deformed Yang-Baxter context.


title:
The time constant vanishes only on the percolation cone in directed
  first passage percolation

abstract:
  We consider the directed first passage percolation model on ${\bf Z}^2$. In
this model, we assign independently to each edge $e$ a passage time $t(e)$ with
a common distribution $F$. We denote by $\vec{T}({\bf 0}, (r,\theta))$ the
passage time from the origin to $(r, \theta)$ by a northeast path for $(r,
\theta)\in {\bf R}^+\times [0,\pi/2]$. It is known that $\vec{T}({\bf 0}, (r,
\theta))/r$ converges to a time constant $\vec{\mu}_F (\theta)$. Let
$\vec{p}_c$ denote the critical probability for oriented percolation. In this
paper, we show that the time constant has a phase transition divided by
$\vec{p}_c$, as follows:
  (1) If $F(0) < \vec{p}_c$, then $\vec{\mu}_F(\theta) >0$ for all $0\leq
\theta\leq \pi/2$.
  (2) If $F(0) = \vec{p}_c$, then $\vec{\mu}_F(\theta) >0$ if and only if
$\theta\neq \pi/4$.
  (3) If $F(0)=p > \vec{p}_c$, then there exists a percolation cone between
$\theta_p^-$ and $\theta_p^+$ for
  $0\leq \theta^-_p< \theta^+_p \leq \pi/2$ such that $\vec{\mu} (\theta) >0$
if and only if $\theta\not\in [\theta_p^-, \theta^+_p]$. Furthermore, all the
moments of $\vec{T}({\bf 0}, (r, \theta))$ converge whenever $\theta\in
[\theta_p^-, \theta^+_p]$. As applications, we describe the shape of the
directed growth model on the distribution of $F$. We give a phase transition
for the shape divided by $\vec{p}_c$.


title: Complex interpolation of compact operators mapping into lattice couples

abstract:
  Suppose that (A_0,A_1) and (B_0,B_1) are Banach couples, and that T is a
linear operator which maps A_0 compactly into B_0 and A_1 boundedly (or even
compactly) into B_1. Does this imply that T maps [A_0,A_1]_s to [B_0,B_1]_s
compactly for 0<s<1 ? (Here, as usual, [A_0,A_1]_s denotes the complex
interpolation space of Alberto Calderon.) This question has been open for 44
years. Affirmative answers are known for it in many special cases. We answer it
affirmatively in the case where (A_0,A_1) is arbitrary and (B_0,B_1) is a
couple of Banach lattices having absolutely continuous norms or the Fatou
property. Our result has some overlap with a recent result by Evgeniy
Pustylnik.


title:
Applications of Group Analysis to the Three-Dimensional Equations of
  Fluids with Internal Inertia

abstract:
  Group classification of the three-dimensional equations describing flows of
fluids with internal inertia, where the potential function $W=
W(\rho,\dot{\rho})$, is presented. The given equations include such models as
the non-linear one-velocity model of a bubbly fluid with incompressible liquid
phase at small volume concentration of gas bubbles, and the dispersive shallow
water model. These models are obtained for special types of the function
$W(\rho,\dot{\rho})$. Group classification separates out the function
$W(\rho,\dot{\rho})$ at 15 different cases. Another part of the manuscript is
devoted to one class of partially invariant solutions. This solution is
constructed on the base of all rotations. In the gas dynamics such class of
solutions is called the Ovsyannikov vortex. Group classification of the system
of equations for invariant functions is obtained. Complete analysis of
invariant solutions for the special type of a potential function is given.


title: Time Warp Edit Distance

abstract:
  This technical report details a family of time warp distances on the set of
discrete time series. This family is constructed as an editing distance whose
elementary operations apply on linear segments. A specific parameter allows
controlling the stiffness of the elastic matching. It is well suited for the
processing of event data for which each data sample is associated with a
timestamp, not necessarily obtained according to a constant sampling rate. Some
properties verified by these distances are proposed and proved in this report.


title: On linear versions of some addition theorems

abstract:
  Let K \subset L be a field extension. Given K-subspaces A,B of L, we study
the subspace spanned by the product set AB = {ab | a \in A, b \in B}. We obtain
some lower bounds on the dimension of this subspace and on dim B^n in terms of
dim A, dim B and n. This is achieved by establishing linear versions of
constructions and results in additive number theory mainly due to Kemperman and
Olson.


