title:
Simulations of the Local Universe Constrained by Observational Peculiar
  Velocities

abstract:
  Peculiar velocities, obtained from direct distance measurements, are data of
choice to achieve constrained simulations of the Local Universe reliable down
to a scale of a few Megaparsecs. Unlike redshift surveys, peculiar velocities
are direct tracers of the underlying gravitational field as they trace both
baryonic and dark matter. This paper presents the first attempt to use solely
observational peculiar velocities to constrain cosmological simulations of the
nearby universe. In order to set up Initial Conditions, a Reverse Zel'dovich
Approximation (RZA) is used to displace constraints from their positions at z=0
to their precursors' locations at higher redshifts. An additional new feature
replaces original observed radial peculiar velocity vectors by their full 3D
reconstructions provided by the Wiener-Filter (WF) estimator. Subsequently, the
Constrained Realization of Gaussian fields technique (CR) is applied to build
various realizations of the Initial Conditions. The WF/RZA/CR method is first
tested on realistic mock catalogs built from a reference simulation similar to
the Local Universe. These mocks include errors on peculiar velocities, on
data-point positions and a large continuous zone devoid of data in order to
mimic galactic extinction. Large scale structures are recovered with a typical
accuracy of 5 Megaparsecs/h in position, the best realizations reaching a 2-3
Mpc/h precision, the limit imposed by the RZA linear theory. Then, the method
is applied to the first observational radial peculiar velocity catalog of the
project Cosmicflows. This paper is a proof of concept that the WF/RZA/CR method
can be applied to observational peculiar velocities to successfully build
constrained Initial Conditions.


title:
Developments in the Khintchine-Meinardus probabilistic method for
  asymptotic enumeration

abstract:
  A theorem of Meinardus provides asymptotics of the number of weighted
partitions under certain assumptions on associated ordinary and Dirichlet
generating functions. The ordinary generating functions are closely related to
Euler's generating function $\prod_{k=1}^\infty S(z^k)$ for partitions, where
$S(z)=(1-z)^{-1}$. By applying a method due to Khintchine, we extend Meinardus'
theorem to find the asymptotics of the coefficients of generating functions of
the form $\prod_{k=1}^\infty S(a_kz^k)^{b_k}$ for sequences $a_k$, $b_k$ and
general $S(z)$. We also reformulate the hypotheses of the theorem in terms of
generating functions. This allows us to prove rigorously the asymptotics of
Gentile statistics and to study the asymptotics of combinatorial objects with
distinct components.


title:
A hybrid mathematical model for self-organizing cell migration in the
  zebrafish lateral line

abstract:
  In this paper we propose a "discrete in continuous" mathematical model for
the morphogenesis of the posterior lateral line system in zebrafishes. Our
model follows closely the results obtained in recent biological experiments. We
rely on a hybrid description: discrete for the cellular level and continuous
for the molecular level. We prove the existence of steady solutions consistent
with the formation of particular biological structure, the neuromasts.
Dynamical numerical simulations are performed to show the behavior of the model
and its qualitative and quantitative accuracy to describe the evolution of the
cell aggregate.


title:
Stability of Hamiltonian relative equilibria in symmetric magnetically
  confined rigid bodies

abstract:
  This work studies the symmetries, the associated momentum map, and relative
equilibria of a mechanical system consisting of a small axisymmetric magnetic
body-dipole in an also axisymmetric external magnetic field that additionally
exhibits a mirror symmetry; we call this system the ``orbitron". We study the
nonlinear stability of a branch of equatorial quasiorbital relative equilibria
using the energy-momentum method and we provide sufficient conditions for their
$\mathbb{T}^2$--stability that complete partial stability relations already
existing in the literature. These stability prescriptions are explicitly
written down in terms of the some of the field parameters, which can be used in
the design of stable solutions. We propose new linear methods to determine
instability regions in the context of relative equilibria that we use to
conclude the sharpness of some of the nonlinear stability conditions obtained.


title:
Depolarization of multiple scattered light in atmospheres due to
  anisotropy of small grains and molecules

abstract:
  Freely oriented small anisotropic grains and molecules depolarize radiation
both in single scattering and in the process of multiple scattering. Especially
large depolarization occurs for resonant scattering corresponding to the
electron transitions between the energy levels with very different quantum
numbers. The existence of light absorption also changes essentially the angular
distribution and polarization of radiation, outgoing from an atmosphere. In the
present paper we consider these effects in detail both for continuum radiation
and for resonant lines. Because the term describing the depolarization deals
with isotropic radiation, we consider the axially symmetric part of radiation.
We derived the formulas for observed intensity and polarization using the
invariance-principles both for continuum and resonant scattering. We confine
ourselves to two problems - the diffuse reflection of the light beam from
semi-infinite atmosphere, and the Milne problem.


title: Particle Production Measurements using the MIPP Detector at Fermilab

abstract:
  The Main Injector Particle Production (MIPP) experiment is a fixed target
hadron production experiment at Fermilab. It measures particle production in
interactions of 120 GeV/c primary protons from the Main Injector and secondary
beams of $\pi^{\pm}, \rm{K}^{\pm}$, p and $\bar{\rm{p}}$ from 5 to 90 GeV/c on
nuclear targets which include H, Be, C, Bi and U, and a dedicated run with the
NuMI target. MIPP is a high acceptance spectrometer which provides excellent
charged particle identification using Time Projection Chamber (TPC), Time of
Flight (ToF), multicell Cherenkov (CKOV), Ring Imaging Cherenkov (RICH)
detectors, and Calorimeter for neutrons. We present inelastic cross section
measurements for 58 and 85 GeV/c p-H interactions, and 58 and 120 GeV/c p-C
interactions. A new method is described to account for the low multiplicity
inefficiencies in the interaction trigger using KNO scaling. Inelastic cross
sections as a function of multiplicity are also presented. The MIPP data are
compared with the Monte Carlo predictions and previous measurements. We also
describe an algorithm to identify charged particles
($\pi^{\pm}/\rm{p}/\bar{\rm{p}}$ etc.), and present the charged pion and kaon
spectra from the interactions of 120 GeV/c protons with carbon target.


title: Low-Temperature Magnetic Anomaly in Magnetite

abstract:
  We have studied experimentally the responses of high quality single crystals
of stoichiometric synthetic magnetite to applied weak dc and ac magnetic fields
in the range of 6 K to 60 K, far below the Verwey transition. The results can
be compared to so called Magnetic After Effects (MAE) measurements, which are
the most extensive magnetic measurements of magnetite at these temperatures. We
present a novel point of view on the relaxation phenomena encountered at these
temperatures - the Low Temperature Anomaly, addressing the striking difference
between the results of conventional ac susceptibility measurements and those
accompanying MAE measurements, i.e. periodic excitations with strong magnetic
pulses. We also draw a connection between this anomaly and the so called
glass-like transition and discuss possible mechanisms responsible for these
effects.


title:
Overshoot in biological systems modeled by Markov chains: a
  nonequilibrium dynamic phenomenon

abstract:
  A number of biological systems can be modeled by Markov chains. Recently,
there has been an increasing concern about when biological systems modeled by
Markov chains will perform a dynamic phenomenon called overshoot. In this
article, we found that the steady-state behavior of the system will have a
great effect on the occurrence of overshoot. We confirmed that overshoot in
general cannot occur in systems which will finally approach an equilibrium
steady state. We further classified overshoot into two types, named as simple
overshoot and oscillating overshoot. We showed that except for extreme cases,
oscillating overshoot will occur if the system is far from equilibrium. All
these results clearly show that overshoot is a nonequilibrium dynamic
phenomenon with energy consumption. In addition, the main result in this
article is validated with real experimental data.


title: Making a Be star: the role of rotation and pulsations

abstract:
  The Be phenomenon, i.e. the ejection of matter from Be stars into a
circumstellar disk, has been a long lasting mystery. In the last few years, the
CoRoT satellite brought clear evidence that Be outbursts are directly
correlated to pulsations and rapid rotation. In particular the stochastic
excitation of gravito-inertial modes, such as those detected by CoRoT in the
hot Be star HD 51452, is enhanced thanks to rapid rotation. These waves
increase the transport of angular momentum and help to bring the already rapid
stellar rotation to its critical value at the surface, allowing the star to
eject material. Below we summarize the recent observational and theoretical
findings and describe the new picture of the Be phenomenon which arose from
these results.


title:
Combining magnetic and seismic studies to constrain processes in massive
  stars

abstract:
  The presence of pulsations influences the local parameters at the surface of
massive stars and thus it modifies the Zeeman magnetic signatures. Therefore it
makes the characterisation of a magnetic field in pulsating stars more
difficult and the characterisation of pulsations is thus required for the study
of magnetic massive stars. Conversely, the presence of a magnetic field can
inhibit differential rotation and mixing in massive stars and thus provides
important constraints for seismic modelling based on pulsation studies. As a
consequence, it is necessary to combine spectropolarimetric and seismic studies
for all massive classical pulsators. Below we show examples of such combined
studies and the interplay between physical processes.


title:
Deterministic entanglement distillation for secure double-server blind
  quantum computation

abstract:
  Blind quantum computation (BQC) provides an efficient method for the client
who does not have enough sophisticated technology and knowledge to perform
universal quantum computation. The single-server BQC protocol requires the
client to have some minimum quantum ability, while the double-server BQC
protocol makes the client's device completely classical, resorting to the pure
and clean Bell-state shared by two servers. In this paper, we provide a
deterministic entanglement distillation protocol in a practical noisy
environment for the double-server BQC protocol. This protocol can obtain the
pure maximally entangled Bell state with the success probability of 100% in
principle. The distilled maximally entangled states can be remaind to perform
the BQC protocol subsequently. The parties who perform the distillation
protocol do not need to exchange the classical information and they learn
nothing from the client. It makes this protocol unconditionally secure and
suitable for current BQC protocol.


title: UVMag: a UV and optical spectropolarimeter for stellar physics

abstract:
  UVMag is a space project currently under R&D study. It consists in a
medium-size telescope equipped with a spectropolarimeter to observe in the UV
and optical wavelength domains simultaneously. Its first goal is to obtain time
series of selected magnetic stars over their rotation period, to study them
from their surface to their environment, in particular their wind and
magnetospheres. As the star rotates it will be possible to reconstruct 3D maps
of the star and its surroundings. The second goal of UVMag is to obtain two
observations of a large sample of stars to construct a new database of UV and
optical spectropolarimetric measurements.


