title: Criteria for guaranteed breakdown in two-phase inhomogeneous bodies

abstract:
  Lower bounds are obtained on the maximum field strength in one or both phases
in a body containing two-phases. These bounds only incorporate boundary data
that can be obtained from measurements at the surface of the body, and thus may
be useful for determining if breakdown has necessarily occurred in one of the
phases, or that some other nonlinearities have occurred. It is assumed the
response of the phases is linear up to the point of electric, dielectric, or
elastic breakdown, or up to the point of the onset of nonlinearities. These
bounds are calculated for conductivity, with one or two sets of boundary
conditions, for complex conductivity (as appropriate at fixed frequency when
the wavelength is much larger than the body, i.e., for quasistatics), and for
two-dimensional elasticity. Sometimes the bounds are optimal when the field is
constant in one of the phases, and using the algorithm of Kang, Kim, and Milton
(2012) a wide variety of inclusion shapes having this property, for
appropriately chosen bodies and appropriate boundary conditions, are
numerically constructed. Such inclusions are known as $E_\Omega$-inclusions.


title:
Laws of the Iterated Logarithm for random walks on Random Conductance
  Models

abstract:
  We derive laws of the iterated logarithm for random walks on random
conductance models under the assumption that the random walks enjoy long time
sub-Gaussian heat kernel estimates.


title: The invariances of power law size distributions

abstract:
  Size varies. Small things are typically more frequent than large things. The
logarithm of frequency often declines linearly with the logarithm of size. That
power law relation forms one of the common patterns of nature. Why does the
complexity of nature reduce to such a simple pattern? Why do things as
different as tree size and enzyme rate follow similarly simple patterns? Here I
analyze such patterns by their invariant properties. For example, a common
pattern should not change when adding a constant value to all observations.
That shift is essentially the renumbering of the points on a ruler without
changing the metric information provided by the ruler. A ruler is shift
invariant only when its scale is properly calibrated to the pattern being
measured. Stretch invariance corresponds to the conservation of the total
amount of something, such as the total biomass and consequently the average
size. Rotational invariance corresponds to pattern that does not depend on the
order in which underlying processes occur, for example, a scale that additively
combines the component processes leading to observed values. I use tree size as
an example to illustrate how the key invariances shape pattern. A simple
interpretation of common pattern follows. That simple interpretation connects
the normal distribution to a wide variety of other common patterns through the
transformations of scale set by the fundamental invariances.


title: A strengthening of a theorem of Bourgain-Kontorovich-V

abstract:
  Zaremba's conjecture (1971) states that every positive integer number $d$ can
be represented as a denominator (continuant) of a finite continued fraction
$\frac{b}{d}=[d_1,d_2,\ldots,d_{k}],$ with all partial quotients
$d_1,d_2,\ldots,d_{k}$ being bounded by an absolute constant $A.$ Recently (in
2011) several new theorems concerning this conjecture were proved by Bourgain
and Kontorovich. The easiest of them states that the set of numbers satisfying
Zaremba's conjecture with $A=50$ has positive proportion in $\mathbb{N}.$ In
2014 Kan and Frolenkov proved this result with $A=5.$ Let
$\mathfrak{C}_{\mathcal{A}}$ be the set of infinite continued fractions whose
partial quotients belong to $\mathcal{A}$
$$\mathfrak{C}_{\mathcal{A}}=\left\{[d_1,\ldots,d_j,\ldots]:
d_j\in\mathcal{A},\,j=1,\ldots\right\}$$ and let $\delta$ be the Hausdorff
dimension of $\mathfrak{C}_{\mathcal{A}}.$ Naw this result proved with $A=4$
and $\delta>0.7807\ldots$.


title: Superadiabatic quantum state transfer in spin chains

abstract:
  In this letter we propose a superadiabatic protocol where quantum state
transfer can be achieved with arbitrarily high accuracy and minimal control
across long spin chains with an odd number of spins. The quantum state transfer
protocol only requires the control of the couplings between the qubits on the
edge and the spin chain. We predict fidelities above 0.99 for an evolution of
nanoseconds using typical spin exchange coupling values of {\mu}eV.
Furthermore, by building a superadiabatic formalism on top of this protocol, we
propose a effective superadiabatic protocol that retains the minimal control
over the spin chain and improves the fidelity by up to 20%.


title:
The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes
  equations

abstract:
  We present a new hydrodynamic model consisting of the pressureless Euler
equations and the isentropic compressible Navier-Stokes equations where the
coupling of two systems is through the drag force. This coupled system can be
derived, in the hydrodynamic limit, from the particle-fluid equations that are
frequently used to study the medical sprays, aerosols and sedimentation
problems. For the proposed system, we first construct the local-in-time
classical solutions in an appropriate $L^2$ Sobolev space. We also establish
the \emph{a priori} large-time behavior estimate by constructing a Lyapunov
functional measuring the fluctuation of momentum and mass from the averaged
quantities, and using this together with the bootstrapping argument, we obtain
the global classical solution. The large-time behavior estimate asserts that
the velocity functions of the pressureless Euler and the compressible
Navier-Stokes equations are aligned exponentially fast as time tends to
infinity.


title: Emergent dynamics of the Cucker-Smale flocking model and its variants

abstract:
  In this chapter, we present the Cucker-Smale type flocking models, and
discuss their mathematical structures and flocking theorems in terms of
coupling strength, interaction topologies and initial data. In 2007, two
mathematicians Felipe Cucker and Steve Smale introduced a second-order particle
model which resembles Newton's equations in $N$-body system, and present how
their simple model can exhibit emergent flocking behavior under sufficient
conditions expressed only in terms of parameters and initial data. After
Cucker-Smale's seminal works, their model has received lots of attention from
applied math and control engineering communities. We discuss the state-of-art
for the flocking theorems to Cucker-Smale type flocking models.


title:
Structured low-rank recovery of piecewise constant signals with
  performance guarantees

abstract:
  We derive theoretical guarantees for the exact recovery of piecewise constant
two-dimensional images from a minimal number of non-uniform Fourier samples
using a convex matrix completion algorithm. We assume the discontinuities of
the image are localized to the zero level-set of a bandlimited function, which
induces certain linear dependencies in Fourier domain, such that a multifold
Toeplitz matrix built from the Fourier data is known to be low-rank. The
recovery algorithm arranges the known Fourier samples into the structured
matrix then attempts recovery of the missing Fourier data by minimizing the
nuclear norm subject to structure and data constraints. This work adapts
results by Chen and Chi on the recovery of isolated Diracs via nuclear norm
minimization of a similar multifold Hankel structure. We show that exact
recovery is possible with high probability when the bandlimited function
describing the edge set satisfies an incoherency property. Finally, we
demonstrate the algorithm on the recovery of undersampled MRI data.


title: Green's theorem for crossed products by Hilbert $C^*$-bimodules

abstract:
  Green's theorem gives a Morita equivalence $C_0(G/H,A)\rtimes G\sim A\rtimes
H$ for a closed subgroup $H$ of a locally compact group $G$ acting on a
$C^*$-algebra $A$. We prove an analogue of Green's theorem in the case
$G=\mathbb{Z}$, where the automorphism generating the action is replaced by a
Hilbert $C^*$-bimodule.


title:
Multistage Robust Unit Commitment with Dynamic Uncertainty Sets and
  Energy Storage

abstract:
  The deep penetration of wind and solar power is a critical component of the
future power grid. However, the intermittency and stochasticity of these
renewable resources bring significant challenges to the reliable and economic
operation of power systems. Motivated by these challenges, we present a
multistage adaptive robust optimization model for the unit commitment (UC)
problem, which models the sequential nature of the dispatch process and
utilizes a new type of dynamic uncertainty sets to capture the temporal and
spatial correlations of wind and solar power. The model also considers the
operation of energy storage devices. We propose a simplified and effective
affine policy for dispatch decisions, and develop an efficient algorithmic
framework using a combination of constraint generation and duality based
reformulation with various improvements. Extensive computational experiments
show that the proposed method can efficiently solve multistage robust UC
problems on the Polish 2736-bus system under high dimensional uncertainty of 60
wind farms and 30 solar farms. The computational results also suggest that the
proposed model leads to significant benefits in both costs and reliability over
robust models with traditional uncertainty sets as well as deterministic models
with reserve rules.


title: Personal Recollection, 1945 - 1960

abstract:
  This article gives a sketch of teachers and colleagues who have had strong
influence on my becoming a particle physicist.


title: PAS-MC: Privacy-preserving Analytics Stream for the Mobile Cloud

abstract:
  In today's digital world, personal data is being continuously collected and
analyzed without data owners' consent and choice. As data owners constantly
generate data on their personal devices, the tension of storing private data on
their own devices yet allowing third party analysts to perform aggregate
analytics yields an interesting dilemma.
  This paper introduces PAS-MC, the first practical privacy-preserving and
anonymity stream analytics system. PAS-MC ensures that each data owner locally
privatizes their sensitive data before responding to analysts' queries. PAS-MC
also protects against traffic analysis attacks with minimal trust
vulnerabilities.We evaluate the scheme over the California Transportation
Dataset and show that we can privately and anonymously stream vehicular
location updates yet preserve high accuracy.


title:
An Initial Seed Selection Algorithm for K-means Clustering of
  Georeferenced Data to Improve Replicability of Cluster Assignments for
  Mapping Application

abstract:
  K-means is one of the most widely used clustering algorithms in various
disciplines, especially for large datasets. However the method is known to be
highly sensitive to initial seed selection of cluster centers. K-means++ has
been proposed to overcome this problem and has been shown to have better
accuracy and computational efficiency than k-means. In many clustering problems
though -such as when classifying georeferenced data for mapping applications-
standardization of clustering methodology, specifically, the ability to arrive
at the same cluster assignment for every run of the method i.e. replicability
of the methodology, may be of greater significance than any perceived measure
of accuracy, especially when the solution is known to be non-unique, as in the
case of k-means clustering. Here we propose a simple initial seed selection
algorithm for k-means clustering along one attribute that draws initial cluster
boundaries along the 'deepest valleys' or greatest gaps in dataset. Thus, it
incorporates a measure to maximize distance between consecutive cluster centers
which augments the conventional k-means optimization for minimum distance
between cluster center and cluster members. Unlike existing initialization
methods, no additional parameters or degrees of freedom are introduced to the
clustering algorithm. This improves the replicability of cluster assignments by
as much as 100% over k-means and k-means++, virtually reducing the variance
over different runs to zero, without introducing any additional parameters to
the clustering process. Further, the proposed method is more computationally
efficient than k-means++ and in some cases, more accurate.