title: Gravitational Radiation from Primordial Helical MHD Turbulence

abstract:
  We consider gravitational waves (GWs) generated by primordial inverse-cascade
helical magneto-hydrodynamical (MHD) turbulence produced by bubble collisions
at the electroweak phase transitions (EWPT). Compared to the unmagnetized EWPT
case, the spectrum of MHD-turbulence-generated GWs peaks at lower frequency
with larger amplitude and can be detected by the proposed Laser Interferometer
Space Antenna (LISA).


title: Small amplitude quasi-breathers and oscillons

abstract:
  Quasi-breathers (QB) are time-periodic solutions with weak spatial
localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006).
QB's provide a simple description of oscillons (very long-living spatially
localized time dependent solutions). The small amplitude limit of QB's is
worked out in a large class of scalar theories with a general self-interaction
potential, in $D$ spatial dimensions. It is shown that the problem of small
amplitude QB's is reduced to a universal elliptic partial differential
equation. It is also found that there is the critical dimension, $D_{crit}=4$,
above which no small amplitude QB's exist. The QB's obtained this way are shown
to provide very good initial data for oscillons. Thus these QB's provide the
solution of the complicated, nonlinear time dependent problem of small
amplitude oscillons in scalar theories.


title: Do confinement and darkness have the same conceptual roots?

abstract:
  In this note the connection between "perfect dark matter" and
string-localization as the tightest noncompact localized matter is pursued in
the context of Yang Mills theories. A programmatic approach based on the
observation that behind the serious infrared problems which prevented the use
of the axial gauge there is unique covariant semiinfinite string-like field,
which flucuates in the endpoint as well as in the string direction, is
formulated and the open problems are explained. Whereas hitherto the gauge
formalism in its local gauge invariants accounted for the observed hadrons the
new formalism based on the consistent use of string-localized vectorpotentials
has a good chance to unravel the nonlocal part in which energy-momentum
carrying dark/confined objects (gluons, quarks,..) may be residing.
  PACS: 95.35+d, 11.10-z, 11.30 Cp


title: On contracting hyperplane elements from a 3-connected matroid

abstract:
  Let $\tilde{K}_{3,n}$, $n\geq 3$, be the simple graph obtained from $K_{3,n}$
by adding three edges to a vertex part of size three. We prove that if $H$ is a
hyperplane of a 3-connected matroid $M$ and $M \not\cong M^*(\tilde{K}_{3,n})$,
then there is an element $x$ in $H$ such that the simple matroid associated
with $M/x$ is 3-connected.


title:
Wavelet and Curvelet Moments for Image Classification: Application to
  Aggregate Mixture Grading

abstract:
  We show the potential for classifying images of mixtures of aggregate, based
themselves on varying, albeit well-defined, sizes and shapes, in order to
provide a far more effective approach compared to the classification of
individual sizes and shapes. While a dominant (additive, stationary) Gaussian
noise component in image data will ensure that wavelet coefficients are of
Gaussian distribution, long tailed distributions (symptomatic, for example, of
extreme values) may well hold in practice for wavelet coefficients. Energy (2nd
order moment) has often been used for image characterization for image
content-based retrieval, and higher order moments may be important also, not
least for capturing long tailed distributional behavior. In this work, we
assess 2nd, 3rd and 4th order moments of multiresolution transform -- wavelet
and curvelet transform -- coefficients as features. As analysis methodology,
taking account of image types, multiresolution transforms, and moments of
coefficients in the scales or bands, we use correspondence analysis as well as
k-nearest neighbors supervised classification.


title: A Remark on Triangle-Critical Graphs

abstract:
  A connected $k$-chromatic graph $G$ with $k \geq 3$ is said to be
triangle-critical, if every edge of $G$ is contained in an induced triangle of
$G$ and the removal of any triangle from $G$ decreases the chromatic number of
$G$ by three. B. Toft posed the problem of showing that the complete graphs on
more than two vertices are the only triangle-critical graphs. By applying a
method of M. Stiebitz [Discrete Math. 64 (1987), 91--93], we answer the problem
affirmatively for triangle-critical $k$-chromatic graphs with $k \leq 6$.