title:
Electronic Structure of Magnetic Semiconductor CdCr_2Te_4: A Possible
  Spin-Dependent Symmetry Filter

abstract:
  We present a theoretical investigation of the electronic and magnetic
structure of spinel CdCr_2Te_4 using density functional theory, its extensions
via onsite Hubbard U interactions, and a screened-hybrid-functional exchange
potential. We find that the ground state is semiconducting within the latter
approach, and within this magnetic-semiconducting system we compute the complex
band structure, finding a slowly decaying evanescent $\tilde{\Delta}_1$ state
possibly suitable for realizing a spin-dependent symmetry filter effect.


title:
Room-temperature ultra-sensitive mass spectrometer via dynamic
  decoupling

abstract:
  We propose an ultra-sensitive mass spectrometer based on a coupled
quantum-bit-oscillator system. Under dynamical decoupling control of the
quantum bit (qubit), the qubit coherence exhibits a comb structure in time
domain. The time-comb structure enables high precision measurement of
oscillator frequency, which can be used as an ultra-sensitive mass
spectrometer. Surprisingly, in ideal case, the sensitivity of the proposed mass
spectrometer, which scales with the temperature $T$ as $T^{-1/2}$, has better
performance in higher temperature. While taking into account qubit and
oscillator decay, we show that the optimal sensitivity is independent on
environmental temperature $T$. With present technology on solid state spin
qubit and high-quality optomechanical system, our proposal is feasible to
realize an ultra-sensitive mass spectrometer in room temperature.


title: Reductions and Contractions of 1-loop Tensor Feynman Integrals

abstract:
  We report on the progress in constructing contracted one-loop tensors.
Analytic results for rank R=4 tensors, cross-checked numerically, are presented
for the first time.


title: Strong Anderson localization in cold atom quantum quenches

abstract:
  Signatures of strong Anderson localization in the momentum distribution of a
cold atom cloud after a quantum quench are studied. We consider a quasi
one-dimensional cloud initially prepared in a well defined momentum state, and
expanding for some time in a disorder speckle potential. Anderson localization
leads to a formation of a coherence peak in the \emph{forward} scattering
direction (as opposed to the common weak localization backscattering peak). We
present a microscopic, and fully time resolved description of the phenomenon,
covering the entire diffusion--to--localization crossover. Our results should
be observable by present day technology.


title:
Determination of the Surface Plasmons Polaritons extraction efficiency
  from a self-assembled plasmonic crystal

abstract:
  We experimentally measure and analytically describe the fluorescence
enhancement obtained by depositing CdSe/CdS nanocrystals onto a gold plasmonic
crystal, a two-dimensional grating of macroscopic size obtained by gold
deposition on a self-assembled opal. We show evidences of nanocrystals
near-field coupling to the gold Surface Plasmons Polaritons (SPP) followed by
grating-induced SPP re-emission to far-field. We develop a theoretical
framework and an original method in order to evaluate, from photoluminescence
experiments, the SPP extraction efficiency of a grating.


title: On linear operators with s-nuclear adjoints: $0< s \le 1$

abstract:
  If $ s\in (0,1]$ and $ T$ is a linear operator with $ s$-nuclear adjoint from
a Banach space $ X$ to a Banach space $ Y$ and if one of the spaces $ X^*$ or $
Y^{***}$ has the approximation property of order $s,$ $AP_s,$ then the operator
$ T$ is nuclear. The result is in a sense exact. For example, it is shown that
for each $r\in (2/3, 1]$ there exist a Banach space $Z_0$ and a non-nuclear
operator $ T: Z_0^{**}\to Z_0$ so that $Z_0^{**}$ has a Schauder basis, $
Z_0^{***}$ has the $AP_s$ for every $s\in (0,r)$ and $T^*$ is $r$-nuclear.


title:
More data speeds up training time in learning halfspaces over sparse
  vectors

abstract:
  The increased availability of data in recent years has led several authors to
ask whether it is possible to use data as a {\em computational} resource. That
is, if more data is available, beyond the sample complexity limit, is it
possible to use the extra examples to speed up the computation time required to
perform the learning task?
  We give the first positive answer to this question for a {\em natural
supervised learning problem} --- we consider agnostic PAC learning of
halfspaces over $3$-sparse vectors in $\{-1,1,0\}^n$. This class is
inefficiently learnable using $O\left(n/\epsilon^2\right)$ examples. Our main
contribution is a novel, non-cryptographic, methodology for establishing
computational-statistical gaps, which allows us to show that, under a widely
believed assumption that refuting random $\mathrm{3CNF}$ formulas is hard, it
is impossible to efficiently learn this class using only
$O\left(n/\epsilon^2\right)$ examples. We further show that under stronger
hardness assumptions, even $O\left(n^{1.499}/\epsilon^2\right)$ examples do not
suffice. On the other hand, we show a new algorithm that learns this class
efficiently using $\tilde{\Omega}\left(n^2/\epsilon^2\right)$ examples. This
formally establishes the tradeoff between sample and computational complexity
for a natural supervised learning problem.


title: From average case complexity to improper learning complexity

abstract:
  The basic problem in the PAC model of computational learning theory is to
determine which hypothesis classes are efficiently learnable. There is
presently a dearth of results showing hardness of learning problems. Moreover,
the existing lower bounds fall short of the best known algorithms.
  The biggest challenge in proving complexity results is to establish hardness
of {\em improper learning} (a.k.a. representation independent learning).The
difficulty in proving lower bounds for improper learning is that the standard
reductions from $\mathbf{NP}$-hard problems do not seem to apply in this
context. There is essentially only one known approach to proving lower bounds
on improper learning. It was initiated in (Kearns and Valiant 89) and relies on
cryptographic assumptions.
  We introduce a new technique for proving hardness of improper learning, based
on reductions from problems that are hard on average. We put forward a (fairly
strong) generalization of Feige's assumption (Feige 02) about the complexity of
refuting random constraint satisfaction problems. Combining this assumption
with our new technique yields far reaching implications. In particular,
  1. Learning $\mathrm{DNF}$'s is hard.
  2. Agnostically learning halfspaces with a constant approximation ratio is
hard.
  3. Learning an intersection of $\omega(1)$ halfspaces is hard.


title: Measures of uncertainty in market network analysis

abstract:
  Statistical uncertainty of different filtration techniques for market network
analysis is studied. Two measures of statistical uncertainty are discussed. One
is based on conditional risk for multiple decision statistical procedures and
another one is based on average fraction of errors. It is shown that for some
important cases the second measure is a particular case of the first one.
Statistical uncertainty for some popular market network structures is analyzed.
Results of numerical evaluation of statistical uncertainty for minimum spanning
tree, market graph, maximum cliques and maximum independent sets are given. The
most stable structures are derived.


title: Gravitational lensing of wormholes in the galactic halo region

abstract:
  A recent study by Rahaman et al. has shown that the galactic halo possesses
the necessary properties for supporting traversable wormholes, based on two
observational results, the density profile due to Navarro et al. and the
observed flat rotation curves of galaxies. Using a method for calculating the
deflection angle pioneered by V. Bozza, it is shown that the deflection angle
diverges at the throat of the wormhole. The resulting photon sphere has a
radius of 0.40 ly. Given the dark-matter background, detection may be possible
from past data using ordinary light.


title:
Modified scattering for the cubic Schr\"odinger equation on product
  spaces and applications

abstract:
  We consider the cubic nonlinear Schr\"odinger equation posed on the spatial
domain $\mathbb{R}\times \mathbb{T}^d$. We prove modified scattering and
construct modified wave operators for small initial and final data respectively
($1\leq d\leq 4)$. The key novelty comes from the fact that the modified
asymptotic dynamics are dictated by the resonant system of this equation, which
sustains interesting dynamics when $d\geq 2$. As a consequence, we obtain
global solutions to the defocusing and focusing problems on $\mathbb{R}\times
\mathbb{T}^d$ (for any $d\geq 2$) with infinitely growing high Sobolev norms
$H^s$.


title:
A Quantitative Evaluation Framework for Missing Value Imputation
  Algorithms

abstract:
  We consider the problem of quantitatively evaluating missing value imputation
algorithms. Given a dataset with missing values and a choice of several
imputation algorithms to fill them in, there is currently no principled way to
rank the algorithms using a quantitative metric. We develop a framework based
on treating imputation evaluation as a problem of comparing two distributions
and show how it can be used to compute quantitative metrics. We present an
efficient procedure for applying this framework to practical datasets,
demonstrate several metrics derived from the existing literature on comparing
distributions, and propose a new metric called Neighborhood-based Dissimilarity
Score which is fast to compute and provides similar results. Results are shown
on several datasets, metrics, and imputations algorithms.


title:
Level spacing statistics and spectral correlations in the diffuse van
  der Waals clusters

abstract:
  We present a statistical analysis of eigenenergies and discuss several
measures of spectral fluctuations and spectral correlations for the van der
Waals clusters of different sizes. We show that the clusters become more and
more complex with increase in cluster size. We study nearest-neighbour level
spacing distribution $P(s)$, the level number variance $\Sigma^2(L)$, and the
Dyson-Mehta $\Delta_3-$statistics for various cluster sizes. For large clusters
we find that although the Bohigas-Giannoni-Schmit (BGS) conjecture seems to be
valid, it does not exhibit true signatures of quantum chaos. However
contrasting conjecture of Berry and Tabor is observed with smaller cluster
size. For small number of bosons, we observe the existence of large number of
quasi-degenerate states in low-lying excitation which exhibits the Shnirelman
peak in $P(s)$ distribution. We also find a narrow region of intermediate
spectrum which can be described by semi-Poisson statistics whereas the higher
levels are regular and exhibit Poisson statistics. These observations are
further supported by the analysis of the distribution of the ratio of
consecutive level spacings $P(r)$ which is independent of unfolding procedure
and thereby provides a tool for more transparent comparison with experimental
findings than $P(s)$. Thus our detail numerical study clearly shows that the
van der Waals clusters become more correlated with the increase in cluster
size.


title:
Performance of multifractal detrended fluctuation analysis on short time
  series

abstract:
  The performance of the multifractal detrended analysis on short time series
is evaluated for synthetic samples of several mono- and multifractal models.
The reconstruction of the generalized Hurst exponents is used to determine the
range of applicability of the method and the precision of its results as a
function of the decreasing length of the series. As an application the series
of the daily exchange rate between the U.S. dollar and the euro is studied.


title:
Constant Coefficients in the Radial Komatu-Loewner Equation for Multiple
  Slits

abstract:
  The radial Komatu-Loewner equation is a differential equation for certain
normalized conformal mappings that can be used to describe the growth of slits
within multiply connected domains. We show that it is possible to choose
constant coefficients in this equation in order to generate given disjoint
slits and that those coefficients are uniquely determined under a suitable
normalization of the differential equation.


