title:
Towards K-means-friendly Spaces: Simultaneous Deep Learning and
  Clustering

abstract:
  Most learning approaches treat dimensionality reduction (DR) and clustering
separately (i.e., sequentially), but recent research has shown that optimizing
the two tasks jointly can substantially improve the performance of both. The
premise behind the latter genre is that the data samples are obtained via
linear transformation of latent representations that are easy to cluster; but
in practice, the transformation from the latent space to the data can be more
complicated. In this work, we assume that this transformation is an unknown and
possibly nonlinear function. To recover the `clustering-friendly' latent
representations and to better cluster the data, we propose a joint DR and
K-means clustering approach in which DR is accomplished via learning a deep
neural network (DNN). The motivation is to keep the advantages of jointly
optimizing the two tasks, while exploiting the deep neural network's ability to
approximate any nonlinear function. This way, the proposed approach can work
well for a broad class of generative models. Towards this end, we carefully
design the DNN structure and the associated joint optimization criterion, and
propose an effective and scalable algorithm to handle the formulated
optimization problem. Experiments using different real datasets are employed to
showcase the effectiveness of the proposed approach.


title:
Sample Efficient Optimization for Learning Controllers for Bipedal
  Locomotion

abstract:
  Learning policies for bipedal locomotion can be difficult, as experiments are
expensive and simulation does not usually transfer well to hardware. To counter
this, we need al- gorithms that are sample efficient and inherently safe.
Bayesian Optimization is a powerful sample-efficient tool for optimizing
non-convex black-box functions. However, its performance can degrade in higher
dimensions. We develop a distance metric for bipedal locomotion that enhances
the sample-efficiency of Bayesian Optimization and use it to train a 16
dimensional neuromuscular model for planar walking. This distance metric
reflects some basic gait features of healthy walking and helps us quickly
eliminate a majority of unstable controllers. With our approach we can learn
policies for walking in less than 100 trials for a range of challenging
settings. In simulation, we show results on two different costs and on various
terrains including rough ground and ramps, sloping upwards and downwards. We
also perturb our models with unknown inertial disturbances analogous with
differences between simulation and hardware. These results are promising, as
they indicate that this method can potentially be used to learn control
policies on hardware.


title:
Exact State Revival in a Spin Chain with Next-To-Nearest Neighbour
  Interactions

abstract:
  An extension with next-to-nearest neighbour interactions of the simplest XX
spin chain with perfect state transfer (PST) is presented. The conditions for
PST and entanglement generation (balanced fractional revival) can be obtained
exactly and are discussed.


title: Bannai-Ito algebras and the $osp(1,2)$ superalgebra

abstract:
  The Bannai-Ito algebra $B(n)$ of rank $(n-2)$ is defined as the algebra
generated by the Casimir operators arising in the $n$-fold tensor product of
the $osp(1,2)$ superalgebra. The structure relations are presented and
representations in bases determined by maximal Abelian subalgebras are
discussed. Comments on realizations as symmetry algebras of physical models are
offered.


title: Communication-efficient Distributed Sparse Linear Discriminant Analysis

abstract:
  We propose a communication-efficient distributed estimation method for sparse
linear discriminant analysis (LDA) in the high dimensional regime. Our method
distributes the data of size $N$ into $m$ machines, and estimates a local
sparse LDA estimator on each machine using the data subset of size $N/m$. After
the distributed estimation, our method aggregates the debiased local estimators
from $m$ machines, and sparsifies the aggregated estimator. We show that the
aggregated estimator attains the same statistical rate as the centralized
estimation method, as long as the number of machines $m$ is chosen
appropriately. Moreover, we prove that our method can attain the model
selection consistency under a milder condition than the centralized method.
Experiments on both synthetic and real datasets corroborate our theory.


title: Trees That Grow

abstract:
  We study the notion of extensibility in functional data types, as a new
approach to the problem of decorating abstract syntax trees with additional
sets of information. We observed the need for such extensibility while
redesigning the data types representing Haskell abstract syntax inside GHC.
  Specifically, we describe our approach to the tree-decoration problem using a
novel syntactic machinery in Haskell for expressing extensible data types. We
show that the syntactic machinery is complete in that it can express all the
syntactically possible forms of extensions to algebraic data type declarations.
Then, we describe an encoding of the syntactic machinery based on the existing
features in Glasgow Haskell Compiler(GHC).


title:
Relating games of Menger, countable fan tightness, and selective
  separability

abstract:
  By adapting techniques of Arhangel'skii, Barman, and Dow, we may equate the
existence of perfect-information, Markov, and tactical strategies between two
interesting selection games. These results shed some light on Gruenhage's
question asking whether all strategically selectively separable spaces are
Markov selectively separable.


title:
Random walks with fractally correlated traps: Stretched exponential and
  power law survival kinetics

abstract:
  We consider the survival probability $f(t)$ of a random walk with a constant
hopping rate $w$ on a host lattice of fractal dimension $d$ and spectral
dimension $d_s\le 2$, with spatially correlated traps. The traps form a
sublattice with fractal dimension $d_a<d$ and are characterized by the
absorption rate $w_a$ which may be finite (imperfect traps) or infinite
(perfect traps). Initial coordinates are chosen randomly at or within a fixed
distance of a trap. For weakly absorbing traps ($w_a\ll w$), we find that
$f(t)$ can be closely approximated by a stretched exponential function over the
initial stage of relaxation, with stretching exponent $\alpha=1-(d-d_a)/d_w$,
where $d_w$ is the random walk dimension of the host lattice. At the end of
this initial stage there occurs a crossover to power law kinetics $f(t)\sim
t^{-\alpha}$ with the same exponent $\alpha$ as for the stretched exponential
regime. For strong absorption $w_a>w$, including the limit of perfect traps
$w_a\to \infty$, the stretched exponential regime is absent and the decay of
$f(t)$ follows, after a short transient, the aforementioned power law for all
times.