title: A Search for WIMPs with the First Five-Tower Data from CDMS

abstract:
  We report first results from the Cryogenic Dark Matter Search (CDMS II)
experiment running with its full complement of 30 cryogenic particle detectors
at the Soudan Underground Laboratory. This report is based on the analysis of
data acquired between October 2006 and July 2007 from 15 Ge detectors (3.75
kg), giving an effective exposure of 121.3 kg-d (averaged over recoil energies
10--100 keV, weighted for a weakly interacting massive particle (WIMP) mass of
60 \gev). A blind analysis, incorporating improved techniques for event
reconstruction and data quality monitoring, resulted in zero observed events.
This analysis sets an upper limit on the WIMP-nucleon spin-independent cross
section of 6.6$\times10^{-44}$ cm$^2$ (4.6$\times10^{-44}$ cm$^2$ when combined
with previous CDMS Soudan data) at the 90% confidence level for a WIMP mass of
60 \gev. By providing the best sensitivity for dark matter WIMPs with masses
above 42 GeV/c$^2$, this work significantly restricts the parameter space for
some of the favored supersymmetric models.


title: Probing the Central Regions of Nearby Compact Elliptical Galaxies

abstract:
  K-band spectroscopic observations recorded with NIFS+ALTAIR on Gemini North
are used to probe the central arcsec of the compact elliptical galaxies NGC
4486B, NGC 5846A, and M32. The angular resolution of these data is ~0.1 arcsec
FWHM. The central stellar contents of NGC 4486B and NGC 5846A are similar, in
the sense that they occupy the same regions of the (Ca I, 12CO), (Na I, 12CO)
and (13CO, 12CO) diagrams. The NGC 4486B and NGC 5846A observations depart from
the sequence defined by solar neighborhood giants in the (Na I, 12CO) diagram,
in a sense that is consistent with both galaxies having non-solar chemical
mixtures. For comparison, the M32 data is consistent with a chemical enrichment
history like that in the Galactic disk; M32 could not have formed from the
stripping of a larger elliptical galaxy. The behaviour of the near-infrared
line indices as a function of radius is also investigated. The radial gradients
that are present in NGC 4486B and NGC 5846A at large radii break down or
reverse within the central few tenths of an arcsec. Evidence is presented that
the nuclear regions of NGC 4486B and NGC 5846A harbour intermediate age
populations.


title:
Biological activity in the wake of an island close to a coastal
  upwelling

abstract:
  Hydrodynamic forcing plays an important role in shaping the dynamics of
marine organisms, in particular of plankton. In this work we study the
planktonic biological activity in the wake of an island which is close to an
upwelling region. Our research is based on numerical analysis of a kinematic
flow mimicking the hydrodynamics in the wake, coupled to a three-component
plankton model. Depending on model parameters different phenomena are
described: a) The lack of transport of nutrients and plankton across the wake,
so that the influence of upwelling on primary production on the other side of
the wake is blocked. b) For sufficiently high vorticity, the role of the wake
in facilitating this transport and leading to an enhancement of primary
production. Finally c) we show that under certain conditions the interplay
between wake structures and biological growth leads to plankton blooms inside
mesoscale hydrodynamic vortices that act as incubators of primary production.

categories: nlin.CD physics.ao-ph physics.flu-dyn q-bio.PE


title: Paths of fluctuation induced switching

abstract:
  We demonstrate that the paths followed by a system in fluctuation-activated
switching form a narrow tube in phase space. A theory of the path distribution
is developed and its direct measurement is performed in a micromechanical
oscillator. The experimental and theoretical results are in excellent
agreement, with no adjustable parameters. We also demonstrate the lack of
time-reversal symmetry in switching of systems far from thermal equilibrium.


title: Three-mode opto-acoustic parametric interactions with coupled cavity

abstract:
  We theoretically analyze three-mode opto-acoustic parametric interactions in
a coupled Fabry-Perot cavity, where one acoustic mode interacts with two
optical modes. We show explicitly that extra degrees of freedom in a coupled
cavity allow explorations of both parametric instability and cooling regimes
with high parametric gain in a single table top experiment. This work can
motivate experimental realizations of the three-mode parametric instability
which might be an issue in next-generation gravitational-wave detectors with
high optical-power cavities, helping in the development of better models, and
in developing techniques for controls. In addition, we show that the same
scheme can be implemented in the resolved-sideband acoustic-mode cooling.


title: Approximate Capacity of Gaussian Relay Networks

abstract:
  We present an achievable rate for general Gaussian relay networks. We show
that the achievable rate is within a constant number of bits from the
information-theoretic cut-set upper bound on the capacity of these networks.
This constant depends on the topology of the network, but not the values of the
channel gains. Therefore, we uniformly characterize the capacity of Gaussian
relay networks within a constant number of bits, for all channel parameters.