title: Probable alpha and $14$^C cluster emission from hyper Ac nuclei

abstract:
  A systematic study on the probability for the emission of 4^He and 14^C
cluster from hyper ${207-234}^$Ac and non-strange normal ${207-234}^$Ac nuclei
are performed for the first time using our fission model, the Coulomb and
proximity potential model (CPPM). The predicted half lives show that hyper
${207-234}^$Ac nuclei are unstable against 4^He emission and 14^C emission from
hyper ${217-228}^$Ac are favorable for measurement. Our study also show that
hyper ${207-234}^$Ac are stable against hyper 4^He and 14^C emission. The role
of neutron shell closure (N=126) in hyper 214^Fr daughter and role of proton/
neutron shell closure (Z =82, N =126) in hyper 210^Bi daughter are also
revealed. As hyper-nuclei decays to normal nuclei by mesonic/non-mesonic decay
and since most of the predicted half lives for 4^He and 14^C emission from
normal Ac nuclei are favourable for measurement, we presume that alpha and 14^C
cluster emission from hyper Ac nuclei can be detected in laboratory in a
cascade (two-step) process.


title: Bayesian Analysis of ODE's: solver optimal accuracy and Bayes factors

abstract:
  In most relevant cases in the Bayesian analysis of ODE inverse problems, a
numerical solver needs to be used. Therefore, we cannot work with the exact
theoretical posterior distribution but only with an approximate posterior
deriving from the error in the numerical solver. To compare a numerical and the
theoretical posterior distributions we propose to use Bayes Factors (BF),
considering both of them as models for the data at hand. We prove that the
theoretical vs a numerical posterior BF tends to 1, in the same order (of the
step size used) as the numerical forward map solver does. For higher order
solvers (eg. Runge-Kutta) the Bayes Factor is already nearly 1 for step sizes
that would take far less computational effort. Considerable CPU time may be
saved by using coarser solvers that nevertheless produce practically error free
posteriors. Two examples are presented where nearly 90% CPU time is saved while
all inference results are identical to using a solver with a much finer time
step.


title:
Hamiltonian and Lagrangian for the trajectory of the empirical
  distribution and the empirical measure of Markov processes

abstract:
  We compute the Hamiltonian and Lagrangian associated to the large deviations
of the trajectory of the empirical distribution for independent Markov
processes, and of the empirical measure for translation invariant interacting
Markov processes. We treat both the case of jump processes (continuous-time
Markov chains and interacting particle systems) as well as diffusion processes.
For diffusion processes, the Lagrangian is a quadratic form of the deviation of
the trajectory from the Kolmogorov forward equation. In all cases, the
Lagrangian can be interpreted as a relative entropy or relative entropy density
per unit time.


title: Fixed points of Composition Sum Operators

abstract:
  In the renormalisation analysis of critical phenomena in quasi-periodic
systems, a fundamental role is often played by fixed points of functional
recurrences of the form \begin{equation*} f_{n}(x) = \sum_{i=1}^\ell a_i(x)
f_{n_i} (\alpha_i(x)) \,, \end{equation*} where the $\alpha_i$, $a_i$ are known
functions and the $n_i$ are given and satisfy $n-2 \le n_i \le n-1 $. We
develop a general theory of fixed points of ``Composition Sum Operators''
derived from such recurrences, and apply it to test for fixed points in key
classes of complex analytic functions with singularities. Finally we
demonstrate the construction of the full space of fixed points of one important
class, for the much studied operator \begin{equation*} Mf(x) = f(-\omega x) +
f(\omega^2 x + \omega)\,, \quad \omega = (\sqrt{5}-1)/2\,. \end{equation*} The
construction reveals previously unknown solutions.


abstract:
  The groups of automorphisms of the Lie algebras of formally analytic vector
fields with constant divergence are found.


title: Ultrafilter convergence in ordered topological spaces

abstract:
  We characterize ultrafilter convergence and ultrafilter compactness in
linearly ordered and generalized ordered topological spaces. In such spaces,
and for every ultrafilter $D$, the notions of $D$-compactness and of
$D$-pseudocompactness are equivalent. Any product of initially
$\lambda$-compact generalized ordered topological spaces is still initially
$\lambda$-compact. On the other hand, preservation under products of certain
compactness properties are independent from the usual axioms for set theory.


title:
CPIC: a Curvilinear Particle-In-Cell code for plasma-material
  interaction studies

abstract:
  We describe a new electrostatic Particle-In-Cell (PIC) code in curvilinear
geometry called Curvilinear PIC (CPIC). The code models the microscopic
(kinetic) evolution of a plasma with the PIC method, coupled with an adaptive
computational grid that can conform to arbitrarily shaped domains. CPIC is
particularly suited for multiscale problems associated with the interaction of
complex objects with plasmas. A map is introduced between the physical space
and the logical space, where the grid is uniform and Cartesian. In CPIC, most
operations are performed in logical space. CPIC was designed following criteria
of versatility, robustness and performance. Its main features are the use of
structured meshes, a scalable field solver based on the black box multigrid
algorithm and a hybrid mover, where particles' position is in logical space
while the velocity is in physical space. Test examples involving the
interaction of a plasma with material boundaries are presented.


title: Transformation devices: carpets in space and space-time

abstract:
  Here we extend the theory of space-time or event cloaking into that based on
the carpet or ground-plane reflective surface. Further, by recasting and
generalizing a scalar acoustic wave model into a new mathematically covariant
form, we also show how transformation theories for optics and acoustics can be
combined into a single prescription. The single prescription, however, still
respects the fundamental differences between electromagnetic and acoustic
waves, which then provide us with an existence test for any desired
transformation device -- are the required material properties (the required
constitutive parameters) physically permitted by the wave theory being designed
for? Whilst electromagnetism is a flexible theory permitting almost any
transformation device (T-device) design, we show that the acoustic model used
here is more restricted.


title: Bordered Floer Homology of (2,2n)-Torus Link Complement

abstract:
  We compute bordered Floer homology CFDD of (2,2n)-torus link complement, and
discuss assorted examples and type-DD structure homotopy equivalence.


title: EM vs Weak Structure Functions in DIS processes

abstract:
  We obatin the ratio $F_i^A/F_i^{D}$(i=2,3, A=Be, C, Fe, Pb; D=Deuteron) in
the case of weak and electromagnetic nuclear structure functions. For this,
relativistic nuclear spectral function which incorporate the effects of Fermi
motion, binding and nucleon correlations is used. We also consider the pion and
rho meson cloud contributions and shadowing and antishadowing effects.


title: Applying quantitative semantics to higher-order quantum computing

abstract:
  Finding a denotational semantics for higher order quantum computation is a
long-standing problem in the semantics of quantum programming languages. Most
past approaches to this problem fell short in one way or another, either
limiting the language to an unusably small finitary fragment, or giving up
important features of quantum physics such as entanglement. In this paper, we
propose a denotational semantics for a quantum lambda calculus with recursion
and an infinite data type, using constructions from quantitative semantics of
linear logic.


title:
Nuclear Dependence in Weak Structure Functions and the Determination of
  Weak Mixing Angle

abstract:
  We have studied nuclear medium effects in the weak structure functions
$F^A_2(x)$ and $F^A_3(x)$ and in the extraction of weak mixing angle using
Paschos Wolfenstein(PW) relation.
  We have modified the PW relation for nonisoscalar nuclear target. We have
incorporated the medium effects like Pauli blocking, Fermi motion, nuclear
binding energy, nucleon correlations, pion $\&$ rho cloud contributions, and
shadowing and antishadowing effects.


title: Laurent Biorthogonal Polynomials and Riordan Arrays

abstract:
  We show that Laurent biorthogonal polynomials whose defining three-term
recurrence have constant coefficients have coefficient arrays that are Riordan
arrays. For each such family of Laurent biorthogonal polynomials we associate
in a natural way a family of orthogonal polynomials. We also extend these
results to a notion of generalized orthogonal polynomials whose recurrence
depends on three parameters.


title: Weak Strangeness and Eta Production

abstract:
  We have studied strange particle production off nucleons through $\Delta S =0
$ and $|\Delta S| = 1$ channels, and specifically single kaon/antikaon, eta,
associated particle production for neutrino/antineutrino induced processes as
well as antineutrino induced single hyperon production processes.
  We have developed a microscopical model based on the SU(3) chiral
Lagrangians. The basic parameters of the model are $f_\pi$, the pion decay
constant, Cabibbo angle, the proton and neutron magnetic moments and the axial
vector coupling constants for the baryons octet. For antikaon production we
have also included
  $\Sigma^*(1385)$ resonance and for eta production $S_{11}(1535)$ and
$S_{11}(1650)$ resonances are included.


title: On the distance in some bipartite graphs $L_{k,n}$

abstract:
  The paper presents some bipartite graph $L_{k,n}$, so called $(k,n)$-level
graph, that arise by taking $k$-th and $(n-k)$-th levels of $n$-dimensional
Boolean algebra. Two results are establised: (1) precise description of a
distance (a shotest path) beteen arbitrary vertices and (2) solution of the
problem how many vertices may be reached in $i$ steps starting from some intial
point.


title:
Intertwining operator associated to the complex Dunkl operator of type
  $G(m,1,N)$

abstract:
  In this work, we consider the Dunkl complex reflection operators related to
the group $G(m,1,N)$ in the complex plane \begin{align*}
T_i=\frac{\partial}{\partial z_i}+k_0\sum_{j\neq
i}\sum_{r=0}^{m-1}\frac{1-s_i^{-r}(i,j)s_i^r} {z_i-\varepsilon^r
z_j}+\sum_{j=1}^{m-1}k_j\sum_{r=0}^{m-1}\frac{\varepsilon^{-rj}s_i^r}{z_i},
\,\,1\leq i\leq N. \end{align*} We first review the theory of Dunkl operators
for complex reflection groups we recall some results related to the
hyper--Bessel functions, which are solutions of a higher order differential
equation. Secondly, we construct a new explicit intertwining operator between
the operator $T_i$ and the partial derivative operator
$\frac{\partial}{\partial x_i}.$ As application we given an explicit solution
of the system: $$ T_if(x)=\kappa\lambda_i f(x),\,\,\, f(0)=1.$$


title:
Newton based Stochastic Optimization using q-Gaussian Smoothed
  Functional Algorithms

abstract:
  We present the first q-Gaussian smoothed functional (SF) estimator of the
Hessian and the first Newton-based stochastic optimization algorithm that
estimates both the Hessian and the gradient of the objective function using
q-Gaussian perturbations. Our algorithm requires only two system simulations
(regardless of the parameter dimension) and estimates both the gradient and the
Hessian at each update epoch using these. We also present a proof of
convergence of the proposed algorithm. In a related recent work (Ghoshdastidar
et al., 2013), we presented gradient SF algorithms based on the q-Gaussian
perturbations. Our work extends prior work on smoothed functional algorithms by
generalizing the class of perturbation distributions as most distributions
reported in the literature for which SF algorithms are known to work and turn
out to be special cases of the q-Gaussian distribution. Besides studying the
convergence properties of our algorithm analytically, we also show the results
of several numerical simulations on a model of a queuing network, that
illustrate the significance of the proposed method. In particular, we observe
that our algorithm performs better in most cases, over a wide range of
q-values, in comparison to Newton SF algorithms with the Gaussian (Bhatnagar,
2007) and Cauchy perturbations, as well as the gradient q-Gaussian SF
algorithms (Ghoshdastidar et al., 2013).