title: A global constraint for closed itemset mining

abstract:
  Discovering the set of closed frequent patterns is one of the fundamental
problems in Data Mining. Recent Constraint Programming (CP) approaches for
declarative itemset mining have proven their usefulness and flexibility. But
the wide use of reified constraints in current CP approaches raises many
difficulties to cope with high dimensional datasets. This paper proposes CLOSED
PATTERN global constraint which does not require any reified constraints nor
any extra variables to encode efficiently the Closed Frequent Pattern Mining
(CFPM) constraint. CLOSED-PATTERN captures the particular semantics of the CFPM
problem in order to ensure a polynomial pruning algorithm ensuring domain
consistency. The computational properties of our constraint are analyzed and
their practical effectiveness is experimentally evaluated.


title:
Scaling indicator and planning plane: an indicator and a visual tool for
  exploring the relationship between urban form, energy efficiency and carbon
  emissions

abstract:
  Ecosystems and other naturally resilient systems exhibit allometric scaling
in the distribution of sizes of their elements. In this paper we define an
allometry inspired scaling indicator for cities that is a first step towards
quantifying the resilience borne of a complex systems' hierarchical structural
composition. The scaling indicator is calculated using large census datasets
and is analogous to fractal dimension in spatial analysis. Lack of numerical
rigor and the resulting variation in scaling indicators -inherent in the use of
box counting mechanism for fractal dimension calculation for cities- has been
one of the hindrances in the adoption of fractal dimension as an urban
indicator of note. The intra-urban indicator of scaling in population density
distribution developed here is calculated for 58 US cities using a methodology
that produces replicable results, employing large census-block wise population
datasets from the 2010 US Census 2010 and the 2007 US Economic Census. We show
that rising disparity -as measured by the proposed indicator of population
density distribution in census blocks in metropolitan statistical areas (using
US Census 2010 data) adversely affects energy consumption efficiency and carbon
emissions in cities and leads to a higher urban carbon footprint. We then
define a planning plane as a visual and analytic tool for incorporation of
scaling indicator analysis into policy and decision-making.


title:
Funding Data from Publication Acknowledgements: Coverage, Uses and
  Limitations

abstract:
  This article contributes to the development of methods for analysing research
funding systems by exploring the robustness and comparability of emerging
approaches to generate funding landscapes useful for policy making. We use a
novel dataset of manually extracted and coded data on the funding
acknowledgements of 7,510 publications representing UK cancer research in the
year 2011 and compare these 'reference data' with funding data provided by Web
of Science (WoS) and MEDLINE/PubMed. Findings show high recall (about 93%) of
WoS funding data. By contrast, MEDLINE/PubMed data retrieved less than half of
the UK cancer publications acknowledging at least one funder. Conversely, both
databases have high precision (+90%): i.e. few cases of publications with no
acknowledgement to funders are identified as having funding data. Nonetheless,
funders acknowledged in UK cancer publications were not correctly listed by
MEDLINE/PubMed and WoS in about 75% and 32% of the cases, respectively.
'Reference data' on the UK cancer research funding system are then used as a
case-study to demonstrate the utility of funding data for strategic
intelligence applications (e.g. mapping of funding landscape, comparison of
funders' research portfolios).


title: Normal vector of a random hyperplane

abstract:
  Let v_1,...,v_{n-1} be n-1 independent vectors in R^n (or C^n). We study x,
the unit normal vector of the hyperplane spanned by the v_i. Our main finding
is that x resembles a random vector chosen uniformly from the unit sphere,
under some randomness assumption on the v_i.
  Our result has applications in random matrix theory. Consider an n by n
random matrix with iid entries. We first prove an exponential bound on the
upper tail for the least singular value, improving the earlier linear bound by
Rudelson and Vershynin. Next, we derive optimal delocalization for the
eigenvectors corresponding to eigenvalues of small modulus.


title:
Proximity effect and Ising superconductivity in
  superconductor/transition metal dichalcogenide heterostructures

abstract:
  Recently, it was experimentally realized that 2D superconducting transition
metal dichalcogenides (TMD) such as gated MoS$_2$ and monolayer NbSe$_2$ have
in-plane upper critical magnetic fields much higher than the Pauli limit. This
is due to the so-called Ising spin-orbit coupling (SOC) of TMD which pins the
electron spins along the out-of-plane directions and protects the Cooper pairs
from in-plane magnetic fields. However, many TMD materials with extremely large
Ising SOC, in the order of a few hundred meV, are not superconducting. In this
work, we show that TMD materials can induce strong Ising SOC on ordinary
$s$-wave superconductors through proximity effect. By solving the
self-consistent gap equation of the TMD/superconductor heterostructure, we
found that the $H_{c2}$ of the $s$-wave superconductor can be strongly
enhanced. Importantly, when the in-plane field is larger than the Pauli limit
field and weaker than $H_{c2}$, the heterostructure becomes a nodal topological
superconductor which supports Majorana flat bands.


title: Phase-Aligned Spectral Filtering for Decomposing Spatiotemporal Dynamics

abstract:
  Spatiotemporal dynamics is central to a wide range of applications from
climatology, computer vision to neural sciences. From temporal observations
taken on a high-dimensional vector of spatial locations, we seek to derive
knowledge about such dynamics via data assimilation and modeling. It is assumed
that the observed spatiotemporal data represent superimposed lower-rank smooth
oscillations and movements from a generative dynamic system, mixed with
higher-rank random noises. Separating the signals from noises is essential for
us to visualize, model and understand these lower-rank dynamic systems. It is
also often the case that such a lower-rank dynamic system have multiple
independent components, corresponding to different trends or functionalities of
the system under study. In this paper, we present a novel filtering framework
for identifying lower-rank dynamics and its components embedded in a high
dimensional spatiotemporal system. It is based on an approach of structural
decomposition and phase-aligned construction in the frequency domain. In both
our simulated examples and real data applications, we illustrate that the
proposed method is able to separate and identify meaningful lower-rank
movements, while existing methods fail.


title:
Collisional shift and broadening of the transition lines in pionic
  helium

abstract:
  We calculate the density shift and broadening of selected dipole transition
lines of pionic helium in gaseous helium at low temperatures up to T=12 K and
pressure up to a few bar. In the approximation of binary collisions the shift
and broadening depend linearly on the density; we evaluate the slope of this
linear dependence for a few spectral lines of known experimental interest, and
also investigate its temperature dependence. We find a blue shift of the
resonance frequencies of the $(n,l)=(16,15) \rightarrow (16,14)$, $(17,16)
\rightarrow (17,15)$, and $(16,15)\rightarrow(17,14)$ unfavored transitions,
and a red shift for the favored one $(17,16) \rightarrow (16,15)$. The results
are intended to significantly increase the efficiency of the laser spectroscopy
investigations of pionic helium and help the interpretation of the experimental
data.


title: On the Upsilon invariant and satellite knots

abstract:
  We study the effect of satellite operations on the Upsilon invariant of
Ozsvath-Stipsicz-Szabo. We obtain results concerning when a knot and its
satellites are independent; for example, we show that the set
$\{D_{2^i,1}\}_{i=1}^\infty$ is a basis for an infinite rank summand of the
group of smooth concordance classes of topologically slice knots, for D the
positive clasped untwisted Whitehead double of any knot with positive
tau-invariant, e.g. the right-handed trefoil. We also prove that the image of
the Mazur satellite operator on the smooth knot concordance group contains an
infinite rank subgroup of topologically slice knots.


title: Dehn surgery on complicated fibered knots in the 3-sphere

abstract:
  Let K be a fibered knot in the 3-sphere. We show that if the monodromy of K
is sufficiently complicated, then Dehn surgery on K cannot yield a lens space.
Work of Yi Ni shows that if K has a lens space surgery then it is fibered.
Combining this with our result we see that if K has a lens space surgery then
it is fibered and the monodromy is relatively simple.


title: Path integral approach to theories of diffusion-influenced reactions

abstract:
  The path decomposition expansion represents the propagator of the
irreversible reaction as a convolution of the first-passage, last-passage and
rebinding time probability densities. Using path integral technique, we give an
elementary, yet rigorous, proof of the path decomposition expansion of the
Green's functions describing the non-reactive case and the irreversible
reaction of an isolated pair of molecules. To this end, we exploit the
connection between boundary value problems and interaction potential problems
with $\delta$- and $\delta'$-function perturbation. In particular, we employ a
known exact summation of a perturbation series to derive exact relations
between the Green's functions of the perturbed and unperturbed problem. Along
the way, we are able to derive a number of additional exact identities that
relate the propagators describing the free-space, the non-reactive as well as
the completely and partially reactive case.


title: Analytic Properties of the Sum $B_{1}(h,k)$

abstract:
  In \cite{csc}, Cetin et al. defined a new special finite sum which is denoted
by $B_{1}(h,k)$. In this paper, with the help of the Hardy and Dedekind sums we
will give many properties of the sum $B_{1}(h,k).$ Then we will give the
connections of this sum with the other well-known finite sums such as the
Dedekind sums, the Hardy sums, the Simsek sums $Y(h,k)$ and the sum
$C_{1}(h,k)$. By using the Fibonacci numbers and two-term polynomial relation,
we will also give a new property of the sum $B_{1}(h,k)$.


title: The Birkhoff theorem and string clouds

abstract:
  We consider spherically symmetric space-times in GR under the unconventional
assumptions that the spherical radius $r$ is either a constant or has a null
gradient in the $(t,x)$ subspace orthogonal to the symmetry spheres (i.e.,
$(\partial r)^2 = 0$). It is shown that solutions to the Einstein equations
with $r = \rm const$ contain an extra (fourth) spatial or temporal Killing
vector and thus satisfy the Birkhoff theorem under an additional physically
motivated condition that the lateral pressure is functionally related to the
energy density. This leads to solutions that directly generalize the
Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar
conditions, solutions with $(\partial r)^2 = 0$ but $r\ne\rm const$, supported
by an anisotropic fluid, contain a null Killing vector, which again indicates a
Birkhoff-like behavior of the system. Similar space-times supported by pure
radiation (in particular, a massless radiative scalar field) contain a null
Killing vector without additional assumptions, which leads to one more
extension of the Birkhoff theorem. Exact radial wave solutions have been found
(i) with an anisotropic fluid and (ii) with a gas of radially directed cosmic
strings (or a "string cloud") combined with pure radiation. Furthermore, it is
shown that a perfect fluid with isotropic pressure and a massive or
self-interacting scalar field cannot be sources of gravitational fields with a
null but nonzero gradient of $r$.