title:
Measurement of electron antineutrino oscillation based on 1230 days of
  operation of the Daya Bay experiment

abstract:
  A measurement of electron antineutrino oscillation by the Daya Bay Reactor
Neutrino Experiment is described in detail. Six 2.9-GW$_{\rm
  th}$ nuclear power reactors of the Daya Bay and Ling Ao nuclear power
facilities served as intense sources of $\overline{\nu}_{e}$'s. Comparison of
the $\overline{\nu}_{e}$ rate and energy spectrum measured by antineutrino
detectors far from the nuclear reactors ($\sim$1500-1950 m) relative to
detectors near the reactors ($\sim$350-600 m) allowed a precise measurement of
$\overline{\nu}_{e}$ disappearance. More than 2.5 million $\overline{\nu}_{e}$
inverse beta decay interactions were observed, based on the combination of 217
days of operation of six antineutrino detectors (Dec. 2011--Jul. 2012) with a
subsequent 1013 days using the complete configuration of eight detectors (Oct.
2012--Jul. 2015). The $\overline{\nu}_{e}$ rate observed at the far detectors
relative to the near detectors showed a significant deficit, $R=0.949 \pm
0.002(\mathrm{stat.}) \pm 0.002(\mathrm{syst.})$. The energy dependence of
$\overline{\nu}_{e}$ disappearance showed the distinct variation predicted by
neutrino oscillation. Analysis using an approximation for the three-flavor
oscillation probability yielded the flavor-mixing angle
$\sin^22\theta_{13}=0.0841 \pm 0.0027(\mathrm{stat.}) \pm
0.0019(\mathrm{syst.})$ and the effective neutrino mass-squared difference of
$\left|{\Delta}m^2_{\mathrm{ee}}\right|=(2.50 \pm 0.06(\mathrm{stat.}) \pm
0.06(\mathrm{syst.})) \times 10^{-3}\ {\rm eV}^2$. Analysis using the exact
three-flavor probability found ${\Delta}m^2_{32}=(2.45 \pm 0.06(\mathrm{stat.})
\pm 0.06(\mathrm{syst.})) \times 10^{-3}\ {\rm eV}^2$ assuming the normal
neutrino mass hierarchy and ${\Delta}m^2_{32}=(-2.56 \pm 0.06(\mathrm{stat.})
\pm 0.06(\mathrm{syst.})) \times 10^{-3}\ {\rm eV}^2$ for the inverted
hierarchy.


title: Linear Mode-Mixing of Phonons with Trapped Ions

abstract:
  We propose a method to manipulate the normal modes in a chain of trapped ions
using only two lasers. Linear chains of trapped ions have proven experimentally
to be highly controllable quantum systems with a variety of refined techniques
for preparation, evolution, and readout, however, typically for quantum
information processing applications people have been interested in using the
internal levels of the ions as the computational basis. We analyse the case
where the motional degrees of freedom of the ions is the quantum system of
interest, and where the internal levels are leveraged to facilitate
interactions. In particular, we focus on an analysis of mode-mixing of phonons
in different normal modes to mimic the quantum optical equivalent of a beam
splitter.


title: Dynamic Stacked Generalization for Node Classification on Networks

abstract:
  We propose a novel stacked generalization (stacking) method as a dynamic
ensemble technique using a pool of heterogeneous classifiers for node label
classification on networks. The proposed method assigns component models a set
of functional coefficients, which can vary smoothly with certain topological
features of a node. Compared to the traditional stacking model, the proposed
method can dynamically adjust the weights of individual models as we move
across the graph and provide a more versatile and significantly more accurate
stacking model for label prediction on a network. We demonstrate the benefits
of the proposed model using both a simulation study and real data analysis.


title:
Beyond Spatial Auto-Regressive Models: Predicting Housing Prices with
  Satellite Imagery

abstract:
  When modeling geo-spatial data, it is critical to capture spatial
correlations for achieving high accuracy. Spatial Auto-Regression (SAR) is a
common tool used to model such data, where the spatial contiguity matrix (W)
encodes the spatial correlations. However, the efficacy of SAR is limited by
two factors. First, it depends on the choice of contiguity matrix, which is
typically not learnt from data, but instead, is assumed to be known apriori.
Second, it assumes that the observations can be explained by linear models. In
this paper, we propose a Convolutional Neural Network (CNN) framework to model
geo-spatial data (specifi- cally housing prices), to learn the spatial
correlations automatically. We show that neighborhood information embedded in
satellite imagery can be leveraged to achieve the desired spatial smoothing. An
additional upside of our framework is the relaxation of linear assumption on
the data. Specific challenges we tackle while implementing our framework
include, (i) how much of the neighborhood is relevant while estimating housing
prices? (ii) what is the right approach to capture multiple resolutions of
satellite imagery? and (iii) what other data-sources can help improve the
estimation of spatial correlations? We demonstrate a marked improvement of 57%
on top of the SAR baseline through the use of features from deep neural
networks for the cities of London, Birmingham and Liverpool.