title: SLE boundary visits

abstract:
  We study the probabilities with which chordal Schramm-Loewner Evolutions
(SLE) visit small neighborhoods of boundary points. We find formulas for
general chordal SLE boundary visiting probability amplitudes, also known as SLE
boundary zig-zags or order refined SLE multi-point Green's functions on the
boundary. Remarkably, an exact answer can be found to this important SLE
question for an arbitrarily large number of marked points. The main technique
employed is a spin chain-Coulomb gas correspondence between tensor product
representations of a quantum group and functions given by Dotsenko-Fateev type
integrals. We show how to express these integral formulas in terms of
regularized real integrals, and we discuss their numerical evaluation.
  The results are universal in the sense that apart from an overall
multiplicative constant the same formula gives the amplitude for many different
formulations of the SLE boundary visit problem. The formula also applies to
renormalized boundary visit probabilities for interfaces in critical lattice
models of statistical mechanics: we compare the results with numerical
simulations of percolation, loop-erased random walk, and Fortuin-Kasteleyn
random cluster models at Q=2 and Q=3, and find good agreement.

categories: math-ph cond-mat.stat-mech hep-th math.MP math.PR


title: A stability result for the union-closed size problem

abstract:
  A family of sets is called union-closed if whenever $A$ and $B$ are sets of
the family, so is $A\cup B$. The long-standing union-closed conjecture states
that if a family of subsets of $[n]$ is union-closed, some element appears in
at least half the sets of the family. A natural weakening is that the
union-closed conjecture holds for large families; that is, families consisting
of at least $p_02^n$ sets for some constant $p_0$. The first result in this
direction appears in a recent paper of Balla, Bollob\'as and Eccles
\cite{BaBoEc}, who showed that union-closed families of at least
$\frac{2}{3}2^n$ sets satisfy the conjecture --- they proved this by
determining the minimum possible average size of a set in a union-closed family
of given size. However, the methods used in that paper cannot prove a better
constant than $\frac{2}{3}$. Here, we provide a stability result for the main
theorem of \cite{BaBoEc}, and as a consequence we prove the union-closed
conjecture for families of at least $(\frac{2}{3}-c)2^n$ sets, for a positive
constant $c$.


title: Rainbow Connection of Random Regular Graphs

abstract:
  An edge colored graph $G$ is rainbow edge connected if any two vertices are
connected by a path whose edges have distinct colors. The rainbow connection of
a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors
that are needed in order to make $G$ rainbow connected.
  In this work we study the rainbow connection of the random $r$-regular graph
$G=G(n,r)$ of order $n$, where $r\ge 4$ is a constant. We prove that with
probability tending to one as $n$ goes to infinity the rainbow connection of
$G$ satisfies $rc(G)=O(\log n)$, which is best possible up to a hidden
constant.


title:
Toward the estimation of background fluctuations under newly-observed
  signals in particle physics

abstract:
  When the number of events associated with a signal process is estimated in
particle physics, it is common practice to extrapolate background distributions
from control regions to a predefined signal window. This allows accurate
estimation of the expected, or average, number of background events under the
signal. However, in general, the actual number of background events can deviate
from the average due to fluctuations in the data. Such a difference can be
sizable when compared to the number of signal events in the early stages of
data analysis following the observation of a new particle, as well as in the
analysis of rare decay channels. We report on the development of a data-driven
technique that aims to estimate the actual, as opposed to the expected, number
of background events in a predefined signal window. We discuss results on toy
Monte Carlo data and provide a preliminary estimate of systematic uncertainty.


title:
Spectral Engineering of Slow Light, Cavity Line Narrowing, and Pulse
  Compression

abstract:
  More than 4 orders of magnitude of cavity-linewidth narrowing in a
rare-earth-ion-doped crystal cavity, emanating from strong intracavity
dispersion caused by off-resonant interaction with dopant ions, is
demonstrated. The dispersion profiles are engineered using optical pumping
techniques creating significant semipermanent but reprogrammable changes of the
rare-earth absorption profiles. Several cavity modes are shown within the
spectral transmission window. Several possible applications of this phenomenon
are discussed.


title: Approaching the BFKL pomeron via integrable classical solutions

abstract:
  We identify classical string solutions which directly give the classical part
of the strong coupling pomeron intercept. The relevant solution is a close
cousin of the GKP folded string, which is not surprising given the known
relation with twist-2 operators. Our methods are applicable, however, also for
nonzero conformal spin where we do not have a clear link with anomalous
dimensions of a concrete class of operators. We analyze the BFKL folded string
from the algebraic curve perspective and investigate its possible particle
content.


title: Statics and dynamics of fluids in nanotubes

abstract:
  The purpose of this article is to study the statics and dynamics of nanotubes
by using the methods of continuum mechanics. The nanotube can be filled with
only a liquid or a vapour phase according to the physicochemical
characteristics of the wall and to the disjoining pressure associated with the
liquid and vapour mother bulks of the fluid, regardless of the nature of the
external mother bulk. In dynamics, flows through nanotubes can be much more
important than classical Poiseuille flows. When the external mother bulk is of
vapour, the flow can be a million times larger than the classical flows when
slippage on wall does not exist.

categories: physics.flu-dyn cond-mat.soft math-ph math.MP


title: Ultracold-atom quantum simulator for attosecond science

abstract:
  A quantum simulator based on ultracold optically trapped atoms for simulating
the physics of atoms and molecules in ultrashort intense laser fields is
introduced. The slowing down by about 13 orders of magnitude allows to watch in
slow motion the tunneling and recollision processes that form the heart of
attosecond science. The extreme flexibility of the simulator promises a deeper
understanding of strong-field physics, especially for many-body systems beyond
the reach of classical computers. The quantum simulator can experimentally
straightforwardly be realized and is shown to recover the ionization
characteristics of atoms in the different regimes of laser-matter interaction.


title:
A renormalization group method by harmonic extensions and the classical
  dipole gas

abstract:
  In this paper we develop a new renormalization group method, which is based
on conditional expectations and harmonic extensions, to study functional
integrals related with small perturbations of Gaussian fields. In this new
method one integrates Gaussian fields inside domains at all scales conditioning
on the fields outside these domains, and by variation principle solves local
elliptic problems. It does not rely on an a priori decomposition of the
Gaussian covariance. We apply this method to the model of classical dipole gas
on the lattice, and show that the scaling limit of the generating function with
smooth test functions is the generating function of the renormalized Gaussian
free field.


title: On the metallicity of open clusters II. Spectroscopy

abstract:
  In a series of three papers, we investigate the current status of published
metallicities for open clusters that were derived from a variety of photometric
and spectroscopic methods. The current article focuses on spectroscopic
methods. The aim is to compile a comprehensive set of clusters with the most
reliable metallicities from high-resolution spectroscopic studies. This set of
metallicities will be the basis for a calibration of metallicities from
different methods. The literature was searched for [Fe/H] estimates of
individual member stars of open clusters based on the analysis of
high-resolution spectra. For comparison, we also compiled [Fe/H] estimates
based on spectra with low and intermediate resolution. At medium and high
resolution, we found that differences in the analysis methods have a stronger
effect on metallicity than quality differences in the observations. We retained
only highly probable cluster members and introduced a restriction on
atmospheric parameters. We combined 641 individual metallicity values for 458
stars in 78 open clusters from 86 publications to form our final set of
high-quality cluster metallicities. The photometric metallicities discussed in
the first paper of this series are systematically lower than the spectroscopic
ones by about 0.1 dex, and the differences show a scatter of about 0.2 dex. In
a preliminary comparison of our spectroscopic sample with models of Galactic
chemical evolution, none of the models predicts the observed radial metallicity
gradient. Photometric metallicities show a large intrinsic dispersion, while
the more accurate spectroscopic sample presented in this paper comprises fewer
than half the number of clusters. Only a sophisticated combination of all
available photometric and spectroscopic data will allow us to trace the
metallicity distribution in the Galactic disk on a local and global scale.


title: Bifurcation of Solutions to the Allen-Cahn Equation

abstract:
  We use Morse Homology to study bifurcation of the solution sets of the
Allen-Cahn Equation.


title:
Elastic proton-proton scattering from ISR to LHC energies, focusing on
  the dip region

abstract:
  The differential cross-section of elastic proton-proton collisions is studied
at ISR and LHC energies, utilizing a quark-diquark model, that generalizes
earlier models of Bialas and Bzdak, and, in addition, a model of Glauber and
Velasco. These studies suggest that the increase of the total pp cross-section
is mainly due to an increase of the separation of the quark and the diquark
with increasing energies. Within the investigated class of models, two simple
and model-independent phenomenological relations were found, that connect the
total pp scattering cross-section to the effective quark, diquark size and
their average separation, on one hand, and to the position of the dip of the
differential cross-section, on the other hand. The latter t(dip) sigma(tot) ~
const relation can be used to predict t(dip), the position of the dip of
elastic pp scattering for future colliding energies, and for other reactions,
where sigma(tot) is either known or can be reliably estimated.