title: Generating Semi-Synthetic Validation Benchmarks for Embryomics

abstract:
  Systematic validation is an essential part of algorithm development. The
enormous dataset sizes and the complexity observed in many recent time-resolved
3D fluorescence microscopy imaging experiments, however, prohibit a
comprehensive manual ground truth generation. Moreover, existing simulated
benchmarks in this field are often too simple or too specialized to
sufficiently validate the observed image analysis problems. We present a new
semi-synthetic approach to generate realistic 3D+t benchmarks that combines
challenging cellular movement dynamics of real embryos with simulated
fluorescent nuclei and artificial image distortions including various
parametrizable options like cell numbers, acquisition deficiencies or multiview
simulations. We successfully applied the approach to simulate the development
of a zebrafish embryo with thousands of cells over 14 hours of its early
existence.


title: Singular continuous spectrum for singular potential

abstract:
  We prove that Schr\"odinger operators with meromorphic potentials
$(H_{\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+
\frac{g(\theta+n\alpha)}{f(\theta+n\alpha)} u_n$ have purely singular
continuous spectrum on the set $\{E: L(E)<\delta{(\alpha,\theta)}\}$, where
$\delta$ is an explicit function, and $L$ is the Lyapunov exponent. This
extends results of Jitomirskaya and Liu for the Maryland model and of Avila,
You and Zhou for the almost Mathieu operator, to the general family of
meromorphic potentials.


title:
Search for Screened Interactions Associated with Dark Energy Below the
  100 $\mathrm{\mu m}$ Length Scale

abstract:
  We present the results of a search for unknown interactions that couple to
mass between an optically levitated microsphere and a gold-coated silicon
cantilever. The scale and geometry of the apparatus enables a search for new
forces that appear at distances below 100 $\mu$m and which would have evaded
previous searches due to screening mechanisms. The data are consistent with
electrostatic backgrounds and place upper limits on the strength of new
interactions at $<0.1$ fN in the geometry tested. For the specific example of a
chameleon interaction with an inverse power law potential, these results
exclude matter couplings $\beta > 5.6 \times 10^4$ in the region of parameter
space where the self-coupling $\Lambda \gtrsim 5$ meV and the microspheres are
not fully screened.


title: The Impact of a Supernova Remnant on Fast Radio Bursts

abstract:
  Fast radio bursts (FRBs) are millisecond bursts of radio radiation whose
progenitors so far remain mysterious. Nevertheless, the timescales and
energetics of the events have lead to many theories associating FRBs with young
neutron stars. Motivated by this, I explore the interaction of FRBs with young
supernova remnants (SNRs), and I discuss the potential observational
consequences and constraints of such a scenario. As the SN ejecta plows into
the interstellar medium (ISM), a reverse shock is generated that passes back
through the material and ionizes it. This leads to a dispersion measure (DM)
associated with the SNR as well as a time derivative for DM. Times when DM is
high are generally overshadowed by free-free absorption, which, depending on
the mass of the ejecta and the density of the ISM, may be probed at frequencies
of $400\,{\rm MHz}$ to $1.4\,{\rm GHz}$ on timescales of $\sim100-500\,{\rm
yrs}$ after the SN. Magnetic fields generated at the reverse shock may be high
enough to explain Faraday rotation that has been measured for one FRB. If FRBs
are powered by the spin energy of a young NS (rather than magnetic energy), the
NS must have a magnetic field $\lesssim10^{11}-10^{12}\,{\rm G}$ to ensure that
it does not spin down too quickly while the SNR is still optically thick at
radio frequencies. In the future, once there are distance measurements to FRBs
and their energetics are better understood, the spin of the NS can also be
constrained.


title:
Comments on Second caloric virial coefficients for real gases and
  combined spherical symmetric potential for simple molecular interactions

abstract:
  It is shown that the interaction potentials for argon, krypton, xenon, carbon
dioxide, ammonia, water, n-pentane, n-octane, 1-propanol, suggested in [1]
cannot describe experimental second density virial coefficient data within
their uncertainty over a wide temperature range.


title: Polonyi Inflation

abstract:
  Spontaneously broken supersymmetry (SUSY) and a vanishingly small
cosmological constant imply that R symmetry must be spontaneously broken at low
energies. Based on this observation, we suppose that, in the sector responsible
for low-energy R symmetry breaking, a discrete R symmetry remains preserved at
high energies and only becomes dynamically broken at relatively late times in
the cosmological evolution, i.e., after the dynamical breaking of SUSY. Prior
to R symmetry breaking, the Universe is then bound to be in a quasi-de Sitter
phase---which offers a dynamical explanation for the occurrence of cosmic
inflation. This scenario yields a new perspective on the interplay between SUSY
breaking and inflation, which neatly fits into the paradigm of high-scale SUSY:
inflation is driven by the SUSY-breaking vacuum energy density, while the
chiral field responsible for SUSY breaking, the Polonyi field, serves as the
inflaton. Because R symmetry is broken only after inflation, slow-roll
inflation is not spoiled by otherwise dangerous gravitational corrections in
supergravity. We illustrate our idea by means of a concrete example, in which
both SUSY and R symmetry are broken by strong gauge dynamics and in which
late-time R symmetry breaking is triggered by a small inflaton field value. In
this model, the scales of inflation and SUSY breaking are unified; the
inflationary predictions are similar to those of F-term hybrid inflation in
supergravity; reheating proceeds via gravitino decay at temperatures consistent
with thermal leptogenesis; and the sparticle mass spectrum follows from pure
gravity mediation. Dark matter consists of thermally produced winos with a mass
in the TeV range.


title: Reverse Mathematics of Matroids

abstract:
  Matroids generalize the familiar notion of linear dependence from linear
algebra. Following a brief discussion of founding work in computability and
matroids, we use the techniques of reverse mathematics to determine the logical
strength of some basis theorems for matroids and enumerated matroids. Next,
using Weihrauch reducibility, we relate the basis results to combinatorial
choice principles and statements about vector spaces. Finally, we formalize
some of the Weihrauch reductions to extract related reverse mathematics
results. In particular, we show that the existence of bases for vector spaces
of bounded dimension is equivalent to the induction scheme for $\Sigma^0_2$
formulas.


title: Optimized Treatment Schedules for Chronic Myeloid Leukemia

abstract:
  Over the past decade, several targeted therapies (e.g. imatinib, dasatinib,
nilotinib) have been developed to treat Chronic Myeloid Leukemia (CML). Despite
an initial response to therapy, drug resistance remains a problem for some CML
patients. Recent studies have shown that resistance mutations that preexist
treatment can be detected in a substan- tial number of patients, and that this
may be associated with eventual treatment failure. One proposed method to
extend treatment efficacy is to use a combination of multiple targeted
therapies. However, the design of such combination therapies (timing, sequence,
etc.) remains an open challenge. In this work we mathematically model the
dynamics of CML response to combination therapy and analyze the impact of
combination treatment schedules on treatment efficacy in patients with
preexisting resistance. We then propose an optimization problem to find the
best schedule of multiple therapies based on the evolution of CML according to
our ordinary differential equation model. This resulting optimiza- tion problem
is nontrivial due to the presence of ordinary different equation constraints
and integer variables. Our model also incorporates realistic drug toxicity
constraints by tracking the dynamics of patient neutrophil counts in response
to therapy. Using realis- tic parameter estimates, we determine optimal
combination strategies that maximize time until treatment failure.


title:
Enhanced micropolar model for wave propagation in ordered granular
  materials

abstract:
  The vibrational properties of a face-centered cubic granular crystal of
monodisperse particles are predicted using a discrete model as well as two
micropolar models, first the classical Cosserat and second an enhanced
Cosserat-type model, that properly takes into account all degrees of freedom at
the contacts between the particles. The continuum models are derived from the
discrete model via a micro-macro transition of the discrete relative
displacements and particle rotations to the respective continuum field
variables. Next, only the long wavelength approximations of the models are
compared and, considering the discrete model as reference, the Cosserat model
shows inconsistent predictions of the bulk wave dispersion relations. This can
be explained by an insufficient modeling of sliding mode of particle
interactions in the Cosserat model. An enhanced micropolar model is proposed
including only one new elastic tensor from the more complete second order
gradient micropolar theory. This enhanced micropolar model then involves the
minimum number of elastic constants to consistently predict the dispersion
relations in the long wavelength limit.


title: The tangent space of the punctual Hilbert scheme

abstract:
  The purpose of this paper is to study the Zariski tangent space of the
punctual Hilbert scheme parametrizing subschemes of a smooth surface which are
supported at a single point. We give a lower bound on the dimension of the
tangent space in general and show the bound is sharp for subschemes of the
affine plane cut out by monomials. Furthermore for monomial subschemes we give
an explicit combinatorial formula for the dimension of the tangent space.


title: On the group of units and the Picard group of a product

abstract:
  Let S be a reduced scheme and let f: X--> S and g: Y-->S be faithfully flat
morphisms locally of finite presentation with geometrically connected and
geometrically reduced maximal fibers. We discuss the canonical maps
G_{m,S}(X)+G_{m,S}(Y)-->G_{m,S}(X x_{S} Y) and Pic X+Pic Y-->Pic(X x_{S} Y)
induced by f and g (both sums are direct). Under certain additional conditions
on X,Y,S, f and g, we describe the kernel and cokernel of the preceding maps,
thereby extending known results when S is the spectrum of a field.


title: Long-Term Stability of Planets in the $\alpha$ Centauri System

abstract:
  We evaluate the extent of the regions within the $\alpha$ Centauri AB star
system where small planets are able to orbit for billion-year timescales, and
we calculate the positions on the sky plane where planets on stable orbits
about either stellar component may appear. We confirm the qualitative results
of Wiegert and Holman (AJ 113, 1445, 1997) regarding the approximate size of
the regions of stable orbits, which are larger for retrograde orbits relative
to the binary than for prograde orbits. Additionally, we find that mean motion
resonances with the binary orbit leave an imprint on the limits of orbital
stability, and the effects of the Lidov-Kozai mechanism are also readily
apparent.