title: Landau-Zener transition driven by a slow noise

abstract:
  The effect of a slow noise in non-diagonal matrix element, J(t), that
describes the diabatic level coupling, on the probability of the Landau-Zener
transition is studied. For slow noise, the correlation time, \tau_c, of J(t) is
much longer than the characteristic time of the transition. Existing theory for
this case suggests that the average transition probability is the result of
averaging of the conventional Landau-Zener probability, calculated for a given
constant J, over the distribution of J. We calculate a finite-\tau_c correction
to this classical result. Our main finding is that this correction is dominated
by sparse realizations of noise for which J(t) passes through zero within a
narrow time interval near the level crossing. Two models of noise, random
telegraph noise and gaussian noise, are considered. Naturally, in both models
the average probability of transition decreases upon decreasing \tau_c. For
gaussian noise we identify two domains of this fall-off with specific
dependencies of average transition probability on \tau_c.


title: Local max-cut in smoothed polynomial time

abstract:
  In 1988, Johnson, Papadimitriou and Yannakakis wrote that "Practically all
the empirical evidence would lead us to conclude that finding locally optimal
solutions is much easier than solving NP-hard problems". Since then the
empirical evidence has continued to amass, but formal proofs of this phenomenon
have remained elusive. A canonical (and indeed complete) example is the local
max-cut problem, for which no polynomial time method is known. In a
breakthrough paper, Etscheid and R\"oglin proved that the smoothed complexity
of local max-cut is quasi-polynomial, i.e., if arbitrary bounded weights are
randomly perturbed, a local maximum can be found in $n^{O(\log n)}$ steps. In
this paper we prove smoothed polynomial complexity for local max-cut, thus
confirming that finding local optima for max-cut is much easier than solving
it.


title: Mentoring Partnerships in Science Education

abstract:
  The authors use an action research (AR) approach in a collegiate studio
physics class to investigate the power of partnerships via conferences as they
relate to issues of establishing a student/mentor rapport, empowering students
to reduce inequity, and the successes and barriers to hearing students' voices.
The graduate teaching assistant (TA, Author 1) conducted one-on-one conferences
with 29 students, elicited student opinions about the progress of the course,
and talked with faculty, TAs, and an undergraduate supplemental instructor for
other sections of the course. At the end of the semester, the students reported
increased knowledge of the TA as a person and as an instructor, and vice versa.
Sixty-five percent of students reported no interest in changing circumstances
to make it easier to talk about personal concerns with the TA. College students
reluctantly voiced their opinions about the course, possibly due to the power
structure of the classroom. Other TAs in the department expressed mostly
disinterest in the project, while faculty members were interested in student
learning but skeptical of student empowerment. A case study of one student is
presented, wherein his attendance improved in the course and he received
additional help outside class, both possibly as a result of the student/TA
conferences. Students in this studio physics section were more likely to
interact directly with faculty or TAs during lectures, but less likely to do so
during lab sessions, than were students in a non-studio physics section.


title: Power-Law Distributions in a Two-sided Market and Net Neutrality

abstract:
  "Net neutrality" often refers to the policy dictating that an Internet
service provider (ISP) cannot charge content providers (CPs) for delivering
their content to consumers. Many past quantitative models designed to determine
whether net neutrality is a good idea have been rather equivocal in their
conclusions. Here we propose a very simple two-sided market model, in which the
types of the consumers and the CPs are {\em power-law distributed} --- a kind
of distribution known to often arise precisely in connection with
Internet-related phenomena. We derive mostly analytical, closed-form results
for several regimes: (a) Net neutrality, (b) social optimum, (c) maximum
revenue by the ISP, or (d) maximum ISP revenue under quality differentiation.
One unexpected conclusion is that (a) and (b) will differ significantly, unless
average CP productivity is very high.


title: (1,1) L-space knots

abstract:
  We characterize the (1, 1) knots in the three-sphere and lens spaces that
admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these
manifolds admit non- trivial L-space surgeries. We also recover a
characterization of the Berge manifold amongst 1-bridge braid exteriors.


title: Estimation of low rank density matrices by Pauli measurements

abstract:
  Density matrices are positively semi-definite Hermitian matrices with unit
trace that describe the states of quantum systems. Many quantum systems of
physical interest can be represented as high-dimensional low rank density
matrices. A popular problem in {\it quantum state tomography} (QST) is to
estimate the unknown low rank density matrix of a quantum system by conducting
Pauli measurements. Our main contribution is twofold. First, we establish the
minimax lower bounds in Schatten $p$-norms with $1\leq p\leq +\infty$ for low
rank density matrices estimation by Pauli measurements. In our previous paper,
these minimax lower bounds are proved under the trace regression model with
Gaussian noise and the noise is assumed to have common variance. In this paper,
we prove these bounds under the Binomial observation model which meets the
actual model in QST.
  Second, we study the Dantzig estimator (DE) for estimating the unknown low
rank density matrix under the Binomial observation model by using Pauli
measurements. In our previous papers, we studied the least squares estimator
and the projection estimator, where we proved the optimal convergence rates for
the least squares estimator in Schatten $p$-norms with $1\leq p\leq 2$ and,
under a stronger condition, the optimal convergence rates for the projection
estimator in Schatten $p$-norms with $1\leq p\leq +\infty$. In this paper, we
show that the results of these two distinct estimators can be simultaneously
obtained by the Dantzig estimator. Moreover, better convergence rates in
Schatten norm distances can be proved for Dantzig estimator under conditions
weaker than those needed in previous papers. When the objective function of DE
is replaced by the negative von Neumann entropy, we obtain sharp convergence
rate in Kullback-Leibler divergence.