title:
Analyzing the Optimal Neighborhood: Algorithms for Budgeted and Partial
  Connected Dominating Set Problems

abstract:
  We study partial and budgeted versions of the well studied connected
dominating set problem. In the partial connected dominating set problem, we are
given an undirected graph G = (V,E) and an integer n', and the goal is to find
a minimum subset of vertices that induces a connected subgraph of G and
dominates at least n' vertices. We obtain the first polynomial time algorithm
with an O(\ln \Delta) approximation factor for this problem, thereby
significantly extending the results of Guha and Khuller (Algorithmica, Vol.
20(4), Pages 374-387, 1998) for the connected dominating set problem. We note
that none of the methods developed earlier can be applied directly to solve
this problem. In the budgeted connected dominating set problem, there is a
budget on the number of vertices we can select, and the goal is to dominate as
many vertices as possible. We obtain a (1/13)(1 - 1/e) approximation algorithm
for this problem. Finally, we show that our techniques extend to a more general
setting where the profit function associated with a subset of vertices is a
monotone "special" submodular function. This generalization captures the
connected dominating set problem with capacities and/or weighted profits as
special cases. This implies a O(\ln q) approximation (where q denotes the
quota) and an O(1) approximation algorithms for the partial and budgeted
versions of these problems. While the algorithms are simple, the results make a
surprising use of the greedy set cover framework in defining a useful profit
function.


title: Finite volume renormalization scheme for fermionic operators

abstract:
  We propose a new finite volume renormalization scheme. Our scheme is based on
the Gradient Flow applied to both fermion and gauge fields and, much like the
Schr\"odinger functional method, allows for a nonperturbative determination of
the scale dependence of operators using a step-scaling approach. We give some
preliminary results for the pseudo-scalar density in the quenched
approximation.


title:
Direct solutions to tropical optimization problems with nonlinear
  objective functions and boundary constraints

abstract:
  We examine two multidimensional optimization problems that are formulated in
terms of tropical mathematics. The problems are to minimize nonlinear objective
functions, which are defined through the multiplicative conjugate vector
transposition on vectors of a finite-dimensional semimodule over an idempotent
semifield, and subject to boundary constraints. The solution approach is
implemented, which involves the derivation of the sharp bounds on the objective
functions, followed by determination of vectors that yield the bound. Based on
the approach, direct solutions to the problems are obtained in a compact vector
form. To illustrate, we apply the results to solving constrained Chebyshev
approximation and location problems, and give numerical examples.


title: Les Houches lectures on inflationary observables and string theory

abstract:
  These lectures cover the theoretical structure and phenomenology of some
basic mechanisms for inflation. A full treatment of the problem requires
`ultraviolet completion' because of the sensitivity of inflation to quantum
gravity effects, while the observables are elegantly parameterized using low
energy field theory. String theory provides novel mechanisms for inflation,
some subject to significant observational tests, with highly UV-sensitive
tensor mode measurements being a prime example. Although the ultraviolet
completion is not directly accessible experimentally, some of these mechanisms
have helped stimulate a more systematic analysis of the space of low energy
theories and signatures relevant for data analysis, including searches for
non-Gaussianity and additional structure in the power spectrum. We include a
pedagogical overview of string compactifications, with a focus on candidate
inflatons and their symmetry structure. In the last lecture we attack the
problem of thought-experimental observables in inflation, developing a
generalization of gauge-gravity duality that relies on the structure of the
scalar potential in string theory.


title:
Non-homogeneity of the density of states of tunneling two-level systems
  at low energies

abstract:
  Amorphous solids, and many disordered lattices, exhibit a remarkable
qualitative and quantitative universality in their acoustic properties at
temperature $\lesssim 3$K. This phenomenon is attributed to the existence of
tunneling two level systems (TTLSs), characterized by a homogenous density of
states (DOS) at energies much lower than the disorder energy ($\approx 0.1$eV).
Here we calculate numerically, from first principles, the DOS of KBr:CN glass,
the archetypal disordered lattice showing universality. In contrast to the
standard tunneling model, we find that the DOS diminishes abruptly at $\approx
3$ K, and that tunneling states differ essentially by their symmetry under
inversion. This structure of the TTLSs dictates the low temperature below which
universality is observed, and the quantitative universality of the acoustic
properties in glasses. Consequences to the properties of glasses at
intermediate temperatures, as well as to the microscopic structure of amorphous
solids, are discussed.


title: Dual Hyperbolic Conchoidal Motion

abstract:
  Dual spherical conchoidal motion has been defined by Yapar. In this work, we
define this motion on a dual hyperbolic unit sphere in the dual Lorentzian
space with dual signature, and the results carried to the Lorentzian lines
space by means of the Study s mapping. We also obtain the study maps of the
orbits drawn on the fixed dual hyperbolic unit sphere by unit dual vectors of
an orthonormal base .


title: Transport maps for Beta-matrix models and Universality

abstract:
  We construct approximate transport maps for non-critical Beta-matrix models,
that is, maps so that the push forward of a non-critical Beta-matrix model with
a given potential is a non-critical Beta-matrix model with another potential,
up to a small error in the total variation distance. As a consequence, we
deduce that local statistics have the same asymptotic behavior for both models.


title:
A strong laser impact on spin precession of a charged particle in the
  semi-relativistic interaction regime

abstract:
  In the present note new effects concerned the dynamics of a charged spin-1/2
particle in a strong monochromatic plane wave background are discussed beyond
the conventional dipole approximation. Namely using the semiclassical approach
in the semi-relativistic regime it is shown that the magnetic forces associated
with the laser field have been retained and alter the spin evolution
appreciably.


title:
Self-sustained oscillations in nanoelectromechanical systems induced by
  Kondo resonance

abstract:
  We investigate instability and dynamical properties of nanoelectromechanical
systems represented by a single-electron device containing movable quantum dot
attached to a vibrating cantilever via asymmetric tunnel contact. The Kondo
resonance in electron tunneling between source and shuttle facilitates
self-sustained oscillations originated from strong coupling of mechanical and
electronic/spin degrees of freedom. We analyze stability diagram for
two-channel Kondo shuttling regime due to limitations given by the
electromotive force acting on a moving shuttle and find that the saturation
amplitude of oscillation is associated with the retardation effect of
Kondo-cloud. The results shed light on possible ways of experimental
realization of dynamical probe for the Kondo-cloud by using high tunability of
mechanical dissipation as well as supersensitive detection of mechanical
displacement.


title: Counting the Palstars

abstract:
  A palstar (after Knuth, Morris, and Pratt) is a concatenation of even-length
palindromes. We show that, asymptotically, there are $\Theta(\alpha_k^n)$
palstars of length $2n$ over a $k$-letter alphabet, where $\alpha_k$ is a
constant such that $2k-1 < \alpha_k < 2k-{1 \over 2}$. In particular, $\alpha_2
\doteq 3.33513193$.


title: Statistical Mechanics of Surjective Cellular Automata

abstract:
  Reversible cellular automata are seen as microscopic physical models, and
their states of macroscopic equilibrium are described using invariant
probability measures. We establish a connection between the invariance of Gibbs
measures and the conservation of additive quantities in surjective cellular
automata. Namely, we show that the simplex of shift-invariant Gibbs measures
associated to a Hamiltonian is invariant under a surjective cellular automaton
if and only if the cellular automaton conserves the Hamiltonian. A special case
is the (well-known) invariance of the uniform Bernoulli measure under
surjective cellular automata, which corresponds to the conservation of the
trivial Hamiltonian. As an application, we obtain results indicating the lack
of (non-trivial) Gibbs or Markov invariant measures for "sufficiently chaotic"
cellular automata. We discuss the relevance of the randomization property of
algebraic cellular automata to the problem of approach to macroscopic
equilibrium, and pose several open questions.
  As an aside, a shift-invariant pre-image of a Gibbs measure under a
pre-injective factor map between shifts of finite type turns out to be always a
Gibbs measure. We provide a sufficient condition under which the image of a
Gibbs measure under a pre-injective factor map is not a Gibbs measure. We point
out a potential application of pre-injective factor maps as a tool in the study
of phase transitions in statistical mechanical models.

categories: math.DS cond-mat.stat-mech math-ph math.MP nlin.CG


title:
Change of variable formul{\ae} for regularizing slowly decaying and
  oscillatory Cauchy and Hilbert transforms

abstract:
  Formul{\ae} are derived for expressing Cauchy and Hilbert transforms of a
function $f$ in terms of Cauchy and Hilbert transforms of $f(x^r)$. When $r$ is
an integer, this corresponds to evaluating the Cauchy transform of $f(x^r)$ at
all choices of $z^{1/r}$. Related formu\ae\ for rational $r$ result in a
reduction to a generalized Cauchy transform living on a Riemann surface, which
in turn is reducible to the standard Cauchy transform. These formul{\ae} are
used to regularize the behaviour of functions that are slowly decaying or
oscillatory, in order to facilitate numerical computation and extend asymptotic
results.


title:
On Improving the Balance between the Completion Time and Decoding Delay
  in Instantly Decodable Network Coded Systems

abstract:
  This paper studies the complicated interplay of the completion time (as a
measure of throughput) and the decoding delay performance in instantly
decodable network coded (IDNC) systems over wireless broadcast erasure channels
with memory, and proposes two new algorithms that improve the balance between
the completion time and decoding delay of broadcasting a block of packets. We
first formulate the IDNC packet selection problem that provides joint control
of the completion time and decoding delay as a statistical shortest path (SSP)
problem. However, since finding the optimal packet selection policy using the
SSP technique is computationally complex, we employ its geometric structure to
find some guidelines and use them to propose two heuristic packet selection
algorithms that can efficiently improve the balance between the completion time
and decoding delay for broadcast erasure channels with a wide range of memory
conditions. It is shown that each one of the two proposed algorithms is
superior for a specific range of memory conditions. Furthermore, we show that
the proposed algorithms achieve an improved fairness in terms of the decoding
delay across all receivers.


title:
Mixed Estimates for Degenerate Multilinear Operators Associated to
  Simplexes

abstract:
  We prove that the degenerate trilinear operator $C_3^{-1,1,1}$ given by the
formula
  \begin{eqnarray*} C_3^{-1,1,1}(f_1, f_2, f_3)(x)=\int_{x_1 < x_2 < x_3}
\hat{f_1}(x_1) \hat{f_2}(x_2) \hat{f_3}(x_3) e^{2\pi i x (-x_1 + x_2 + x_3)}
dx_1dx_2 dx_3 \end{eqnarray*} satisfies the new estimates \begin{eqnarray*}
  ||C_3^{-1,1,1}(f_1, f_2,
f_3)||_{\frac{1}{\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}}} \lesssim_{p_1,
p_2, p_3} ||\hat{f}_1||_{p^\prime_1} ||f_2||_{p_2}||f_3||_{p_3}
  \end{eqnarray*} for all $f_1 \in L^{p_1}(\mathbb{R}): \hat{f}_1 \in
L^{p_1^\prime}(\mathbb{R}) , f_2 \in L^{p_2}(\mathbb{R})$, and $f_3 \in
L^{p_3}(\mathbb{R})$ such that $2 <p_1 \leq \infty, 1 < p_2, p_3 < \infty,
\frac{1}{p_1}+\frac{1}{p_2} <1$, and $\frac{1}{p_2}+\frac{1}{p_3} <3/2$. Mixed
estimates for some generalizations of $C_3^{-1,1,1}$ are also shown.