title: Asymptotically Conical Associative 3-folds

abstract:
  Given an associative 3-fold in R^7 which is asymptotically conical with
generic rate less than 1, we show that its moduli space of deformations is
locally homeomorphic to the kernel of a smooth map between smooth manifolds.
Moreover, the virtual dimension of the moduli space is computed and shown to be
non-negative for rates greater than -1, whereas the associative 3-fold is
expected to be isolated for rates less than or equal to -1.


title: Topological Field Theory of Time-Reversal Invariant Insulators

abstract:
  We show that the fundamental time reversal invariant (TRI) insulator exists
in 4+1 dimensions, where the effective field theory is described by the 4+1
dimensional Chern-Simons theory and the topological properties of the
electronic structure is classified by the second Chern number. These
topological properties are the natural generalizations of the time reversal
breaking (TRB) quantum Hall insulator in 2+1 dimensions. The TRI quantum spin
Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimension
can be obtained as descendants from the fundamental TRI insulator in 4+1
dimensions through a dimensional reduction procedure. The effective topological
field theory, and the $Z_2$ topological classification for the TRI insulators
in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All
physically measurable topological response functions of the TRI insulators are
completely described by the effective topological field theory. Our effective
topological field theory predicts a number of novel and measurable phenomena,
the most striking of which is the topological magneto-electric effect, where an
electric field generates a magnetic field in the same direction, with an
universal constant of proportionality quantized in odd multiples of the fine
structure constant $\alpha=e^2/\hbar c$. Finally, we present a general
classification of all topological insulators in various dimensions, and
describe them in terms of a unified topological Chern-Simons field theory in
phase space.


title:
Decoherence-free preparation of Dicke states of trapped ions by
  collective stimulated Raman adiabatic passage

abstract:
  We propose a simple technique for the generation of arbitrary-sized Dicke
states in a chain of trapped ions. The method uses global addressing of the
entire chain by two pairs of delayed but partially overlapping laser pulses to
engineer a collective adiabatic passage along a multi-ion dark state. Our
technique, which is a many-particle generalization of stimulated Raman
adiabatic passage (STIRAP), is decoherence-free with respect to spontaneous
emission and robust against moderate fluctuations in the experimental
parameters. Furthermore, because the process is very rapid, the effects of
heating are almost negligible under realistic experimental conditions. We
predict that the overall fidelity of synthesis of a Dicke state involving ten
ions sharing two excitations should approach 98% with currently achievable
experimental parameters.


title: Interval Estimation of Bounded Variable Means via Inverse Sampling

abstract:
  In this paper, we develop interval estimation methods for means of bounded
random variables based on a sequential procedure such that the sampling is
continued until the sample sum is no less than a prescribed threshold.


title:
Reflectionless Sharp Bends and Corners in Waveguides Using
  Epsilon-Near-Zero Effects

abstract:
  Following our recent theoretical and experimental results that show how
zero-permittivity metamaterials may provide anomalous tunneling and energy
squeezing through ultranarrow waveguide channels, here we report an
experimental investigation of the bending features relative to this
counterintuitive resonant effect. We generate the required effectively-zero
permittivity using a waveguide operating at the cut-off of its dominant mode,
and we show how sharp and narrow bends may be inserted within the propagation
channel without causing any sensible reflection or loss.


title: Intermittency and Localization

abstract:
  In this paper, we show how simple logistic growth that was studied
intensively during the last 200 years in many domains of science could be
extended in a rather simple way and with these extensions is capable to produce
a collection of behaviors widely observed in an enormous number of real-life
systems in Economics, Sociology, Biology, Ecology and more.


title: The Intermediate Polar EI UMa: A Pre-Polar Cataclysmic Variable

abstract:
  We present optical and X-ray time-series photometry of EI UMa that reveal
modulation at 746 and 770 s, which we interpret as the white dwarf spin and
spin-orbit sidebands. These detections, combined with previous X-ray studies,
establish EI UMa as an intermediate polar. We estimate the mass accretion rate
to be ~ 3.6 x 10^{17} g s^{-1}, which is close to, and likely greater than, the
critical rate above which dwarf nova instabilities are suppressed. We also
estimate the white dwarf to have a large magnetic moment mu > (3.4 +/- 0.2) x
10^{33} G cm^3. The high mass accretion rate and magnetic moment imply the
existence of an accretion ring rather than a disk, and along with the
relatively long orbital period, these suggest that EI UMa is a rare example of
a pre-polar cataclysmic variable.