title:
Modeling the early evolution of massive OB stars with an experimental
  wind routine

abstract:
  Stellar evolution models of massive stars are very sensitive to the adopted
mass-loss scheme. The magnitude and evolution of mass-loss rates significantly
affect the main sequence evolution, and the properties of post-main sequence
objects, including their rotational velocities. Driven by potential
discrepancies between theoretically predicted and observationally derived
mass-loss rates in the OB star range, we particularly aim to investigate the
response to mass-loss rates that are lower than currently adopted, in parallel
with the mass-loss behavior at the "first" bi-stability jump. We perform 1D
hydrodynamical model calculations of single $20 - 60 \, M_{\odot}$ Galactic ($Z
= 0.014$) stars where the effects of stellar winds are already significant
during the main sequence phase. We develop an experimental wind routine to
examine the behavior and response of the models under the influence of
different mass-loss rates. This observationally guided, simple and flexible
wind routine is not a new mass-loss description but a useful tool based on the
Wind-momentum Luminosity Relation and other scaling relations, and provides a
meaningful base for various tests and comparisons. The main result of this
study indicates a dichotomy when accounting for currently debated problems
regarding mass-loss rates of hot massive stars. In a fully diffusive approach,
and for commonly adopted initial rotational velocities, lower mass-loss rates
than theoretically predicted require to invoke an additional source of angular
momentum loss (either due to bi-stability braking, or yet unidentified) to
brake down surface rotational velocities. [...]


title: Integer Quantum Hall Effect of Interacting Electrons in Graphene

abstract:
  By taking into account the charge and spin orderings and the exchange
interactions between all the Landau levels, we investigate the integer quantum
Hall effect of electrons in graphene using the mean-field theory. At the
fillings $\nu = 4n+2$ with $n = 0, 1, \cdots$, the system is in the
high-symmetry state with the Landau levels four-fold degenerated. We show that
with doping the degenerated lowest empty levels can be sequentially filled one
level by one level, the filled level is lower than the empty ones because of
the symmetry breaking. This result explains the step $\Delta\nu$ = 1 in the
integer quantized Hall conductivity of the experimental observations. We also
present in the supplemental material a high efficient method for dealing with
huge number of the Coulomb couplings between all the levels.


title:
Term-Class-Max-Support (TCMS): A Simple Text Document Categorization
  Approach Using Term-Class Relevance Measure

abstract:
  In this paper, a simple text categorization method using term-class relevance
measures is proposed. Initially, text documents are processed to extract
significant terms present in them. For every term extracted from a document, we
compute its importance in preserving the content of a class through a novel
term-weighting scheme known as Term_Class Relevance (TCR) measure proposed by
Guru and Suhil (2015) [1]. In this way, for every term, its relevance for all
the classes present in the corpus is computed and stored in the knowledgebase.
During testing, the terms present in the test document are extracted and the
term-class relevance of each term is obtained from the stored knowledgebase. To
achieve quick search of term weights, Btree indexing data structure has been
adapted. Finally, the class which receives maximum support in terms of
term-class relevance is decided to be the class of the given test document. The
proposed method works in logarithmic complexity in testing time and simple to
implement when compared to any other text categorization techniques available
in literature. The experiments conducted on various benchmarking datasets have
revealed that the performance of the proposed method is satisfactory and
encouraging.


title: A System Level Approach to Controller Synthesis

abstract:
  Biological and advanced cyberphysical control systems often have limited,
sparse, uncertain, and distributed communication and computing in addition to
sensing and actuation. Fortunately, the corresponding plants and performance
requirements are also sparse and structured, and this must be exploited to make
constrained controller design feasible and tractable. We introduce a new
"system level" (SL) approach involving three complementary SL elements. System
Level Parameterizations (SLPs) generalize state space and Youla
parameterizations of all stabilizing controllers and the responses they
achieve, and combine with System Level Constraints (SLCs) to parameterize the
largest known class of constrained stabilizing controllers that admit a convex
characterization, generalizing quadratic invariance (QI). SLPs also lead to a
generalization of detectability and stabilizability, suggesting the existence
of a rich separation structure, that when combined with SLCs, is naturally
applicable to structurally constrained controllers and systems. We further
provide a catalog of useful SLCs, most importantly including sparsity, delay,
and locality constraints on both communication and computing internal to the
controller, and external system performance. The resulting System Level
Synthesis (SLS) problems that arise define the broadest known class of
constrained optimal control problems that can be solved using convex
programming. An example illustrates how this system level approach can
systematically explore tradeoffs in controller performance, robustness, and
synthesis/implementation complexity.


title: First stability eigenvalue of singular minimal hypersurfaces in spheres

abstract:
  In this short note we extend an estimate due to J. Simons on the first
stability eigenvalue of minimal hypersurfaces in spheres to the singular
setting. Specifically, we show that any singular minimal hypersurface in
$S^{n+1}$, which is not totally geodesic and satisfies the \alpha-structural
hypothesis, has first stability eigenvalue at most -2n, with equality if and
only if it is a product of two round spheres. The equality case was settled
independently in the classical setting by Wu and Perdomo.