title:
New realizations of modular forms in Calabi-Yau threefolds arising from
  $\phi^4$ theory

abstract:
  It has been found experimentally by Brown and Schnetz that the number of
points over ${\mathbb F}_p$ of a graph hypersurface is often related to the
coefficients of a modular form. In this paper I prove this relation for one
example of a modular form of weight $4$ and two of weight $3$, refine the
statement and suggest a method of proving it for four more of weight $4$, and
use the one proved example to construct two new rigid Calabi-Yau threefolds
that realize Hecke eigenforms of weight $4$ (one provably and one
conjecturally).


title: Refinement of the Bousso-Engelhardt Area Law

abstract:
  Past holographic screens are codimension-one surfaces of indefinite signature
that are foliated by marginally anti-trapped surfaces called leaves. Future
holographic screens are defined similarly except with marginally trapped
leaves. Bousso and Engelhardt recently showed that the leaves of past and
future holographic screens have monotonic area. We prove a stronger area law
that shows that subregions of leaves also have monotonic area. For every past
and future holographic screen, there exists a family of leaf-orthogonal curves
called the fibration of the screen. Any region in a leaf can be translated
along the fibration to a leaf of larger area. Our result states that the area
of the subregion grows as it is translated.


title:
On some Algebraic Properties for q-Meixner Multiple Orthogonal
  Polynomials of the First Kind

abstract:
  We study a new family of q-Meixner multiple orthogonal polynomials of the
first kind. The discrete orthogonality conditions are considered over a
non-uniform lattice with respect to different q-analogues of Pascal
distributions. We address some algebraic properties, namely raising and
lowering operators as well as Rodrigues-type. Based on the explicit expressions
for the raising and lowering operator a high-order linear q-difference equation
with polynomial coefficients for the q-Meixner multiple orthogonal polynomials
of the first kind is obtained. Finally, we obtain the nearest neighbor
recurrence relation based on a purely algebraic approach.


title:
Certified Descent Algorithm for shape optimization driven by
  fully-computable a posteriori error estimators

abstract:
  In this paper we introduce a novel certified shape optimization strategy -
named Certified Descent Algorithm (CDA) - to account for the numerical error
introduced by the Finite Element approximation of the shape gradient. We
present a goal-oriented procedure to derive a certified upper bound of the
error in the shape gradient and we construct a fully-computable, constant-free
a posteriori error estimator inspired by the complementary energy principle.
The resulting CDA is able to identify a genuine descent direction at each
iteration and features a reliable stopping criterion. After validating the
error estimator, some numerical simulations of the resulting certified shape
optimization strategy are presented for the well-known inverse identification
problem of Electrical Impedance Tomography.


title:
Correlation networks from flows. The case of forced and time-dependent
  advection-diffusion dynamics

abstract:
  Complex network theory provides an elegant and powerful framework to
statistically investigate different types of systems such as society, brain or
the structure of local and long-range dynamical interrelationships in the
climate system. Network links in climate networks typically imply information,
mass or energy exchange. However, the specific connection between oceanic or
atmospheric flows and the climate network's structure is still unclear. We
propose a theoretical approach for verifying relations between the correlation
matrix and the climate network measures, generalizing previous studies and
overcoming the restriction to stationary flows. Our methods are developed for
correlations of a scalar quantity (temperature, for example) which satisfies an
advection-diffusion dynamics in the presence of forcing and dissipation. Our
approach reveals that correlation networks are not sensitive to steady sources
and sinks and the profound impact of the signal decay rate on the network
topology. We illustrate our results with calculations of degree and clustering
for a meandering flow resembling a geophysical ocean jet.


title: Berry phase of light Bragg-reflected by chiral liquid crystal media

abstract:
  Berry phase is revealed for circularly polarized light when it is
Bragg-reflected by a chiral liquid crystal medium of the same handedness. By
using a chiral nematic layer we demonstrate that if the input plane of the
layer is rotated with respect to a fixed reference frame, then, a geometric
phase effect occurs for the circularly polarized light reflected by the
periodic helical structure of the medium. Theory and numerical simulations are
supported by an experimental observation, disclosing novel applications in the
field of optical manipulation and fundamental optical phenomena.


title:
Near-field radiative heat transfer between arbitrarily-shaped objects
  and a surface

abstract:
  A fluctuational electrodynamics-based formalism for calculating near-field
radiative heat transfer between objects of arbitrary size and shape and an
infinite surface is presented. The surface interactions are treated
analytically via Sommerfeld's theory of electric dipole radiation above an
infinite plane. The volume integral equation for the electric field is
discretized using the thermal discrete dipole approximation (T-DDA). The
framework is verified against exact results in the sphere-surface
configuration, and is applied to analyze near-field radiative heat transfer
between a complex-shaped probe and an infinite plane both made of silica. It is
found that when the probe tip size is approximately equal to or smaller than
the gap d separating the probe and the surface, coupled localized surface
phonon (LSPh)-surface phonon-polariton (SPhP) mediated heat transfer occurs. In
this regime, the net spectral heat rate exhibits four resonant modes due to
LSPhs along the minor axis of the probe while the net total heat rate in the
near field follows a d -0.3 power law. Conversely, when the probe tip size is
much larger than the separation gap d, heat transfer is mediated by SPhPs
resulting in two resonant modes in the net spectral heat rate corresponding to
those of a single emitting silica surface while the net total heat rate
approaches a d -2 power law. It is also demonstrated that a complex-shaped
probe can be approximated by a prolate spheroidal electric dipole when the
thermal wavelength is larger than the major axis of the spheroidal dipole and
when the separation gap d is much larger than the radius of curvature of the
dipole tip facing the surface.


title:
Unphysical features in the application of the Boltzmann collision
  operator in the time dependent modelling of quantum transport

abstract:
  In this work, the use of the Boltzmann collision operator for dissipative
quantum transport is analyzed. Its mathematical role on the description of the
time-evolution of the density matrix during a collision can be understood as
processes of adding and subtracting states. We show that unphysical results can
be present in quantum simulations when the old states (that built the density
matrix associated to an open system before the collision) are different from
the additional states generated by the Boltzmann collision operator. As a
consequence of the Fermi Golden rule, the new generated sates are usually
eigenstates of the momentum or kinetic energy. Then, the different
time-evolutions of old and new states involved in a collision process can
originate negative values of the charge density, even longer after the
collision. This unphysical feature disappears when the Boltzmann collision
operator generates states that were already present in the density matrix of
the quantum system before the collision. Following these ideas, in this paper,
we introduce an algorithm that models phonon-electron interactions through the
Boltzmann collision operator without negative values of the charge density. The
model only requires the exact knowledge, at all times, of the states that build
the density matrix of the open system.


title: Some medical applications of example-based super-resolution

abstract:
  Example-based super-resolution (EBSR) reconstructs a high-resolution image
from a low-resolution image, given a training set of high-resolution images. In
this note I propose some applications of EBSR to medical imaging. A particular
interesting application, which I call "x-ray voxelization", approximates the
result of a CT scan from an x-ray image.


title: A remark on projections of the rotated cube to complex lines

abstract:
  Motivated by relations with a symplectic invariant known as the "cylindrical
symplectic capacity", in this note we study the expectation of the area of a
minimal projection to a complex line for a randomly rotated cube.


title: Learning to Incentivize: Eliciting Effort via Output Agreement

abstract:
  In crowdsourcing when there is a lack of verification for contributed
answers, output agreement mechanisms are often used to incentivize participants
to provide truthful answers when the correct answer is hold by the majority. In
this paper, we focus on using output agreement mechanisms to elicit effort, in
addition to eliciting truthful answers, from a population of workers. We
consider a setting where workers have heterogeneous cost of effort exertion and
examine the data requester's problem of deciding the reward level in output
agreement for optimal elicitation. In particular, when the requester knows the
cost distribution, we derive the optimal reward level for output agreement
mechanisms. This is achieved by first characterizing Bayesian Nash equilibria
of output agreement mechanisms for a given reward level. When the requester
does not know the cost distribution, we develop sequential mechanisms that
combine learning the cost distribution with incentivizing effort exertion to
approximately determine the optimal reward level.


title: Metastability of Bose and Fermi gases on the upper branch

abstract:
  We study three dimensional Bose and Fermi gases in the upper branch, a phase
defined by the absence of bound states in the repulsive interaction regime,
within an approximation that considers only two-body interactions. Employing a
formalism based on the S-matrix, we derive useful analytic expressions that
hold on the upper branch in the weak coupling limit. We determine upper branch
phase diagrams for both bosons and fermions with techniques valid for arbitrary
positive scattering length.


title: Asymptotic Analysis of the Ginzburg-Landau Functional on Point Clouds

abstract:
  The Ginzburg-Landau functional is a phase transition model which is suitable
for clustering or classification type problems. We study the asymptotics of a
sequence of Ginzburg-Landau functionals with anisotropic interaction potentials
on point clouds $\Psi_n$ where $n$ denotes the number data points. In
particular we show the limiting problem, in the sense of $\Gamma$-convergence,
is related to the total variation norm restricted to functions taking binary
values; which can be understood as a surface energy. We generalize the result
known for isotropic interaction potentials to the anisotropic case and add a
result concerning the rate of convergence.


title:
Regularizing Solutions to the MEG Inverse Problem Using Space-Time
  Separable Covariance Functions

abstract:
  In magnetoencephalography (MEG) the conventional approach to source
reconstruction is to solve the underdetermined inverse problem independently
over time and space. Here we present how the conventional approach can be
extended by regularizing the solution in space and time by a Gaussian process
(Gaussian random field) model. Assuming a separable covariance function in
space and time, the computational complexity of the proposed model becomes
(without any further assumptions or restrictions) $\mathcal{O}(t^3 + n^3 +
m^2n)$, where $t$ is the number of time steps, $m$ is the number of sources,
and $n$ is the number of sensors. We apply the method to both simulated and
empirical data, and demonstrate the efficiency and generality of our Bayesian
source reconstruction approach which subsumes various classical approaches in
the literature.


title:
Gravitational waves from primordial black holes collisions in binary
  systems

abstract:
  It was shown by (Nakamura et al. 1997), (Ioka et al. 1998), and (Sasaki et
al. 2016) that primordial black holes (PBHs) binaries can form effectively at
the cosmological stage of radiation dominance, and the merge of the PBHs in
pairs can explain the gravitational wave burst GW150914. In this paper, the
model is re-examined by considering the effect of inflationary dark matter
density perturbations which produce additional tidal forces. As a result, the
merge rate of PBHs binaries and the corresponding rate of the gravitational
bursts are suppressed by the factor $\sim1.5-2$ in comparison with previous
calculations. This rate matches the LIGO data if the PBHs constitute the
$f\sim5\times10^{-4}-5\times10^{-3}$ fraction of dark matter.