title:
High fidelity universal set of quantum gates using non-adiabatic rapid
  passage

abstract:
  Numerical simulation results are presented which suggest that a class of
non-adiabatic rapid passage sweeps first realized experimentally in 1991 should
be capable of implementing a universal set of quantum gates G_{u} that operate
with high fidelity. The gates constituting G_{u} are the Hadamard and NOT
gates, together with variants of the phase, \pi /8, and controlled-phase gates.
The universality of G_{u} is established by showing that it can construct the
universal set consisting of Hadamard, phase, \pi /8, and controlled-NOT gates.
Sweep parameter values are provided which simulations indicate will produce the
different gates in G_{u}, and for which the gate error probability P_{e}
satisfies: (i) P_{e} < 10^{-4} for the one-qubit gates; and (ii) P_{e} < 1.27x
10^{-3} for the modified controlled-phase gate. The sweeps in this class are
non-composite and generate controllable quantum interference effects that allow
the gates in G_{u} to operate non-adiabatically while maintaining high
fidelity. These interference effects have been observed using NMR, and it has
previously been shown how these rapid passage sweeps can be applied to atomic
systems using electric fields. Here we show how these sweeps can be applied to
both superconducting charge and flux qubit systems. The simulations suggest
that the universal set of gates G_{u} produced by these rapid passage sweeps
shows promise as possible elements of a fault-tolerant scheme for quantum
computing.


title:
Algorithmic and combinatorial methods for enumerating the relators of a
  group presentation

abstract:
  The main achievement of this thesis is an algorithm which given a finite
group presentation and natural numbers n and k, computes all the relators of
length and area up to n and k respectively. The complexity of this algorithm is
better by a factor which is over-exponential than that of classical methods
using van Kampen diagrams.


title: Magnetic field of Josephson vortices outside superconductors

abstract:
  We consider the structure of Josephson vortices approaching the junction
boundary with vacuum in large area Josephson junctions with the Josephson
length $\lambda_J$ large relative to the London penetration depth $\lambda_L$.
Using the stability argument for one-dimentional solitons with respect to 2D
perturbations, it is shown that on the scale $\lambda_J$ the Josephson vortices
do not spread near the boundary in the direction of the junction. %, which is
in a striking difference with behavior of Abrikosov vortices exiting
superconductors. The field distribution in vacuum due to the Josephson vortex
is evaluated, the information needed for the Scanning SQUID Microscopy.


title: On $l^2$ norms of some weighted mean matrices

abstract:
  We give another proof of a result of Bennett on the $l^{p}$ operator norms of
some weighted mean matrices for the case $p=2$ and we also present some related
results.


title:
Almost Periodic Szeg\H{o} Cocycles with Uniformly Positive Lyapunov
  Exponents

abstract:
  We exhibit examples of almost periodic Verblunsky coefficients for which
Herman's subharmonicity argument applies and yields that the associated
Lyapunov exponents are uniformly bounded away from zero.


title:
Type II$_1$ von Neumann algebra representations of Hecke operators on
  Maass forms and the Ramanujan-Petersson conjectures

abstract:
  Classical Hecke operators on Maass forms are unitarely equivalent, up to a
commuting phase, to completely positive maps on II$_1$ factors, associated to a
pair of isomorphic subfactors, and an intertwining unitary. This representation
is obtained through a quantized representation of the Hecke operators. in this
representation, the Hecke operators act on the Berezin's quantization,
deformation algebra of the fundamental domain of $\PSL(2,\Z)$ in the upper
halfplane. The Hecke operators are inheriting from the ambient, non-commutative
algebra on which they act, a rich structure of matrix inequalities. Using this
construction we obtain that, for every prime $p$, the essential spectrum of the
classical Hecke operator $T_p$ is contained in the interval $[-2\sqrt p, 2\sqrt
p]$, predicted by the Ramanujan Petersson conjectures. In particular, given an
open interval containing $[-2\sqrt p, 2\sqrt p]$, there are at most a finite
number of possible exceptional eigenvalues lying outside this interval. The
main tool for obtaining this representation of the Hecke operators (unitarely
equivalent to the classical representation, up to commuting phase) is a Schurr
type, positive "square root" of the state on $\PGL(2,\Q)$, measuring the
displacement of fundamental domain by translations in $\PGL(2,\Q)$. The "square
root" is obtained from the matrix coefficients of the discrete series
representations of $\PSL(2,\R)$ restricted to $\PGL(2, \Q)$. The methods in
this paper may also be applied to any finite index, modular subgroup
$\Gamma_0(p^n)$, $n\geq 1$, of $\PSL(2,\Z)$. In this case the essential norm of
the Hecke operator is equal to the norm of the corresponding convolution
operator on the cosets Hilbert space $\ell^2((\Gamma_0(p^n))\backslash
\PSL(2,\Z[1/p])$.