title:
An Efficient and Compact Excitation of Surface Plasmons Using a Si Gable
  Tip

abstract:
  We propose a novel technique to efficiently excite a surface plasmon
polariton (SPP) mode at a gold-glass interface by exploiting the near field
excitation of an engineered high index (silicon) gabled tip at the telecom
wavelengths. The proposed structure can theoretically convert 49% of the input
optical power to a SPP mode. The device is compact, it will facilitate the
on-chip excitation of the SPP, its fabrication is compatible with the standard
Si fabrication processes, and as such, it is expected to be useful in the
design of future integrated sensors.


title: Staggered Flux State in Two-Dimensional Hubbard Models

abstract:
  The stability and other properties of a staggered flux (SF) state or a
correlated d-density wave state are studied for the Hubbard (t-t'-U) model on
extended square lattices, as a low-lying state that competes with the
d(x2-y2)-wave superconductivity (d-SC) and possibly causes the pseudogap
phenomena in underdoped high-Tc cuprates and organic kappa-BEDT-TTF salts. In
calculations, a variational Monte Carlo method is used. In the trial wave
function, a configuration-dependent phase factor, which is vital to treat a
current-carrying state for a large U/t, is introduced in addition to ordinary
correlation factors. Varying U/t, t'/t, and the doping rate (delta)
systematically, we show that the SF state becomes more stable than the normal
state (projected Fermi sea) for a strongly correlated (U/t\gtrsim 5) and
underdoped (delta\lesssim 0.16) area. The decrease in energy is sizable,
particularly in the area where Mott physics prevails and the circular current
(order parameter) is strongly suppressed. These features are consistent with
those for the t-J model. The effect of the frustration t'/t plays a crucial
role in preserving charge homogeneity and appropriately describing the behavior
of hole- and electron-doped cuprates and kappa-BEDT-TTF salts. We argue that
the SF state does not coexist with d-SC and is not a `normal state' from which
d-SC arises. We also show that a spin current (flux or nematic) state is never
stabilized in the same regime.


title: Weight elimination in Serre-type conjectures

abstract:
  We prove the weight elimination direction of the Serre weight conjectures as
formulated by Herzig for forms of $U(n)$ which are compact at infinity and
split at places dividing $p$ in generic situations. That is, we show that all
modular weights for a mod $p$ Galois representation are contained in the set
predicted by Herzig. Under some additional hypotheses, we also show modularity
of all the "obvious" weights.


title:
Capability of the HAWC gamma-ray observatory for the indirect detection
  of ultra-high energy neutrinos

abstract:
  The detection of ultra-high energy neutrinos, with energies in the PeV range
or above, is a topic of great interest in modern astroparticle physics. The
importance comes from the fact that these neutrinos point back to the most
energetic particle accelerators in the Universe, and provide information about
their underlying acceleration mechanisms. Atmospheric neutrinos are a
background for these challenging measurements, but their rate is expected to be
negligible above $\approx$ 1 PeV. In this work we describe the feasibility to
study ultra-high energy neutrinos based on the Earth-skimming technique, by
detecting the charged leptons produced in neutrino-nucleon interactions in a
high mass target. We propose to detect the charged leptons, or their decay
products, with the High Altitude Water Cherenkov (HAWC) observatory, and use as
a large mass target for the neutrino interactions the Pico de Orizaba volcano,
the highest mountain in Mexico. In this work we develop an estimate of the
detection rate using a geometrical model to calculate the effective area of the
observatory. Our results show that it may be feasible to perform measurements
of the ultra-high energy neutrino flux from cosmic origin during the expected
lifetime of the HAWC observatory.


title:
General forms of finite population central limit theorems with
  applications to causal inference

abstract:
  Frequentists' inference often delivers point estimators associated with
confidence intervals or sets for parameters of interest. Constructing the
confidence intervals or sets requires understanding the sampling distributions
of the point estimators, which, in many but not all cases, are related to
asymptotic Normal distributions ensured by central limit theorems. Although
previous literature has established various forms of central limit theorems for
statistical inference in super population models, we still need general and
convenient forms of central limit theorems for some randomization-based causal
analysis of experimental data, where the parameters of interests are functions
of a finite population and randomness comes solely from the treatment
assignment. We use central limit theorems for sample surveys and rank
statistics to establish general forms of the finite population central limit
theorems that are particularly useful for proving asymptotic distributions of
randomization tests under the sharp null hypothesis of zero individual causal
effects, and for obtaining the asymptotic repeated sampling distributions of
the causal effect estimators. The new central limit theorems hold for general
experimental designs with multiple treatment levels and multiple treatment
factors, and are immediately applicable for studying the asymptotic properties
of many methods in causal inference, including instrumental variable,
regression adjustment, rerandomization, clustered randomized experiments, and
so on. Previously, the asymptotic properties of these problems are often based
on heuristic arguments, which in fact rely on general forms of finite
population central limit theorems that have not been established before. Our
new theorems fill in this gap by providing more solid theoretical foundation
for asymptotic randomization-based causal inference.


title: On first integrals of geodesic flows on a two-torus

abstract:
  The problem of the existence of an additional (independent on the energy)
first integral, of a geodesic (or magnetic geodesic) flow, which is polynomial
in momenta is studied. The relation of this problem to the existence of
nontrivial solutions of stationary dispersionless limits of two-dimensional
soliton equations is demonstrated. The nonexistence of an additional quadratic
first integral is established for certain classes of magnetic geodesic flows.