title: On plane polynomial automorphisms commuting with simple derivations

abstract:
  We consider the subgroup Aut(D) consisting of automorphisms of K[x,y]
commuting with a derivation D, where K is an algebraically closed field of
characteristic 0. We prove that if D is simple (i.e. D does not stabilize
non-trivial ideals), then Aut(D)=1, in the case where D is of Shamsuddin type
this result was proven by R.Baltazar in 2014 (arXiv:1412.8373). Moreover, we
describe Aut(D) for Shamsuddin type derivations and deduce that Aut(D)=1 for a
general such derivation implies D is simple.


title:
The index of symmetry of three-dimensional Lie groups with a
  left-invariant metric

abstract:
  We determine the index of symmetry of 3-dimensional unimodular Lie groups
with a left-invariant metric. In particular, we prove that every 3-dimensional
unimodular Lie group admits a left-invariant metric with positive index of
symmetry. We also study the geometry of the quotients by the so-called
foliation of symmetry, and we explain in what cases the group fibers over a
2-dimensional space of constant curvature.


title:
Why Mutant Allele Frequencies in Oncogenes Peak Around 0.40 and Rapidly
  Decrease?

abstract:
  The mutant allele frequencies in oncogenes peak around 0.40 and rapidly
decrease. In this article, we explain why this is the case. Invoking a key
result from mathematical analysis in our model, namely, the inverse function
theorem, we estimate the selection pressures of the mutations as a function of
germline allele frequencies. Under complete dominance of oncogenic mutations,
this selection function is expected to be linearly correlated with the
distribution of the mutant alleles. We demonstrate that this is the case by
investigating the allele frequencies of mutations in oncogenes across various
cancer types, validating our model for mean effective selection. Consistent
with the population genetics model of fitness, the selection function fits a
gamma distribution curve that accurately describes the trend of the mutant
allele frequencies. While existing equations for selection explain evolution at
low allele frequencies, our equations are general formulas for natural
selection under complete dominance operating at all frequencies. We show that
selection exhibits linear behavior at all times, favoring dominant alleles with
respect to the change in recessive allele frequency. Also, these equations
show, selection behaves like power-law against the recessive alleles at low
dominant allele frequency.


title:
Universal asymptotic clone size distribution for general population
  growth

abstract:
  Deterministically growing (wild-type) populations which seed stochastically
developing mutant clones have found an expanding number of applications from
microbial populations to cancer. The special case of exponential wild-type
population growth, usually termed the Luria-Delbr\"uck or Lea-Coulson model, is
often assumed but seldom realistic. In this article we generalise this model to
different types of wild-type population growth, with mutants evolving as a
birth-death branching process. Our focus is on the size distribution of clones
- that is the number of progeny of a founder mutant - which can be mapped to
the total number of mutants. Exact expressions are derived for exponential,
power-law and logistic population growth. Additionally for a large class of
population growth we prove that the long time limit of the clone size
distribution has a general two-parameter form, whose tail decays as a
power-law. Considering metastases in cancer as the mutant clones, upon
analysing a data-set of their size distribution, we indeed find that a
power-law tail is more likely than an exponential one.


title: Tunable Focusing by a Flexible Metasurface

abstract:
  An efficient reflective elastic metasurface with tunable focusing point is
proposed. The metasurface is based on electric resonators embedded in a
stretchable elastic substrate. The focal length is controlled by mean of the
stretching applied applied to the sample. The results predicted by theory and
numerical simulations are experimentally verified. Our proposal shows that
smart engineering elastic metamaterials are an effective platform for new
functional devices based on metamaterials.


title: Angular anisotropy of time delay in XUV/IR photoionization of H$_2^+$

abstract:
  We develop a novel technique for modeling of atomic and molecular ionization
in superposition of XUV and IR fields with characteristics typical for
attosecond streaking and RABBITT experiments. The method is based on solving
the time-dependent Schr\"odinger equation in the coordinate frame expanding
along with the photoelectron wave packet. The efficiency of the method is
demonstrated by calculating angular anisotropy of photoemission time delay of
the H$_2^+$ ion in a field configuration of recent RABBITT experiments.


title:
Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor
  Analysis

abstract:
  Factor analysis aims to determine latent factors, or traits, which summarize
a given data set. Inter-battery factor analysis extends this notion to multiple
views of the data. In this paper we show how a nonlinear, nonparametric version
of these models can be recovered through the Gaussian process latent variable
model. This gives us a flexible formalism for multi-view learning where the
latent variables can be used both for exploratory purposes and for learning
representations that enable efficient inference for ambiguous estimation tasks.
Learning is performed in a Bayesian manner through the formulation of a
variational compression scheme which gives a rigorous lower bound on the log
likelihood. Our Bayesian framework provides strong regularization during
training, allowing the structure of the latent space to be determined
efficiently and automatically. We demonstrate this by producing the first (to
our knowledge) published results of learning from dozens of views, even when
data is scarce. We further show experimental results on several different types
of multi-view data sets and for different kinds of tasks, including exploratory
data analysis, generation, ambiguity modelling through latent priors and
classification.


title: Experimental Status of the CKM Matrix

abstract:
  The CKM matrix, V, relates the quark mass and flavor bases. In the standard
model, V is unitary 3X3, and specified by four arbitrary parameters, including
a phase allowing for $CP$ violation. We review the experimental determination
of V, including the four parameters in the standard model context. This is an
active field; the precision of experimental measurements and theoretical inputs
continues to improve. The consistency of the determination with the standard
model unitarity is investigated. While there remain some issues the overall
agreement with standard model unitarity is good.


title:
An Integrated Circuit for Radio Astronomy Correlators Supporting Large
  Arrays of Antennas

abstract:
  Radio telescopes that employ arrays of many antennas are in operation, and
ever larger ones are being designed and proposed. Signals from the antennas are
combined by cross-correlation. For $N$ antennas, the cost and power consumption
of cross-correlation are proportional to $N^2$ and dominate at sufficiently
large $N$. Here we report the design of an integrated circuit (IC) that
performs digital cross-correlations for arbitrarily many antennas in a
power-efficient way. It uses an intrinsically low-power architecture in which
the movement of data between devices is minimized. In our design, the
correlations are performed in an array of 4096 complex multiply-accumulate
(CMAC) units. This is sufficient to perform all correlations in parallel for 64
signals ($N$=32 antennas with 2 opposite-polarization signals per antenna).
When $N$ is larger, the input data are buffered in an on-chip memory and the
CMACs are re-used as many times as needed to compute all correlations. The
design has been synthesized and simulated so as to obtain accurate estimates of
the IC's size and power consumption. It is intended for fabrication in a 32 nm
silicon-on-insulator process, where it will require less than 12 mm$^2$ of
silicon area and achieve an energy efficiency of 1.76 to 3.3 pJ per CMAC
operation, depending on the number of antennas. Operation has been analyzed in
detail up to $N=4096$. The system-level energy efficiency, including
board-level I/O, power supplies, and controls, is expected to be 5 to 7 pJ per
CMAC operation.


title: Identifying global optimality for dictionary learning

abstract:
  Learning new representations of input observations in machine learning is
often tackled using a factorization of the data. For many such problems,
including sparse coding and matrix completion, learning these factorizations
can be difficult, in terms of efficiency and to guarantee that the solution is
a global minimum. Recently, a general class of objectives have been
introduced-which we term induced dictionary learning models (DLMs)-that have an
induced convex form that enables global optimization. Though attractive
theoretically, this induced form is impractical, particularly for large or
growing datasets. In this work, we investigate the use of practical alternating
minimization algorithms for induced DLMs, that ensure convergence to global
optima. We characterize the stationary points of these models, and, using these
insights, highlight practical choices for the objectives. We then provide
theoretical and empirical evidence that alternating minimization, from a random
initialization, converges to global minima for a large subclass of induced
DLMs. In particular, we take advantage of the existence of the (potentially
unknown) convex induced form, to identify when stationary points are global
minima for the dictionary learning objective. We then provide an empirical
investigation into practical optimization choices for using alternating
minimization for induced DLMs, for both batch and stochastic gradient descent.


title:
Observation of anti-levitation of Landau levels in vanishing magnetic
  fields

abstract:
  We report an anti-levitation behavior of Landau levels in vanishing magnetic
fields in a high quality hetero-junction insulated-gated field-effect
transistor. We found, in the Landau fan diagram of electron density versus
magnetic field, the positions of the magneto-resistance minima at Landau level
fillings \nu=4, 5, 6 move below the 'traditional' Landau level line to lower
electron densities. Moreover, the even and odd filling factors show
quantitatively different behaviors in anti-levitation, suggesting that the
exchange interactions may be important.


title: Improved Uncertainty Relation in the Presence of Quantum Memory

abstract:
  In Coles-Piani's recent remarkable version of the entropic uncertainty
principle, the entropic sum is controlled by the first and second maximum
overlaps between the two projective measurements. We generalize the entropic
uncertainty relation in the presence of quantum memory and find the exact
dependence on all $d$ largest overlaps between two measurements on any
$d$-dimensional Hilbert space. The corresponding entropic uncertainty principle
in the absence of quantum memory is also derived. Our bounds are strictly
tighter than previous entropic bounds in the presence of quantum memory, which
have potential applications to quantum cryptography with entanglement witnesses
and quantum key distributions.


title: Affine planes, ternary rings, and examples of non-Desarguesian planes

abstract:
  The paper is devoted to a detailed self-contained exposition of a part of the
theory of affine planes leading to a construction of affine (or, equivalently,
projective) planes not satisfying the Desarques axiom. It is intended to
complement the introductory expositions of the theory of affine and projective
planes. A novelty of our exposition is a new notation for the ternary operation
in a ternary ring, much more suggestive than the standard one.