title: Directional isoperimetric inequalities and rational homotopy invariants

abstract:
  We estimate the second order linking invariants of Lipschitz maps from an
n-dimensional ellipse. The estimate uses a new directionally-dependent version
of the isoperimetric inequality for cycles inside the ellipse. Using this work,
we prove new lower bounds for the k-dilation of maps from one ellipse to
another.


title: Isoperimetric inequalities and rational homotopy invariants

abstract:
  We estimate the linear isoperimetric constants of an n-dimensional ellipse.
Using these estimates and a technique of Gromov, we estimate the Hopf and
linking invariants of Lipschitz maps from ellipses to round spheres. Using
these estimates, we give a lower bound for the k-dilation of degree non-zero
maps between ellipses.


title: Infinite quantum well: a coherent state approach

abstract:
  A new family of 2-component vector-valued coherent states for the quantum
particle motion in an infinite square well potential is presented. They allow a
consistent quantization of the classical phase space and observables for a
particle in this potential. We then study the resulting position and
(well-defined) momentum operators. We also consider their mean values in
coherent states and their quantum dispersions.


title: The Fluid Nature of Quark-Gluon Plasma

abstract:
  Collisions of heavy nuclei at very high energies offer the exciting
possibility of experimentally exploring the phase transformation from hadronic
to partonic degrees of freedom which is predicted to occur at several times
normal nuclear density and/or for temperatures in excess of $\sim 170$ MeV.
Such a state, often referred to as a quark-gluon plasma, is thought to have
been the dominant form of matter in the universe in the first few microseconds
after the Big Bang. Data from the first five years of heavy ion collisions of
Brookhaven National Laboratory's Relativistic Heavy Ion Collider (RHIC) clearly
demonstrate that these very high temperatures and densities have been achieved.
While there are strong suggestions of the role of quark degrees of freedom in
determining the final-state distributions of the produced matter, there is also
compelling evidence that the matter does {\em not} behave as a quasi-ideal
state of free quarks and gluons. Rather, its behavior is that of a dense fluid
with very low kinematic viscosity exhibiting strong hydrodynamic flow and
nearly complete absorption of high momentum probes. The current status of the
RHIC experimental studies is presented, with a special emphasis on the fluid
properties of the created matter, which may in fact be the most perfect fluid
ever studied in the laboratory.


title: Finite-time singularity in the evolution of hyperinflation episodes

abstract:
  A model proposed by Sornette, Takayasu, and Zhou for describing
hyperinflation regimes based on adaptive expectations expressed in terms of a
power law which leads to a finite-time singularity is revisited. It is
suggested to express the price index evolution explicitly in terms of the
parameters introduced along the theoretical formulation avoiding any
combination of them used in the original work. This procedure allows to study
unambiguously the uncertainties of such parameters when an error is assigned to
the measurement of the price index. In this way, it is possible to determine an
uncertainty in the critical time at which the singularity occurs. For this
purpose, Monte Carlo simulation techniques are applied. The hyperinflation
episodes of Peru (1969-90) and Weimar Germany (1920-3) are reexamined. The
first analyses performed within this framework of the very extreme
hyper-inflations occurred in Greece (1941-4) and Yugoslavia (1991-4) are
reported. The study of the hyperinflation spiral experienced just nowadays in
Zimbabwe predicts a singularity, i.e., a complete economic crash within two
years.


title: Data Traffic Dynamics and Saturation on a Single Link

abstract:
  The dynamics of User Datagram Protocol (UDP) traffic over Ethernet between
two computers are analyzed using nonlinear dynamics which shows that there are
two clear regimes in the data flow: free flow and saturated. The two most
important variables affecting this are the packet size and packet flow rate.
However, this transition is due to a transcritical bifurcation rather than
phase transition in models such as in vehicle traffic or theorized large-scale
computer network congestion. It is hoped this model will help lay the
groundwork for further research on the dynamics of networks, especially
computer networks.