title:
To Frontalize or Not To Frontalize: Do We Really Need Elaborate
  Pre-processing To Improve Face Recognition?

abstract:
  Face recognition performance has improved remarkably in the last decade. Much
of this success can be attributed to the development of deep learning
techniques such as convolutional neural networks (CNNs). While CNNs have pushed
the state-of-the-art forward, their training process requires a large amount of
clean and correctly labelled training data. If a CNN is intended to tolerate
facial pose, then we face an important question: should this training data be
diverse in its pose distribution, or should face images be normalized to a
single pose in a pre-processing step? To address this question, we evaluate a
number of popular facial landmarking and pose correction algorithms to
understand their effect on facial recognition performance. Additionally, we
introduce a new, automatic, single-image frontalization scheme that exceeds the
performance of current algorithms. CNNs trained using sets of different
pre-processing methods are used to extract features from the Point and Shoot
Challenge (PaSC) and CMU Multi-PIE datasets. We assert that the subsequent
verification and recognition performance serves to quantify the effectiveness
of each pose correction scheme.


title:
Regularity and lifespan of small solutions to systems of quasi-linear
  wave equations with multiple speeds,I: almost global existence

abstract:
  In this paper, we show almost global existence of small solutions to the
Cauchy problem for symmetric system of wave equations with quadratic (in 3D) or
cubic (in 2D) nonlinear terms and multiple propagation speeds. To measure the
size of initial data, we employ a weighted Sobolev norm whose regularity index
is the smallest among all the admissible Sobolev norms of integer order. We
must overcome the difficulty caused by the absence of the $H^1$-$L^p$
Klainerman-Sobolev type inequality, in order to obtain a required a priori
bound in the low-order Sobolev norm. The introduction of good substitutes for
this inequality is therefore at the core of this paper. Using the idea of
showing the well-known Lady\v{z}enskaja inequality, we prove some weighted
inequalities, which, together with the generalized Strauss inequality, play a
role as the good substitute.


title:
Where Do the Terms of the Power Series Expansions of Sine and Cosine
  Functions Come from? Involutes!

abstract:
  In the 1930's, a Russian school teacher Y. S. Chaikovsky presented a proof of
the power series expansion of the sine and cosine functions without using
calculus. In doing so he also showed the geometrical meanings of the various
terms in these power series expansions. Chaikovsky's ideas were first published
by Leo S. Gurin as a Note in the American Mathematical Monthly in 1996. The
proofs, though they use only elementary mathematics, require some combinatorial
arguments which may be hard even for bright students.
  This paper is an attempt to bring the ideas of Chaikovsky once again to the
attention of the mathematics teachers and students. The emphasis in this paper
is on establishing the geometrical meanings of the various terms in the power
series expansions of sine and cosine functions. This has been done taking
recourse to methods of calculus.
  Since the concept of an involute is crucial in this investigation, we have
also included a brief discussion on the concept of an involute of a curve and
also a Maxima procedure for computing the parametric equations of the involute
of a given curve.


title: Ordered Factorizations with $k$ Factors

abstract:
  We give an overview of combinatoric properties of the number of ordered
$k$-factorizations $f_k(n,l)$ of an integer, where every factor is greater or
equal to $l$. We show that for a large number $k$ of factors, the value of the
cumulative sum $F_k(x,l)=\sum\nolimits_{n\leq x} f_k(n,l)$ is a polynomial in
$\lfloor \log_l x \rfloor$ and give explicit expressions for the degree and the
coefficients of this polynomial. An average order of the number of ordered
factorizations for a fixed number $k$ of factors greater or equal to 2 is
derived from known results of the divisor problem.


title:
On the effect of a two-rocks boundary on the propagation of nonlinear
  transients of temperature and pressure in deformable porous rocks

abstract:
  We here analyze the propagation of transients of fluid-rock temperature and
pressure through a thin boundary layer, where a steady trend is present,
between two adjacent homogeneous rocks. We focus on the effect of convection on
transients crossing such thin layer. In comparison with early models where this
boundary was assumed a sharp mathematical plane separating the two rocks, here
we show a realistic analysis of such boundary layer that implies a novel
nonlinear model. Its solutions describe large amplitude, quick and sharp
transients characterized by a novel drift and variations of the signal
amplitude, leading to a nonlinear wave propagation. Possible applications are
in volcanic, hydrologic, hydrothermal systems as well as for deep oil drilling.
In addition, this formalism could easily be generalized for the case of a
signal arriving in a rock characterized by a steady trend of pressure and/or
temperature. These effects, being proportional to the initial conditions, can
also give velocity variations not particularly important. A further heuristic
model has therefore been analyzed, i.e. assuming a pressure dependent rock
permeability. In this way, a remarkable increase of the system velocities is
obtained.


title:
Long-distance quantum key distribution using concatenated entanglement
  swapping with practical resources

abstract:
  We present our approach for sharing photons and assessing resultant
four-photon visibility between two distant parties using concatenated
entanglement swapping. In addition we determine the corresponding key
generation rate and the quantum bit-error rate. Our model is based on practical
limitations of resources, including multipair parametric down-conversion
sources, inefficient detectors with dark counts and lossy channels. Through
this approach, we have found that a trade-off is needed between experimental
run-time, pair-production rate and detector efficiency. Concatenated
entanglement swapping enables huge distances for quantum key-distribution but
at the expense of low key generation rate.