title:
The Vortex Signature of Discrete Ferromagnetic Dipoles at the
  LaAlO$_3$/SrTiO$_3$ Interface

abstract:
  A hysteretic in-plane magnetoresistance develops below the superconducting
transition of LaAlO$_3$/SrTiO$_3$ interfaces for $\left|H_{/\!/}\right|<$ 0.15
T, independently of the carrier density or oxygen annealing. We show that this
hysteresis arises from vortex depinning within a thin superconducting layer, in
which the vortices are created by discrete ferromagnetic dipoles located solely
above the layer. We find no evidence for finite-momentum pairing or bulk
magnetism and hence conclude that ferromagnetism is strictly confined to the
interface, where it competes with superconductivity.


title: Primes and the Lambert W function

abstract:
  The Lambert W function, implicitly defined by W(x) exp{W(x)}=x, is a "new"
special function that has recently been the subject of an extended upsurge in
interest and applications. In this note, I point out that the Lambert W
function can also be used to gain a new perspective on the distribution of
primes.


title:
Hydrodynamic Limits and Propagation of Chaos for Interacting Random
  Walks in Domains

abstract:
  A new non-conservative stochastic reaction-diffusion system in which two
families of random walks in two adjacent domains interact near the interface is
introduced and studied in this paper. Such a system can be used to model the
transport of positive and negative charges in a solar cell or the population
dynamics of two segregated species under competition. We show that in the
macroscopic limit, the particle densities converge to the solution of a coupled
nonlinear heat equations. For this, we first prove that propagation of chaos
holds by establishing the uniqueness of a new BBGKY hierarchy. A local central
limit theorem for reflected diffusions in bounded Lipschitz domains is also
established as a crucial tool.


title: Stationary black diholes

abstract:
  In this paper we present and analyze the simplest physically meaningful model
for stationary black diholes - a binary configuration of counter-rotating
Kerr-Newman black holes endowed with opposite electric charges - elaborated in
a physical parametrization on the basis of one of the Ernst-Manko-Ruiz
equatorially antisymmetric solutions of the Einstein-Maxwell equations. The
model saturates the Gabach-Clement inequality for interacting black holes with
struts, and in the absence of rotation it reduces to the Emparan-Teo electric
dihole solution. The physical characteristics of each dihole constituent
satisfy identically the well-known Smarr's mass formula.


title:
Floer cohomology of immersed Lagrangian spheres in smoothings of $A_N$
  surfaces

abstract:
  We calculate the self-Floer cohomology with Z/2 coefficients of some immersed
Lagrangian spheres in the affine symplectic submanifolds of C^3 that are
smoothings of A_N surfaces. The immersed spheres are exact and graded.
Moreover, they satisfy a positivity assumption that allows us to calculate the
Floer cohomology as follows: Given auxiliary data a Morse function on S^2 and a
time-dependent almost complex structure, the Floer cochain complex is the Morse
complex plus two generators for each self-intersection point of the Lagrangian
sphere. The Floer differential is defined by counting combinations of Morse
flow lines and holomorphic strips. Using a Lefschetz fibration allows us to
explicitly calculate all holomorphic strips and describe the Floer
differential. For most of the immersed spheres the Floer differential is zero
(with Z/2-coefficients).


title:
Three-dimensional light-matter interface for collective spin squeezing
  in atomic ensembles

abstract:
  We study the three-dimensional nature of the quantum interface between an
ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled
through a dispersive interaction. To achieve strong entanglement between the
collective atomic spin and the photons, one must match the spatial mode of the
collective radiation of the ensemble with the mode of the laser beam while
minimizing the effects of decoherence due to optical pumping. For ensembles
coupling to a probe field that varies over the extent of the cloud, the set of
atoms that indistinguishably radiates into a desired mode of the field defines
an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is
not characterized by a single parameter, the optical density, but by a
collection of different effective atom numbers that characterize the coherence
and decoherence of the system. To model the dynamics of the system, we develop
a full stochastic master equation, including coherent collective scattering
into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and
backaction due to continuous measurement of the light entangled with the spin
waves. This formalism is used to study the squeezing of a spin wave via
continuous quantum nondemolition (QND) measurement. We find that the greatest
squeezing occurs in parameter regimes where spatial inhomogeneities are
significant, far from the limit in which the interface is well approximated by
a one-dimensional, homogeneous model.


title:
Uplink Scheduling Strategy Based on A Population Game in Vehicular
  Sensor Networks

abstract:
  Recent advances in the integration of vehicular sensor network (VSN)
technology, and crowd sensing leveraging pervasive sensors called onboard units
(OBUs), like smartphones and radio frequency IDentifications to provide sensing
services, have attracted increasing attention from both industry and academy.
Nowadays, existing vehicular sensing applications lack good mechanisms to
improve the maximum achievable throughput and minimizing service time of
participating sensing OBUs in vehicular sensor networks. To fill these gaps, in
this paper, first, we introduce real imperfect link states to the calculation
of Markov chains. Second, we incorporate the result of different link states
for multiple types of vehicles with the calculations of uplink throughput and
service time. Third, in order to accurately calculate the service time of an
OBU, we introduce the steady state probability to calculate the exact time of a
duration for back-off decrement, rather than using the traditional relative
probability. Additionally, to our best knowledge, we first explore a
multichannel scheduling strategy of uplink data access in a single roadside
unit (RSU) by using a non-cooperative game in a RSU coverage region to maximize
the uplink throughput and minimize service time under saturated and unsaturated
traffic loads. To this end, we conduct a theoretical analysis and find the
equilibrium point of the scheduling. The numerical results show that the
solution of the equilibrium points are consistent with optimization problems.


title: Cardinal invariants for $\kappa$-box products

abstract:
  Definition. Let $\kappa$ be an infinite cardinal, let {X(i)} be a (not
necessarily faithfully indexed) set of topological spaces, and let X be the
product of the spaces X(i). The $\kappa$-box product topology on X is the
topology generated by those products of sets U(i) for which
  (a) for each i, U(i) is open in X(i); and
  (b) U(i) = X(i) with fewer than $\kappa$-many exceptions. (Thus, the usual
Tychonoff product topology on X is the $\omega$-box topology.)
  With emphasis on weight, density character, and Souslin number, the authors
study and determine the value of several "cardinal invariants" on the space X
with its $\kappa$-box topology, in terms of the corresponding invariants of the
individual spaces X(i).
  To the authors' knowledge, this work is the first systematic study of its
kind. Some of the results are axiom-sensitive, and some duplicate (and extend,
and make precise) earlier work of Hewitt-Marczewski-Pondiczery, of
Englking-Karlowicz, of Comfort-Negrepontis, and of Cater-Erdos-Galvin.


title:
Robust Adaptive Beamforming Based on Low-Complexity Shrinkage-Based
  Mismatch Estimation

abstract:
  In this work, we propose a low-complexity robust adaptive beamforming (RAB)
technique which estimates the steering vector using a Low-Complexity
Shrinkage-Based Mismatch Estimation (LOCSME) algorithm. The proposed LOCSME
algorithm estimates the covariance matrix of the input data and the
interference-plus-noise covariance (INC) matrix by using the Oracle
Approximating Shrinkage (OAS) method. LOCSME only requires prior knowledge of
the angular sector in which the actual steering vector is located and the
antenna array geometry. LOCSME does not require a costly optimization algorithm
and does not need to know extra information from the interferers, which avoids
direction finding for all interferers. Simulations show that LOCSME outperforms
previously reported RAB algorithms and has a performance very close to the
optimum.


title: Twisted derived equivalences for affine schemes

abstract:
  We show how work of Rickard and To\"en completely resolves the question of
when two twisted affine schemes are derived equivalent.


title: Mechanism of organization increase in complex systems

abstract:
  This paper proposes a variational approach to describe the evolution of
organization of complex systems from first principles, as increased efficiency
of physical action. Most simply stated, physical action is the product of the
energy and time necessary for motion. When complex systems are modeled as flow
networks, this efficiency is defined as a decrease of action for one element to
cross between two nodes, or endpoints of motion - a principle of least unit
action. We find a connection with another principle that of most total action,
or a tendency for increase of the total action of a system. This increase
provides more energy and time for minimization of the constraints to motion in
order to decrease unit action, and therefore to increase organization. Also,
with the decrease of unit action in a system, its capacity for total amount of
action increases. We present a model of positive feedback between action
efficiency and the total amount of action in a complex system, based on a
system of ordinary differential equations, which leads to an exponential growth
with time of each and a power law relation between the two. We present an
agreement of our model with data for core processing units of computers. This
approach can help to describe, measure, manage, design and predict future
behavior of complex systems to achieve the highest rates of self-organization
and robustness.


title: Embed and Conquer: Scalable Embeddings for Kernel k-Means on MapReduce

abstract:
  The kernel $k$-means is an effective method for data clustering which extends
the commonly-used $k$-means algorithm to work on a similarity matrix over
complex data structures. The kernel $k$-means algorithm is however
computationally very complex as it requires the complete data matrix to be
calculated and stored. Further, the kernelized nature of the kernel $k$-means
algorithm hinders the parallelization of its computations on modern
infrastructures for distributed computing. In this paper, we are defining a
family of kernel-based low-dimensional embeddings that allows for scaling
kernel $k$-means on MapReduce via an efficient and unified parallelization
strategy. Afterwards, we propose two methods for low-dimensional embedding that
adhere to our definition of the embedding family. Exploiting the proposed
parallelization strategy, we present two scalable MapReduce algorithms for
kernel $k$-means. We demonstrate the effectiveness and efficiency of the
proposed algorithms through an empirical evaluation on benchmark data sets.


title:
A First-Order Algorithm for the A-Optimal Experimental Design Problem: A
  Mathematical Programming Approach

abstract:
  We develop and analyse a first-order algorithm for the A-optimal experimental
design problem. The problem is first presented as a special case of a
parametric family of optimal design problems for which duality results and
optimality conditions are given. Then, two first-order (Frank-Wolfe type)
algorithms are presented, accompanied by a detailed time-complexity analysis of
the algorithms and computational results on various sized problems.


title: Unstructured sequential testing in sensor networks

abstract:
  We consider the problem of quickly detecting a signal in a sensor network
when the subset of sensors in which signal may be present is completely
unknown. We formulate this problem as a sequential hypothesis testing problem
with a simple null (signal is absent everywhere) and a composite alternative
(signal is present somewhere). We introduce a novel class of scalable
sequential tests which, for any subset of affected sensors, minimize the
expected sample size for a decision asymptotically, that is as the error
probabilities go to 0. Moreover, we propose sequential tests that require
minimal transmission activity from the sensors to the fusion center, while
preserving this asymptotic optimality property.