title:
Excitation of the classical electromagnetic field in a cavity containing
  a thin slab with a time-dependent conductivity

abstract:
  An exact infinite set of coupled ordinary differential equations, describing
the evolution of the modes of the classical electromagnetic field inside an
ideal cavity, containing a thin slab with the time-dependent conductivity
$\sigma(t)$ and dielectric permittivity $\varepsilon(t)$, is derived for the
dispersion-less media. This problem is analyzed in connection with the attempts
to simulate the so called Dynamical Casimir Effect in three-dimensional
electromagnetic cavities, containing a thin semiconductor slab, periodically
illuminated by strong laser pulses. Therefore it is assumed that functions
$\sigma(t)$ and $\delta\varepsilon(t)=\varepsilon(t)-\varepsilon(0)$ are
different from zero during short time intervals (pulses) only. The main goal is
to find the conditions, under which the initial nonzero classical field could
be amplified after a single pulse (or a series of pulses). Approximate
solutions to the dynamical equations are obtained in the cases of "small" and
"big" maximal values of the functions $\sigma(t)$ and $\delta\varepsilon(t)$.
  It is shown, that the single-mode approximation, used in the previous
studies, can be justified in the case of "small" perturbations. But the
initially excited field mode cannot be amplified in this case, if the laser
pulses generate free carriers inside the slab. The amplification could be
possible, in principle, for extremely high maximal values of conductivity and
the concentration of free carries (the model of "almost ideal conductor"),
created inside the slab, under the crucial condition, that the function
$\delta\varepsilon(t)$ is {\em negative}. This result follows from a simple
approximate analytical solution, and it is confirmed by exact numerical
calculations. However, the evaluations show, that the necessary energy of laser
pulses must be, probably, unrealistically high.


title: Algebra of linear recurrence relations in arbitrary characteristic

abstract:
  The goal of this paper is to present an algebraic approach to the basic
results of the theory of linear recurrence relations. This approach is based on
the ideas from the theory of representations of one endomorphisms (a special
case of which is well known as the theory of the Jordan normal form of
matrices). The notion of the divided derivatives, an analogue of the divided
powers, turned out to be crucial for proving the results in a natural way and
in their natural generality. The final form of our methods was influenced by
the the umbral calculus of G.-C. Rota.


title:
The Role of the Kozai-Lidov Mechanism in Black Hole Binary Mergers in
  Galactic Centers

abstract:
  In order to understand the rate of merger of stellar-mass black hole binaries
(BHBs) by gravitational wave (GW) emission it is important to determine the
major pathways to merger. We use numerical simulations to explore the evolution
of BHBs inside the radius of influence of supermassive black holes (SMBHs) in
galactic centers. In this region the evolution of binaries is dominated by
perturbations from the central SMBH. In particular, as first pointed out by
Antonini and Perets, the Kozai-Lidov (KL) mechanism trades relative inclination
of the BHB to the SMBH for eccentricity of the BHB, and for some orientations
can bring the BHB to an eccentricity near unity. At very high eccentricities,
GW emission from the BHB can become efficient, causing the members of the BHB
to coalesce. We use a novel combination of two N-body codes to follow this
evolution. We are forced to simulate small systems to follow the behavior
accurately. We have completed 400 simulations that range from $\sim$ 300 stars
around a $10^{3}$ M$_{\odot}$ black hole to $\sim$ 4500 stars around a $10^{4}$
M$_{\odot}$ black hole. These simulations are the first to follow the internal
orbit of a binary near a SMBH while also following the changes to its external
orbit self-consistently. We find that this mechanism could produce mergers at a
maximum rate per volume of $\sim 100$ Gpc$^{-3}$ yr$^{-1}$ or considerably less
if the inclination oscillations of the binary remain constant as the BHB
inclination to the SMBH changes, or if the binary black hole fraction is small.


title:
Fragility of non-local edge mode transport in the quantum spin Hall
  state

abstract:
  Non-local currents and voltages are better able at withstanding the
deleterious effects of dephasing than local currents and voltages in nanoscale
systems. This hypothesis is known to be true in quantum Hall set-ups. We test
this hypothesis in a four terminal quantum spin Hall set up wherein we compare
the local resistance measurement with the non-local one. In addition to
inelastic scattering induced dephasing we also test resilience of the
resistance measurements in the aforesaid set-ups to disorder and spin-flip
scattering. We find the axiom that non-local resistance is less affected by the
detrimental effects of disorder and dephasing to be in general untrue for
quantum spin Hall case. This has important consequences since it has been
widely communicated that non-local transport through edge channels in
topological insulators will have potential applications in low power
information processing.


title:
Does the Peres experiment using photons test for hyper-complex
  (quaternionic) quantum theories?

abstract:
  Assuming the standard axioms for quaternionic quantum theory and a spatially
localized scattering interaction, the $S$-matrix in quaternionic quantum theory
is complex valued, not quaternionic. Using the standard connections between the
$S$-matrix, the forward scattering amplitude for electromagnetic wave
scattering, and the index of refraction, we show that the index of refraction
is necessarily complex, not quaternionic. This implies that the recent optical
experiment of Procopio et al. based on the Peres proposal does not test for
hyper-complex or quaternionic quantum effects arising within the standard
Hilbert space framework. Such a test requires looking at near zone fields, not
radiation zone fields.


title:
A Hybrid Performance Analysis Technique for Distributed Real-Time
  Embedded Systems

abstract:
  It remains a challenging problem to tightly estimate the worst case response
time of an application in a distributed embedded system, especially when there
are dependencies between tasks. We discovered that the state-of-the art
techniques considering task dependencies either fail to obtain a conservative
bound or produce a loose upper bound. We propose a novel conservative
performance analysis, called hybrid performance analysis, combining the
response time analysis technique and the scheduling time bound analysis
technique to compute a tighter bound fast. Through extensive experiments with
randomly generated graphs, superior performance of our proposed approach
compared with previous methods is confirmed.


title: Bianalytic Maps Between Free Spectrahedra

abstract:
  Linear matrix inequalities (LMIs) $I_d + \sum_{j=1}^g A_jx_j + \sum_{j=1}^g
A_j^*x_j^*\succeq0$ play a role in many areas of applications and the set of
solutions to one is called a spectrahedron. LMIs in (dimension--free) matrix
variables model most problems in linear systems engineering, and their solution
sets D_A are called free spectrahedra. These are exactly the free semialgebraic
convex sets.
  This paper studies free analytic maps between free spectrahedra and, under
certain irreducibility assumptions, classifies all those that are bianalytic.
The foundation of such maps turns out to be a very small class of birational
maps we call convexotonic. The convexotonic maps in g variables sit in
correspondence with g-dimensional algebras. If two bounded free spectrahedra
D_A and D_B meeting our irreducibility assumptions are free bianalytic with map
denoted p, then p must (after possibly an affine linear transform) extend to a
convexotonic map corresponding to a g-dimensional algebra spanned by
(U-I)A_1,...,(U-I)A_g for some unitary U. Furthermore, B and UA are unitarily
equivalent.
  The article also establishes a Positivstellensatz for free analytic functions
whose real part is positive semidefinite on a free spectrahedron and proves a
representation for a free analytic map from D_A to D_B (not necessarily
bianalytic). Another result shows that a function analytic on any radial
expansion of a free spectrahedron is approximable by polynomials uniformly on
the spectrahedron. These theorems are needed for classifying free bianalytic
maps.


title:
Fully Convolutional Recurrent Network for Handwritten Chinese Text
  Recognition

abstract:
  This paper proposes an end-to-end framework, namely fully convolutional
recurrent network (FCRN) for handwritten Chinese text recognition (HCTR).
Unlike traditional methods that rely heavily on segmentation, our FCRN is
trained with online text data directly and learns to associate the pen-tip
trajectory with a sequence of characters. FCRN consists of four parts: a
path-signature layer to extract signature features from the input pen-tip
trajectory, a fully convolutional network to learn informative representation,
a sequence modeling layer to make per-frame predictions on the input sequence
and a transcription layer to translate the predictions into a label sequence.
The FCRN is end-to-end trainable in contrast to conventional methods whose
components are separately trained and tuned. We also present a refined beam
search method that efficiently integrates the language model to decode the FCRN
and significantly improve the recognition results.
  We evaluate the performance of the proposed method on the test sets from the
databases CASIA-OLHWDB and ICDAR 2013 Chinese handwriting recognition
competition, and both achieve state-of-the-art performance with correct rates
of 96.40% and 95.00%, respectively.


title:
Revealing a detailed mass distribution of a high-density core
  MC27/L1521F in Taurus with ALMA

abstract:
  We present the results of ALMA observations of dust continuum emission and
molecular rotational lines toward a dense core MC27 (aka L1521F) in Taurus,
which is considered to be at a very early stage of star formation. The detailed
column density distribution on size scales from a few tens AU to ~10,000 AU
scale are revealed by combining the ALMA (12 m array + 7 m array) data with the
published/unpublished single-dish data. The high angular resolution
observations at 0.87 mm with a synthesized beam size of ~0."74 x 0."32 reveal
that a protostellar source, MMS-1, is not spatially resolved and lacks
associated gas emission, while a starless high-density core, MMS-2, has
substructures both in dust and molecular emission. The averaged radial column
density distribution of the inner part of MC27/L1521F (r $\lesssim$ 3000 AU) is
N(H2) ~r$^{-0.4}$, clearly flatter than that of the outer part, ~r$^{-1.0}$.
The complex velocity/spatial structure obtained with previous ALMA observations
is located inside the inner flatter region, which may reflect the dynamical
status of the dense core.


title: Optimal Quantum Thermometry by Dephasing

abstract:
  Decoherence often happens in the quantum world. We try to utilize quantum
dephasing to build an optimal thermometry. By calculating the
Cram$\acute{e}$r-Rao bound, we prove that the Ramsey measurement is the optimal
way to measure the temperature for uncorrelated particles. Using the optimal
measurement, the metrological equivalence of product and maximally entangled
states of initial quantum probes that always holds. However, using Ramsey
measurement, the metrological equivalence only holds in special situation.
Contrary to frequency estimation, the quantum limit can be surpassed under the
case $\nu<1$. For the general Zeno regime($\nu=2$), uncorrelated product states
are the optimal choose in typical Ramsey spectroscopy set-up. In order to
surpass the standard scaling, we propose to change the interaction strength
with time. Finally, we investigate other environmental influences on the
measurement precision of temperature. Base on it, we define a new way to
measure non-Markovian effect.