title: On disconnected images of connected spaces

abstract:
  We introduce the notion that a zero-dimensional compact space $L$ is a
\emph{Boolean image} of an arbitrary compact space $K$. When $K$ is also
zero-dimensional, this just means that $L$ is a continuous image of $K$.
However, a number of interesting questions arise when we consider connected
compacta $K$.


title:
RGBD-based Parameter Extraction for Door Opening Tasks with Human
  Assists in Nuclear Rescue

abstract:
  The ability to open a door is essential for robots to perform home-serving
and rescuing tasks. A substantial problem is to obtain the necessary parameters
such as the width of the door and the length of the handle. Many researchers
utilize computer vision techniques to extract the parameters automatically
which lead to fine but not very stable results because of the complexity of the
environment. We propose a method that utilizes an RGBD sensor and a GUI for
users to 'point' at the target region with a mouse to acquire 3D information.
Algorithms that can extract important parameters from the selected points are
designed. To avoid large internal force induced by the misalignment of the
robot orientation and the normal of the door plane, we design a module that can
compute the normal of the plane by pointing at three non-collinear points and
then drive the robot to the desired orientation. We carried out experiments on
real robot. The result shows that the designed GUI and algorithms can help find
the necessary parameters stably and get the robot prepared for further
operations.


title:
Topology trivialization transition in random non-gradient autonomous
  ODE's on a sphere

abstract:
  We calculate the mean total number of equilibrium points in a system of $N$
random autonomous ODE's introduced by Cugliandolo et al. in 1997 to describe
non-relaxational glassy dynamics on the high-dimensional sphere. In doing it we
suggest a new approach which allows such a calculation to be done most
straightforwardly, and is based on efficiently incorporating the Langrange
multiplier into the Kac-Rice framework. Analysing the asymptotic behaviour for
large $N$ we confirm that the phenomenon of 'topology trivialization' revealed
earlier for other systems holds also in the present framework with
nonrelaxational dynamics. Namely, by increasing the variance of the random
'magnetic field' term in dynamical equations we find a 'phase transition' from
the exponentially abundant number of equilibria down to just two equilibria.
Classifying the equilibria in the nontrivial phase by stability remains an open
problem.

categories: math-ph cond-mat.dis-nn cond-mat.stat-mech math.DS math.MP


title: Coupled-channel Dalitz plot analysis of $D^+\to K^- \pi^+\pi^+$ decay

abstract:
  We demonstrate that partial wave amplitudes extracted from $D^+\to
K^-\pi^+\pi^+$ Dalitz plot with a unitary coupled-channel model are
significantly different from those obtained with an isobar model. The unitary
coupled-channel model takes account of hadronic rescattering mechanisms
involving all three mesons that have been missed in conventioanl isobar model
analyses. The rescattering mechanisms contribute largely, and can triplicate
the $D^+\to {K}^-\pi^+\pi^+$ decay width within our analysis. These findings
deliver a warning that analysis results obtained with isobar models should be
looked with a caution. The determination of the CKM angle $\gamma/\phi_3$ is a
highly relevant problem.


title: Quaternionic geometry in dimension eight

abstract:
  We describe the 8-dimensional Wolf spaces as cohomogeneity one
SU(3)-manifolds, and discover perturbations of the quaternion-kaehler metric on
the simply-connected 8-manifold G_2/SO(4) that carry a closed fundamental
4-form but are not Einstein.


title:
Location Sensitive Deep Convolutional Neural Networks for Segmentation
  of White Matter Hyperintensities

abstract:
  The anatomical location of imaging features is of crucial importance for
accurate diagnosis in many medical tasks. Convolutional neural networks (CNN)
have had huge successes in computer vision, but they lack the natural ability
to incorporate the anatomical location in their decision making process,
hindering success in some medical image analysis tasks.
  In this paper, to integrate the anatomical location information into the
network, we propose several deep CNN architectures that consider multi-scale
patches or take explicit location features while training. We apply and compare
the proposed architectures for segmentation of white matter hyperintensities in
brain MR images on a large dataset. As a result, we observe that the CNNs that
incorporate location information substantially outperform a conventional
segmentation method with hand-crafted features as well as CNNs that do not
integrate location information. On a test set of 46 scans, the best
configuration of our networks obtained a Dice score of 0.791, compared to 0.797
for an independent human observer. Performance levels of the machine and the
independent human observer were not statistically significantly different
(p-value=0.17).


title:
Strength and stability of active ligand-receptor bonds: a microtubule
  attached to a wall by molecular motor tethers

abstract:
  We develop a stochastic kinetic model of a pre-formed attachment of a
mictrotuble (MT) with a cell cortex, in which the MT is tethered to the cell by
a group of active motor proteins. Such an attachment is a particularly unique
case of ligand-receptor bonds: The MT ligand changes its length (and thus
binding sites) with time by polymerization-depolymerization kinetics, while
multiple motor receptors tend to walk actively along the MT length. These
processes, combined with force-mediated unbinding of the motors, result in an
elaborate behavior of the MT connection to the cell cortex. We present results
for the strength and lifetime of the system through the well-established
force-clamp and force-ramp protocols when external tension is applied to the
MT. The simulation results reveal that the MT-cell attachment behaves as a
catch-bond or slip-bond depending on system parameters. We provide analytical
approximations of the lifetime and discuss implications of our results on
in-vitro experiments.