title: The Third-Order Term in the Normal Approximation for the AWGN Channel

abstract:
  This paper shows that, under the average error probability formalism, the
third-order term in the normal approximation for the additive white Gaussian
noise channel with a maximal or equal power constraint is at least $\frac{1}{2}
\log n + O(1)$. This matches the upper bound derived by
Polyanskiy-Poor-Verd\'{u} (2010).


title: Can CMB Lensing Help Cosmic Shear Surveys?

abstract:
  Yes! Upcoming galaxy shear surveys have the potential to significantly
improve our understanding of dark energy and neutrino mass if lensing
systematics can be sufficiently controlled. The cross-correlations between the
weak lensing shear, galaxy number counts from a galaxy redshift survey, and the
CMB lensing convergence can be used to calibrate the shear multiplicative bias,
one of the most challenging systematics in lensing surveys. These
cross-correlations can significantly reduce the deleterious effects of the
uncertainties in multiplicative bias.


title:
Non-formal deformation quantization and star-exponential of the Poincare
  Group

abstract:
  We recall the construction of non-formal deformation quantization of the
Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated
non-formal star-exponentials.


title:
The Araucaria Project. The distance to the Small Magellanic Cloud from
  late-type eclipsing binaries

abstract:
  We present a distance determination to the Small Magellanic Cloud (SMC) based
on an analysis of four detached, long period, late type eclipsing binaries
discovered by the OGLE Survey. The components of the binaries show negligible
intrinsic variability. A consistent set of stellar parameters was derived with
low statistical and systematic uncertainty. The absolute dimensions of the
stars are calculated with a precision of better than 3%.
  The surface brightness - infrared color relation was used to derive the
distance to each binary. The four systems clump around a distance modulus of (m
- M)=18.99 with a dispersion of only 0.05 mag. Combining these results with the
distance published by Graczyk et al. for the eclipsing binary OGLE SMC113.3
4007 we obtain a mean distance modulus to the SMC of 18.965 +/- 0.025 (stat.)
+/- 0.048 (syst.) mag. This corresponds to a distance of 62.1 +/- 1.9 kpc,
where the error includes both uncertainties. Taking into account other recent
published determinations of the SMC distance we calculated the distance modulus
difference between the SMC and the LMC equal to 0.458 +/- 0.068 mag. Finally we
advocate mu_{SMC}=18.95 +/- 0.07 as a new "canonical" value of the distance
modulus to this galaxy.


title: Characterization of quasy-Gaussian distributions

abstract:
  A new characterization of the multivariate so-called "quasi-Gaussian
distribution" (the authors dared to coin a new term) by means of independence
their Cartesian and polar coordinates proposed.
  The authors try to show that these distributions may essentially differ from
the classical Gaussian distribution. Some properties of these distributions are
studied: calculating of moments and of bilateral tail behavior. Some potential
applications of these distributions and mixtures of the distributions in
demography, philology are discussed in the final section.


title: Anatomy of Graph Matching based on an XQuery and RDF Implementation

abstract:
  Graphs are becoming one of the most popular data modeling paradigms since
they are able to model complex relationships that cannot be easily captured
using traditional data models. One of the major tasks of graph management is
graph matching, which aims to find all of the subgraphs in a data graph that
match a query graph. In the literature, proposals in this context are
classified into two different categories: graph-at-a-time, which process the
whole query graph at the same time, and vertex-at-a-time, which process a
single vertex of the query graph at the same time. In this paper, we propose a
new vertex-at-a-time proposal that is based on graphlets, each of which
comprises a vertex of a graph, all of the immediate neighbors of that vertex,
and all of the edges that relate those neighbors. Furthermore, we also use the
concept of minimum hub covers, each of which comprises a subset of vertices in
the query graph that account for all of the edges in that graph. We present the
algorithms of our proposal and describe an implementation based on XQuery and
RDF. Our evaluation results show that our proposal is appealing to perform
graph matching.


title: Expanders, exact crossed products, and the Baum-Connes conjecture

abstract:
  We reformulate the Baum-Connes conjecture with coefficients by introducing a
new crossed product functor for C*-algebras. All confirming examples for the
original Baum-Connes conjecture remain confirming examples for the reformulated
conjecture, and at present there are no known counterexamples to the
reformulated conjecture. Moreover, some of the known expander-based
counterexamples to the original Baum-Connes conjecture become confirming
examples for our reformulated conjecture.


title:
Derivation of effective spin-orbit Hamiltonians and spin lifetimes, with
  application to SrTiO$_3$ heterostructures

abstract:
  A general approach is derived for constructing an effective spin-orbit
Hamiltonian for nonmagnetic materials, which is useful for calculating
spin-dependent properties near an arbitrary point in momentum space with
pseudospin degeneracy. The formalism is verified through comparisons with other
approaches for III-V semiconductors, and its general applicability is
illustrated by deriving the spin-orbit interaction and predicting spin
lifetimes for strained SrTiO$_3$ and a two-dimensional electron gas in
SrTiO$_3$ (such as at the LaAlO$_3$/SrTiO$_3$ interface). These results suggest
robust spin coherence and spin transport properties in SrTiO$_3$-based
materials at room temperature.


title:
Determining the first order perturbation of a bi-harmonic operator on
  bounded and unbounded domains from partial data

abstract:
  In this paper we study inverse boundary value problems with partial data for
the bi-harmonic operator with first order perturbation. We consider two types
of subsets of $\mathbb{R}^{n}(n\geq 3)$, one is an infinite slab, the other is
a bounded domain. In the case of a slab, we show that, from Dirichlet and
Neumann data given either on the different boundary hyperplanes of the slab or
on the same boundary hyperplane, one can uniquely determine the magnetic
potential and the electric potential.
  In the case of a bounded domain, we show the unique determination of the
magnetic potential and the electric potential from partial Dirichlet and
Neumann data under two different assumptions. The first assumption is that the
magnetic and electric potentials are known in a neighborhood of the boundary,
in this situation we obtain the uniqueness result when the Dirichlet and
Neumann data are only given on two arbitrary open subsets of the boundary. The
second assumption is that the Dirichlet and Neumann data are known on the same
part of the boundary whose complement is a part of a hyperplane, we also
establish the unique determination result in this local data case.


title:
Some New Results on Equivalency of Collusion-Secure Properties for
  Reed-Solomon Codes

abstract:
  A. Silverberg (IEEE Trans. Inform. Theory 49, 2003) proposed a question on
the equivalence of identifiable parent property and traceability property for
Reed-Solomon code family. Earlier studies on Silverberg's problem motivate us
to think of the stronger version of the question on equivalence of separation
and traceability properties. Both, however, still remain open. In this article,
we integrate all the previous works on this problem with an algebraic way, and
present some new results. It is notable that the concept of subspace subcode of
Reed-Solomon code, which was introduced in error-correcting code theory,
provides an interesting prospect for our topic.


title: One-parameter Neutrino Mass Matrix and Symmetry Realization

abstract:
  We investigate the Majorana neutrino mass matrix $M_{\nu}$ with one parameter
in the context of two texture zeros and its symmetry realization by non-Abelian
discrete symmetry. From numerical calculation, we confirm that the textures
$(M_{\nu})_{11,12}=0$ and $(M_{\nu})_{11,13}=0$ are consistent with the current
experimental constraints, and show the correlations between non-zero elements
of $M_{\nu}$. The ratios of non-zero elements of $M_{\nu}$ are constrain in
small regions, and we find simple examples of $M_{\nu}$ with one real mass
parameter. We also discuss symmetry realization of the mass matrix by the
type-II seesaw mechanism based on the binary icosahedral symmetry $A_5'$ .


title:
Fermionized photons in the ground state of one-dimensional coupled
  cavities

abstract:
  The Density Matrix Renormalization Group algorithm is used to characterize
the ground states of one-dimensional coupled cavities in the regime of low
photon densities. Numerical results for photon and spin excitation densities,
one- and two-body correlation functions, superfluid and condensate fractions,
as well as the entanglement entropy and localizable entanglement are obtained
for the Jaynes-Cummings-Hubbard (JCH) model, and are compared with those for
the Bose-Hubbard (BH) model where applicable. The results indicate that a
Tonks-Girardeau phase, in which the photons are strongly fermionized, appears
between the Mott-insulating and superfluid phases as a function of the
inter-cavity coupling. In fact, the superfluid density is found to be zero in a
wide region outside the Mott-insulator phase boundary. The presence of two
different species of excitation (spin and photon) in the JCH model gives rise
to properties with no analog in the BH model, such as the (quasi)condensation
of spin excitations and the spontaneous generation of entanglement between the
atoms confined to each cavity.


title:
Providing Trustworthy Contributions via a Reputation Framework in Social
  Participatory Sensing Systems

abstract:
  Social participatory sensing is a newly proposed paradigm that tries to
address the limitations of participatory sensing by leveraging online social
networks as an infrastructure. A critical issue in the success of this paradigm
is to assure the trustworthiness of contributions provided by participants. In
this paper, we propose an application-agnostic reputation framework for social
participatory sensing systems. Our framework considers both the quality of
contribution and the trustworthiness level of participant within the social
network. These two aspects are then combined via a fuzzy inference system to
arrive at a final trust rating for a contribution. A reputation score is also
calculated for each participant as a resultant of the trust ratings assigned to
him. We adopt the utilization of PageRank algorithm as the building block for
our reputation module. Extensive simulations demonstrate the efficacy of our
framework in achieving high overall trust and assigning accurate reputation
scores.


title: Splitting mixed Hodge structures over affine invariant manifolds

abstract:
  We prove that affine invariant manifolds in strata of flat surfaces are
algebraic varieties. The result is deduced from a generalization of a theorem
of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi
map lands in the torsion of a factor of the Jacobians. This statement can be
viewed as a splitting of certain mixed Hodge structures.


title: Paradoxical Quantum Scattering off a Time Dependent Potential?