title: The Tutte expansion revisited

abstract:
  The Tutte polynomial of a connected graph was originally defined by Tutte as
a sum over all spanning trees of monomials depending on a fixed linear order on
the set of edges. Tuttle proved that while these monomials do depend on the
linear order, the sum does not. The present paper is a result of a reflection
upon this classical theorem of Tutte. It is devoted to an elementary and
detailed proof of this theorem in its natural generality, i.e. not for graphs,
but for matroids.
  In contrast with usual methods, the emphasis is on the properties of maps (as
opposed to elements) naturally associated to a matroid (or a graph) and an
order. In order to fully explain the four-fold symmetry of the proof, we
introduce notion of linking between two matroids on the same set. While every
matroid is, in fact, linked only to itself and to its dual matroid, the notion
of a linking identifies the essential features of the theory and allows to
replace the usual four similar arguments by a single one. This is done in
Theorem 9.1, which is the focal point of the present paper.
  With the exception of Introduction, the present paper is self-contained
modulo basic concepts related to sets and maps. In particular, no knowledge of
the matroid theory or of the graph theory is assumed.


title: Spectropolarimetric capabilities of Ca II 8542 A line

abstract:
  The next generation of space and ground-based solar missions aim to study the
magnetic properties of the solar chromosphere using the infrared Ca II lines
and the He I 10830 {\AA} line. The former seem to be the best candidates to
study the stratification of magnetic fields in the solar chromosphere and their
relation to the other thermodynamical properties underlying the chromospheric
plasma. The purpose of this work is to provide a detailed analysis of the
diagnostic capabilities of the Ca II 8542 {\AA} line, anticipating forthcoming
observational facilities. We study the sensitivity of the Ca II 8542 {\AA} line
to perturbations applied to the physical parameters of reference semi-empirical
1D model atmospheres using response functions and we make use of 3D MHD
simulations to examine the expected polarization signals for moderate magnetic
field strengths. Our results indicate that the Ca II 8542 {\AA} line is mostly
sensitive to the layers enclosed between $\log$ $\tau=[0,-5.5]$, under the
physical conditions that are present in our model atmospheres. In addition, the
simulated magnetic flux tube generates strong longitudinal signals in its
centre and moderate transversal signals, due to the vertical expansion of
magnetic field lines, in its edge. Thus, observing the Ca II 8542 {\AA} line we
will be able to infer the 3D geometry of moderate magnetic field regions.


title:
Decreasing the uncertainty of atomic clocks via real-time noise
  distinguish

abstract:
  The environmental perturbation on atoms is the key factor restricting the
performance of atomic frequency standards, especially in long term scale. In
this letter, we demonstrate a real-time noise distinguish operation of atomic
clocks. The operation improves the statistical uncertainty by about an order of
magnitude of our fountain clock which is deteriorated previously by extra
noises. The frequency offset bring by the extra noise is also corrected. The
experiment proves the real-time noise distinguish operation can reduce the
contribution of ambient noises and improve the uncertainty limit of atomic
clocks.


title:
A Prolonged Southward IMF-Bz Event of May 02--04, 1998: Solar,
  Interplanetary Causes and Geomagnetic Consequences

abstract:
  A detailed investigation was carried out to understand a prolonged (~44
hours) weakly southward interplanetary magnetic field (IMF-Bz) condition during
May 02--04, 1998. In-situ observations, during the period, showed the passage
of an expanding magnetic cloud embedded in an interplanetary coronal mass
ejection (ICME), followed up by a shock and an interplanetary discontinuity
driven by another ICME. It is the arrival of the ICMEs and the upfront shocks
that cause the prolonged southward IMF-Bz condition. The magnetic configuration
of the source regions of the IMF associated with the ICME interval were also
examined, which showed open magnetic field structures, emanating from a small
active region on the north of the heliospheric current sheet (HCS). The
structures remained constantly to the north of the HCS, both on April 29 and
May 01, suggesting no change in their polarity. The draping of these outward
directed radial field lines around the propagating CMEs in the shocked plasma
explained the observed polarity changes of the IMF-Bz at 1 AU. In addition,
multiple enhancements were also detected in the geomagnetic field variations,
which showed a distinct one-to-one correspondence with the density pulses
observed at 1 AU, during 0700--1700 UT on May 03. The spectral analysis of both
the variations showed the same discrete frequencies of 0.48, 0.65 and 0.75 mHz,
demonstrating that the solar wind density enhancements can cause detectable
global geomagnetic disturbances. The observations, thus, provide a deeper
insight into the possible causes and geomagnetic consequences of a prolonged
weakly southward IMF-Bz condition.


title: Gaussian Copula Variational Autoencoders for Mixed Data

abstract:
  The variational autoencoder (VAE) is a generative model with continuous
latent variables where a pair of probabilistic encoder (bottom-up) and decoder
(top-down) is jointly learned by stochastic gradient variational Bayes. We
first elaborate Gaussian VAE, approximating the local covariance matrix of the
decoder as an outer product of the principal direction at a position determined
by a sample drawn from Gaussian distribution. We show that this model, referred
to as VAE-ROC, better captures the data manifold, compared to the standard
Gaussian VAE where independent multivariate Gaussian was used to model the
decoder. Then we extend the VAE-ROC to handle mixed categorical and continuous
data. To this end, we employ Gaussian copula to model the local dependency in
mixed categorical and continuous data, leading to {\em Gaussian copula
variational autoencoder} (GCVAE). As in VAE-ROC, we use the rank-one
approximation for the covariance in the Gaussian copula, to capture the local
dependency structure in the mixed data. Experiments on various datasets
demonstrate the useful behaviour of VAE-ROC and GCVAE, compared to the standard
VAE.


title: Role of a Relay in Bursty Multiple Access Channels

abstract:
  We investigate the role of a relay in multiple access channels (MACs) with
bursty user traffic, where intermittent data traffic restricts the users to
bursty transmissions. As our main result, we characterize the degrees of
freedom (DoF) region of a $K$-user bursty multi-input multi-output (MIMO)
Gaussian MAC with a relay, where Bernoulli random states are introduced to
govern bursty user transmissions. To that end, we extend the noisy network
coding scheme to achieve the cut-set bound. Our main contribution is in
exploring the role of a relay from various perspectives. First, we show that a
relay can provide a DoF gain in bursty channels, unlike in conventional
non-bursty channels. Interestingly, we find that the relaying gain can scale
with additional antennas at the relay to some extent. Moreover, observing that
a relay can help achieve collision-free performances, we establish the
necessary and sufficient condition for attaining collision-free DoF. Lastly, we
consider scenarios in which some physical perturbation shared around the users
may generate data traffic simultaneously, causing transmission patterns across
them to be correlated. We demonstrate that for most cases in such scenarios,
the relaying gain is greater when the users' transmission patterns are more
correlated, hence when more severe collisions take place. Our results have
practical implications in various scenarios of wireless networks such as
device-to-device systems and random media access control protocols.


title:
Nonlinear supercoherent states and geometric phases for the
  supersymmetric harmonic oscillator

abstract:
  Nonlinear supercoherent states, which are eigenstates of nonlinear
deformations of the Kornbluth-Zypman annihilation operator for the
supersymmetric harmonic oscillator, will be studied. They turn out to be
expressed in terms of nonlinear coherent states, associated to the
corresponding deformations of the standard annihilation operator. We will
discuss as well the Heisenberg uncertainty relation for a special particular
case, in order to compare our results with those obtained for the
Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic
oscillator executes an evolution loop, such that the evolution operator becomes
the identity at a certain time, thus the linear and nonlinear supercoherent
states turn out to be cyclic and the corresponding geometric phases will be
evaluated.


title:
Optimal Execution of Limit and Market Orders with Trade Director, Speed
  Limiter, and Fill Uncertainty

abstract:
  We study the optimal execution of market and limit orders with permanent and
temporary price impacts as well as uncertainty in the filling of limit orders.
Our continuous-time model incorporates a trade speed limiter and a trader
director to provide better control on the trading rates. We formulate a
stochastic control problem to determine the optimal dynamic strategy for trade
execution, with a quadratic terminal penalty to ensure complete liquidation. In
addition, we identify conditions on the model parameters to ensure optimality
of the controls and finiteness of the associated value functions. For
comparison, we also solve the schedule-following optimal execution problem that
penalizes deviations from an order schedule. Numerical results are provided to
illustrate the optimal market and limit orders over time.


title: Superconductivity in undoped CaFe2As2 single crystals

abstract:
  Single crystals of undoped CaFe2As2 were grown by a FeAs self-flux method,
and the crystals were quenched in ice-water rapidly after high temperature
growth. The quenched crystal undergoes a collapsed tetragonal structural phase
transition around 80 K revealed by the temperature dependent X-ray diffraction
measurements. Superconductivity below 25 K was observed in the collapsed phase
by resistivity and magnetization measurements. The isothermal magnetization
curve measured at 2 K indicates that this is a typical type-II superconductor.
For comparison, we systematically characterized the properties of the furnace
cooled, quenched, and post-annealed single crystals, and found strong internal
crystallographic strain existing in the quenched samples, which is the key for
the occurrence of superconductivity in the undoped CaFe2As2 single crystals.


title:
Optimising Charged Higgs Boson Searches at the Large Hadron Collider
  Across $b\bar b W^\pm$ Final States

abstract:
  In the light of the most recent data from Higgs boson searches and analyses,
we re-assess the scope of the Large Hadron Collider in accessing heavy charged
Higgs boson signals in $b\bar b W^\pm$ final states, wherein the contributing
channels can be $H^+\to t\bar b$, $hW^\pm, HW^\pm$ and $AW^\pm$. We consider a
2-Higgs Doublet Model Type-II and we assume as production mode $bg\to tH^-$ +
c.c., the dominant one over the range $M_{H^\pm}\ge 480$ GeV, as dictated by
$b\to s\gamma$ constraints. Prospects of detection are found to be significant
for various Run 2 energy and luminosity options.


title:
Channel Estimation for mmWave Massive MIMO Based Access and Backhaul in
  Ultra-Dense Network

abstract:
  Millimeter-wave (mmWave) massive MIMO used for access and backhaul in
ultra-dense network (UDN) has been considered as the promising 5G technique. We
consider such an heterogeneous network (HetNet) that ultra-dense small base
stations (BSs) exploit mmWave massive MIMO for access and backhaul, while
macrocell BS provides the control service with low frequency band. However, the
channel estimation for mmWave massive MIMO can be challenging, since the pilot
overhead to acquire the channels associated with a large number of antennas in
mmWave massive MIMO can be prohibitively high. This paper proposes a structured
compressive sensing (SCS)-based channel estimation scheme, where the angular
sparsity of mmWave channels is exploited to reduce the required pilot overhead.
Specifically, since the path loss for non-line-of-sight paths is much larger
than that for line-of-sight paths, the mmWave massive channels in the angular
domain appear the obvious sparsity. By exploiting such sparsity, the required
pilot overhead only depends on the small number of dominated multipath.
Moreover, the sparsity within the system bandwidth is almost unchanged, which
can be exploited for the further improved performance. Simulation results
demonstrate that the proposed scheme outperforms its counterpart, and it can
approach the performance bound.