abstract:
  We consider the quantum scattering off a time dependent barrier in one
dimension. Our initial state is a right going eigenstate of the Hamiltonian at
time t=0. It consists of a plane wave incoming from the left, a reflected plane
wave on the left of the barrier and a transmitted wave on its right. We find
that at later times, the evolving wave function has a finite overlap with left
going eigenstates of the Hamiltonian at time t=0. For simplicity we present an
exact result for a time dependent delta function potential. Then we show that
our result is not an artifact of that specific choice of the potential. This
surprising result does not agree with our interpretation of the eigenstates of
the Hamiltonian at time t=0. A numerical study of evolving wave packets, does
not find any corresponding real effect. Namely, we do not see on the right hand
side of the barrier any evidence for a left going packet. Our conclusion is
thus that the intriguing result mentioned above is intriguing only due to the
semantics of the interpretation.


title: Growth rates of algebras, I: pointed cube terms

abstract:
  We investigate the function d_A(n), which gives the size of a least size
generating set for A^n.


title: Equidistribution of phase shifts in semiclassical potential scattering

abstract:
  Consider a semiclassical Hamiltonian $H := h^{2} \Delta + V - E$ where
$\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V \in
C^{\infty}_{0}(\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that
under an appropriate dynamical hypothesis on the Hamilton flow corresponding to
$H$, the eigenvalues of the scattering matrix $S_{h}(V)$ define a measure on
$\mathbb{S}^{1}$ that converges to Lebesgue measure away from $1 \in
\mathbb{S}^{1}$ as $h \to 0$.


title: Holographic R\'enyi Entropy and Generalized Entropy method

abstract:
  In this paper we use the method of generalized gravitational entropy in
\cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical
entangling surface, and calculate the R\'enyi entropy with the dual bulk
gravity theory being either Einstein gravity or Lovelock gravity, this approach
is closely related to that in \cite{Casini:2011kv}. For a general entangling
surface we derive the area law of entanglement entropy. The area law is closely
related with the local property of the entangling surface.


title: Communication Lower Bounds via Critical Block Sensitivity

abstract:
  We use critical block sensitivity, a new complexity measure introduced by
Huynh and Nordstr\"om (STOC 2012), to study the communication complexity of
search problems. To begin, we give a simple new proof of the following central
result of Huynh and Nordstr\"om: if $S$ is a search problem with critical block
sensitivity $b$, then every randomised two-party protocol solving a certain
two-party lift of $S$ requires $\Omega(b)$ bits of communication. Besides
simplicity, our proof has the advantage of generalising to the multi-party
setting. We combine these results with new critical block sensitivity lower
bounds for Tseitin and Pebbling search problems to obtain the following
applications:
  (1) Monotone Circuit Depth: We exhibit a monotone $n$-variable function in NP
whose monotone circuits require depth $\Omega(n/\log n)$; previously, a bound
of $\Omega(\sqrt{n})$ was known (Raz and Wigderson, JACM 1992). Moreover, we
prove a $\Theta(\sqrt{n})$ monotone depth bound for a function in monotone P.
  (2) Proof Complexity: We prove new rank lower bounds as well as obtain the
first length--space lower bounds for semi-algebraic proof systems, including
Lov\'asz--Schrijver and Lasserre (SOS) systems. In particular, these results
extend and simplify the works of Beame et al. (SICOMP 2007) and Huynh and
Nordstr\"om.


title: High Redshift Standard Candles: Predicted Cosmological Constraints

abstract:
  We investigate whether future measurements of high redshift standard candles
(HzSCs) will be a powerful probe of dark energy, when compared to other types
of planned dark energy measurements. Active galactic nuclei and gamma ray
bursts have both been proposed as potential HzSC candidates. Due to their high
luminosity, they can be used to probe unexplored regions in the expansion
history of the universe. Information from these regions can help constrain the
properties of dark energy, and in particular, whether it varies over time.
  We consider both linear and piecewise parameterizations of the dark energy
equation of state, $w(z)$, and assess the optimal redshift distribution a
high-redshift standard-candle survey could take to constrain these models.
  The more general the form of the dark energy equation of state $w(z)$ being
tested, the more useful high-redshift standard candles become. For a linear
parameterization of $w(z)$, HzSCs give only small improvements over planned
supernova and baryon acoustic oscillation measurements; a wide redshift range
with many low redshift points is optimal to constrain this linear model.
However to constrain a general, and thus potentially more informative, form of
$w(z)$, having many HzSCs can significantly improve limits on the nature of
dark energy.


title: Averaging for nonlinear systems evolving on Riemannian manifolds

abstract:
  This paper presents an averaging method for nonlinear systems defined on
Riemannian manifolds. We extend closeness of solutions results for ordinary
differential equations on $R^{n}$ to dynamical systems defined on Riemannian
manifolds by employing differential geometry. A generalization of closeness of
solutions for periodic dynamical systems on compact time intervals is derived
for dynamical systems evolving on compact Riemannian manifolds. Under local
asymptotic (exponential) stability of the average vector field, we further
relax the compactness of the ambient Riemannian manifold and obtain the
closeness of solutions on the infinite time interval by employing the notion of
uniform normal neighborhoods of an equilibrium point of a vector field. These
results are also presented for time-varying dynamical systems where their
averaged systems are almost globally asymptotically or exponentially stable on
compact manifolds. The main results of the paper are illustrated by several
examples.


title:
Derandomizing Polynomial Identity over Finite Fields Implies
  Super-Polynomial Circuit Lower Bounds for NEXP

abstract:
  We show that derandomizing polynomial identity testing over an arbitrary
finite field implies that NEXP does not have polynomial size boolean circuits.
In other words, for any finite field F(q) of size q, $PIT_q\in
NSUBEXP\Rightarrow NEXP\not\subseteq P/poly$, where $PIT_q$ is the polynomial
identity testing problem over F(q), and NSUBEXP is the nondeterministic
subexpoential time class of languages. Our result is in contract to Kabanets
and Impagliazzo's existing theorem that derandomizing the polynomial identity
testing in the integer ring Z implies that NEXP does have polynomial size
boolean circuits or permanent over Z does not have polynomial size arithmetic
circuits.


title: Growth Rates of Algebras, III: Growth Rates of Solvable Algebras

abstract:
  We investigate how the behavior of the function d_A(n) that gives the size of
a least size generating set for A^n, influences the structure of a finite
solvable algebra A.


title: A bit of tropical geometry

abstract:
  This friendly introduction to tropical geometry is meant to be accessible to
first year students in mathematics. The topics discussed here are basic
tropical algebra, tropical plane curves, some tropical intersections, and
Viro's patchworking. Each definition is explained with concrete examples and
illustrations. To a great exten, this text is an updated of a translation from
a french text by the first author. There is also a newly added section
highlighting new developments and perspectives on tropical geometry. In
addition, the final section provides an extensive list of references on the
subject.


title: Power Partial Isometry Index and Ascent of a Finite Matrix

abstract:
  We give a complete characterization of nonnegative integers $j$ and $k$ and a
positive integer $n$ for which there is an $n$-by-$n$ matrix with its power
partial isometry index equal to $j$ and its ascent equal to $k$. Recall that
the power partial isometry index $p(A)$ of a matrix $A$ is the supremum,
possibly infinity, of nonnegative integers $j$ such that $I, A, A^2, \ldots,
A^j$ are all partial isometries while the ascent $a(A)$ of $A$ is the smallest
integer $k\ge 0$ for which $\ker A^k$ equals $\ker A^{k+1}$. It was known
before that, for any matrix $A$, either $p(A)\le\min\{a(A), n-1\}$ or
$p(A)=\infty$. In this paper, we prove more precisely that there is an
$n$-by-$n$ matrix $A$ such that $p(A)=j$ and $a(A)=k$ if and only if one of the
following conditions holds: (a) $j=k\le n-1$, (b) $j\le k-1$ and $j+k\le n-1$,
and (c) $j\le k-2$ and $j+k=n$. This answers a question we asked in a previous
paper.


title:
Efficient Runtime Monitoring with Metric Temporal Logic: A Case Study in
  the Android Operating System

abstract:
  We present a design and an implementation of a security policy specification
language based on metric linear-time temporal logic (MTL). MTL features
temporal operators that are indexed by time intervals, allowing one to specify
timing-dependent security policies. The design of the language is driven by the
problem of runtime monitoring of applications in mobile devices. A main case
the study is the privilege escalation attack in the Android operating system,
where an app gains access to certain resource or functionalities that are not
explicitly granted to it by the user, through indirect control flow. To capture
these attacks, we extend MTL with recursive definitions, that are used to
express call chains betwen apps. We then show how the metric operators of MTL,
in combination with recursive definitions, can be used to specify policies to
detect privilege escalation, under various fine grained constraints. We present
a new algorithm, extending that of linear time temporal logic, for monitoring
safety policies written in our specification language. The monitor does not
need to store the entire history of events generated by the apps, something
that is crucial for practical implementations. We modified the Android OS
kernel to allow us to insert our generated monitors modularly. We have tested
the modified OS on an actual device, and show that it is effective in detecting
policy violations.


title:
Method for Direct Measurement of Cosmic Acceleration by 21-cm Absorption
  Systems

abstract:
  So far there is only indirect evidence that the Universe is undergoing an
accelerated expansion. The evidence for cosmic acceleration is based on the
observation of different objects at different distances, and requires invoking
the Copernican cosmological principle, and Einstein's equations of motion. We
examine the direct observability using recession velocity drifts (Sandage-Loeb
effect) of 21cm hydrogen absorption systems in upcoming radio surveys. This
measures the change in velocity of the {\it same} objects separate by a time
interval and is a model-independent measure of acceleration. We forecast that
for a CHIME-like survey with a decade time span, we can detect the acceleration
of a $\Lambda$CDM Universe with $5\sigma$ confidence. This acceleration test
requires modest data analysis and storage changes from the normal processing,
and cannot be recovered retroactively.


title: Power Control Protocols in VANET

abstract:
  Vehicular Ad hoc Networks (VANET) is one of the most challenging research
area in the field of the Mobile Ad hoc Network (MANET), Power control is a
critical issue in VANETwhere is should be managed carefully to help the channel
to have high performance. In this paper a comparative study in the published
protocols in the field of safety message dynamic power control will be
presented and evaluated.


title: Gauge hierarchy problem, supersymmetry and fermionic symmetry

abstract:
  We reconsider the gauge hierarchy problem from the viewpoint of effective
field theories and a high-energy physics, motivated by the alternative scenario
that the standard model holds up to a high-energy scale such as the Planck
scale. The problem is restated as the question whether it is possible to
construct a low-energy effective theory and the interaction with heavy
particles, without spoiling the structure of a high-energy physics supported by
an excellent concept. Based on this reinterpretation, we give a conjecture that
theories with hidden fermionic symmetries can be free from the gauge hierarchy
problem and become candidates of the physics beyond and/or behind the standard
model, and present toy models with particle-ghost symmetries as illustrative
examples and a prototype model for the grand unification.