title: On recovering missing values for sequences in a pathwise setting

abstract:
  The paper suggests a frequency criterion of error-free recoverability of a
missing value for sequences, i.e. discrete time processes, in a pathwise
setting without probabilistic assumptions. The paper establishes error-free
recoverability for classes of square-summable sequences with Z-transform
vanishing at isolated points with a mild rate; the case of non-summable
sequences is not excluded. The transfer functions for recovering algorithm are
presented explicitly.
  Some robustness with respect to noise contamination is established for the
suggested recovering algorithm.


title:
Multi-user Massive MIMO Communication Systems Based on Irregular Antenna
  Arrays

abstract:
  In practical mobile communication engineering applications, surfaces of
antenna array deployment regions are usually uneven. Therefore, massive
multi-input-multi-output (MIMO) communication systems usually transmit wireless
signals by irregular antenna arrays. To evaluate the performance of irregular
antenna arrays, the matrix correlation coefficient and ergodic received gain
are defined for massive MIMO communication systems with mutual coupling
effects. Furthermore, the lower bound of the ergodic achievable rate, symbol
error rate (SER) and average outage probability are firstly derived for
multi-user massive MIMO communication systems using irregular antenna arrays.
Asymptotic results are also derived when the number of antennas approaches
infinity. Numerical results indicate that there exists a maximum achievable
rate when the number of antennas keeps increasing in massive MIMO communication
systems using irregular antenna arrays. Moreover, the irregular antenna array
outperforms the regular antenna array in the achievable rate of massive MIMO
communication systems when the number of antennas is larger than or equal to a
given threshold.


title:
The $k$-spaces property of free Abelian topological groups over
  non-metrizable La\v{s}nev spaces

abstract:
  Given a Tychonoff space $X$, let $A(X)$ be the free Abelian topological group
over $X$ in the sense of Markov. For every $n\in\mathbb{N}$, let $A_n(X)$
denote the subspace of $A(X)$ that consists of words of reduced length at most
$n$ with respect to the free basis $X$. In this paper, we show that $A_4(X)$ is
a $k$-space if and only if $A(X)$ is a $k$-space for the non-metrizable
La\v{s}nev space $X$, which gives a complementary for one result of K.
Yamada's. In addition, we also show that, under the assumption of
$\flat=\omega_1$, the subspace $A_3(X)$ is a $k$-space if and only if $A(X)$ is
a $k$-space for the non-metrizable La\v{s}nev space $X$. However, under the
assumption of $\flat>\omega_1$, we provide a non-metrizable La\v{s}nev space
$X$ such that $A_3(X)$ is a $k$-space but $A(X)$ is not a $k$-space.


title: Deep Aesthetic Quality Assessment with Semantic Information

abstract:
  Human beings often assess the aesthetic quality of an image coupled with the
identification of the image's semantic content. This paper addresses the
correlation issue between automatic aesthetic quality assessment and semantic
recognition. We cast the assessment problem as the main task among a multi-task
deep model, and argue that semantic recognition task offers the key to address
this problem. Based on convolutional neural networks, we employ a single and
simple multi-task framework to efficiently utilize the supervision of aesthetic
and semantic labels. A correlation item between these two tasks is further
introduced to the framework by incorporating the inter-task relationship
learning. This item not only provides some useful insight about the correlation
but also improves assessment accuracy of the aesthetic task. Particularly, an
effective strategy is developed to keep a balance between the two tasks, which
facilitates to optimize the parameters of the framework. Extensive experiments
on the challenging AVA dataset and Photo.net dataset validate the importance of
semantic recognition in aesthetic quality assessment, and demonstrate that
multi-task deep models can discover an effective aesthetic representation to
achieve state-of-the-art results.


title:
Inverse engineering rigorous adiabatic Hamiltonian for non-Hermitian
  system

abstract:
  We generalize the quantum adiabatic theorem to the non-Hermitian system and
build a rigorous adiabaticity condition with respect to the adiabatic phase.
The non-Hermitian Hamiltonian inverse engineering method is proposed for the
purpose to adiabatically drive a artificial quantum state. For the sake of
clearness, we take a concrete two-level system as an example to show the
usefulness of the inverse engineering method. The numerical simulation result
shows that our scheme can work well even under noise if the parameters are
chosen appropriately. We can obtain the desired target state by adjusting extra
rotating magnetic fields at a predefined time. Furthermore, certain noise and
dissipation in the systems is no longer undesirable, but plays a positive role
in our scheme. Therefore, our scheme could provide more choices for the
realization of quantum-state engineering.


title:
Resonant plasmonic terahertz detection in graphene split-gate
  field-effect transistors with lateral p-n junctions

abstract:
  We evaluate the proposed resonant terahertz (THz) detectors on the base of
field-effect transistors (FETs) with split gates, electrically induced lateral
p-n junctions, uniform graphene layer (GL) or perforated (in the p-n junction
depletion region) graphene layer (PGL) channel. The perforated depletion region
forms an array of the nanoconstions or nanoribbons creating the barriers for
the holes and electrons. The operation of the GL-FET- and PGL-FET detectors is
associated with the rectification of the ac current across the lateral p-n
junction enhanced by the excitation of bound plasmonic oscillations in in the
p- and n-sections of the channel. Using the developed device model, we find the
GL-FET and PGL-FET-detectors characteristics. These detectors can exhibit very
high voltage responsivity at the THz radiation frequencies close to the
frequencies of the plasmonic resonances. These frequencies can be effectively
voltage tuned. We show that in PL-FET-detectors the dominant mechanism of the
current rectification is due to the tunneling nonlinearity, whereas in
PGL-FET-detector the current rectification is primarily associated with the
thermionic processes. Due to much lower p-n junction conductance in the
PGL-FET-detectors, their resonant response can be substantially more pronounced
than in the GL-FET-detectors corresponding to fairly high detector
responsivity.


title: Factorization numbers of finite rank $3$ abelian $p$-groups

abstract:
  In this short note we give a formula for the factorization number $F_2(G)$ of
a finite rank $3$ abelian $p$-group $G$. This extends a result in our previous
work \cite{9}.


title: Finite groups with a certain number of cyclic subgroups II

abstract:
  In this note we describe the finite groups $G$ having $|G|-2$ cyclic
subgroups. This partially solves the open problem in the end of \cite{3}.


title:
Stability of Rotating Self-Gravitating Filaments:Stability of Rotating
  Self-Gravitating Filaments: Effects of Magnetic Field

abstract:
  We have performed systemmatic local linear stability analysis on a radially
stratified infinite self-gravitating cylinder of rotating plasma under the
influence of magnetic field. In order to render the system analytically
tractable, we have focussed solely on the axisymmetric modes of perturbations.
Using cylindrical coordinate system, we have derived the critical linear mass
density of a non-rotating filament required for gravitational collapse to ensue
in the presence of azimuthal magnetic field. Moreover, for such filaments
threaded by axial magnetic field, we show that the growth rates of the modes
having non-zero radial wavenumber are reduced more strongly by the magnetic
field than that of the modes having zero radial wavenumber. More importantly,
our study contributes to the understanding of the stability property of
rotating astrophysical filaments that are more often than not influenced by
magnetic fields. In addition to complementing many relevant numerical studies
reported the literature, our results on filaments under the influence of
magnetic field generalize some of the very recent analytical works
(e.g.,~\citet{jog2014}, etc.). For example, here we prove that even a weak
magnetic field can play a dominant role in determining stability of the
filament when the rotation timescale is larger than the free fall timescale. A
filamentary structure with faster rotation is, however, comparatively more
stable for the same magnetic field. The results reported herein, due to strong
locality assumption, are strictly valid for the modes for which one can ignore
the radial variations in the density and the magnetic field profiles.


title: Spirallikeness of shifted hypergeometric functions

abstract:
  In the present paper, we study spirallikenss (including starlikeness) of the
shifted hypergeometric function $f(z)=z_2F_1(a,b;c;z)$ with complex parameters
$a,b,c,$ where $_2F_1(a,b;c;z)$ stands for the Gaussian hypergeometric
function. First, we observe the asymptotic behaviour of $_2F_1(a,b;c;z)$ around
the point $z=1$ to obtain necessary conditions for $f$ to be
$\lambda$-spirallike for a given $\lambda$ with $- \pi/2< \lambda<\pi/2.$ We
next give sufficient conditions for $f$ to be $\lambda$-spirallike. As special
cases, we obtain sufficient conditions of strong starlikeness and examples of
spirallike, but not starlike, shifted hypergeometric functions.


title: Terahertz plasmonic laser radiating in an ultra-narrow beam

abstract:
  Plasmonic lasers (spasers) generate coherent surface-plasmon-polaritons
(SPPs) and could be realized at subwavelength dimensions in metallic cavities
for applications in nanoscale optics. Plasmonic cavities are also utilized for
terahertz quantum-cascade lasers (QCLs), which are the brightest available
solid-state sources of terahertz radiation. A long standing challenge for
spasers is their poor coupling to the far-field radiation. Unlike conventional
lasers that could produce directional beams, spasers have highly divergent
radiation patterns due to their subwavelength apertures. Here, we theoretically
and experimentally demonstrate a new technique for implementing
distributed-feedback (DFB) that is distinct from any other previously utilized
DFB schemes for semiconductor lasers. The so-termed antenna-feedback scheme
leads to single-mode operation in plasmonic lasers, couples the resonant SPP
mode to a highly directional far-field radiation pattern, and integrates hybrid
SPPs in surrounding medium into the operation of the DFB lasers.
Experimentally, the antenna-feedback method, which does not require the phase
matching to a well-defined effective index, is implemented for terahertz QCLs,
and single-mode terahertz QCLs with beam divergence as small as 4 x 4 degree
are demonstrated, which is the narrowest beam reported for any terahertz QCL
to-date. Moreover, in contrast to negligible radiative-field in conventional
photonic band-edge lasers, in which the periodicity follows the integer
multiple of half-wavelength inside active medium, antenna-feedback breaks this
integer-limit for the first time and enhances the radiative-field of lasing
mode. The antenna-feedback scheme is generally applicable to any plasmonic
laser with a Fabry-Perot cavity irrespective of its operating wavelength, and
could bring plasmonic lasers closer to practical applications.