title:
An Efficient Uplink Multi-Connectivity Scheme for 5G mmWave Control
  Plane Applications

abstract:
  The millimeter wave (mmWave) frequencies offer the potential of orders of
magnitude increases in capacity for next-generation cellular systems. However,
links in mmWave networks are susceptible to blockage and may suffer from rapid
variations in quality. Connectivity to multiple cells - at mmWave and/or
traditional frequencies - is considered essential for robust communication. One
of the challenges in supporting multi-connectivity in mmWaves is the
requirement for the network to track the direction of each link in addition to
its power and timing. To address this challenge, we implement a novel uplink
measurement system that, with the joint help of a local coordinator operating
in the legacy band, guarantees continuous monitoring of the channel propagation
conditions and allows for the design of efficient control plane applications,
including handover, beam tracking and initial access. We show that an
uplink-based multi-connectivity approach enables less consuming, better
performing, faster and more stable cell selection and scheduling decisions with
respect to a traditional downlink-based standalone scheme. Moreover, we argue
that the presented framework guarantees (i) efficient tracking of the user in
the presence of the channel dynamics expected at mmWaves, and (ii) fast
reaction to situations in which the primary propagation path is blocked or not
available.


title: Contact manifolds with flexible fillings

abstract:
  We prove that all flexible Weinstein fillings of a given contact manifold
with vanishing first Chern class have isomorphic integral cohomology; in
certain cases, we prove that all flexible fillings are symplectomorphic. As an
application, we show that in dimension at least 5 any almost contact class that
has an almost Weinstein filling has infinitely many different contact
structures. Similar methods are used to construct the first known infinite
family of almost symplectomorphic Weinstein domains whose contact boundaries
are not contactomorphic. We also prove relative analogs of our results, which
we apply to Lagrangians in cotangent bundles.


title: On Finding Small Sets that Influence Large Networks

abstract:
  We consider the problem of selecting a minimum size subset of nodes in a
network, that allows to activate all the nodes of the network. We present a
fast and simple algorithm that, in real-life networks, produces solutions that
outperform the ones obtained by using the best algorithms in the literature. We
also investigate the theoretical performances of our algorithm and give proofs
of optimality for some classes of graphs. From an experimental perspective,
experiments also show that the performance of the algorithms correlates with
the modularity of the analyzed network. Moreover, the more the influence among
communities is hard to propagate, the less the performances of the algorithms
differ. On the other hand, when the network allows some propagation of
influence between different communities, the gap between the solutions returned
by the proposed algorithm and by the previous algorithms in the literature
increases.


title: Bilateral sums related to Ramanujan-like series

abstract:
  We define bilateral series related to Ramanujan-like series for $1/\pi^2$.
Then, we conjecture a property of them and give some applications.


title: Spectral analysis of a generalized buckling problem on a ball

abstract:
  In this paper, the spectrum of the following fourth order problem
\begin{equation*}
  \begin{cases}
  \Delta^2 u+\nu u=-\lambda \Delta u &\text{in } D_1,\newline
  u=\partial_r u= 0 &\text{on } \partial D_1,
  \end{cases} \end{equation*} where $D_1$ is the unit ball in ${\mathbb R}^N$,
is determined for $\nu < 0$ as well as the nodal properties of the
corresponding eigenfunctions. In particular, we show that the first eigenvalue
is simple and that the corresponding eigenfunction is radial and (up to a
multiplicative factor) positive and decreasing with respect to the radius. This
completes earlier results obtained for $\nu \ge 0$ and for $\nu <0$.


title: Translation Quality Estimation using Recurrent Neural Network

abstract:
  This paper describes our submission to the shared task on word/phrase level
Quality Estimation (QE) in the First Conference on Statistical Machine
Translation (WMT16). The objective of the shared task was to predict if the
given word/phrase is a correct/incorrect (OK/BAD) translation in the given
sentence. In this paper, we propose a novel approach for word level Quality
Estimation using Recurrent Neural Network Language Model (RNN-LM) architecture.
RNN-LMs have been found very effective in different Natural Language Processing
(NLP) applications. RNN-LM is mainly used for vector space language modeling
for different NLP problems. For this task, we modify the architecture of
RNN-LM. The modified system predicts a label (OK/BAD) in the slot rather than
predicting the word. The input to the system is a word sequence, similar to the
standard RNN-LM. The approach is language independent and requires only the
translated text for QE. To estimate the phrase level quality, we use the output
of the word level QE system.


title:
Nanoparticle charge-transfer interactions induce surface dependent
  conformational changes in apolipoprotein biocorona

abstract:
  Upon introduction into a biological system, engineered nanomaterials (ENMs)
rapidly associate with a variety of biomolecules such as proteins and lipids to
form a biocorona. The presence of biocorona influences nano-bio interactions
considerably, and could ultimately result in altered biological responses.
Apolipoprotein A-I (ApoA-I), the major constituent of high-density lipoprotein
(HDL), is one of the most prevalent proteins found in ENM-biocorona
irrespective of ENM nature, size, and shape. Given the importance of ApoA-I in
HDL and cholesterol transport, it is necessary to understand the mechanisms of
ApoA-I adsorption and the associated structural changes for assessing
consequences of ENM exposure. Here, we used a comprehensive array of
microscopic and spectroscopic tools to elucidate the interactions between
ApoA-I and 100 nm Ag nanoparticles (AgNPs) with four different surface
functional groups. We found that the protein adsorption and secondary
structural changes are highly dependent on the surface functionality. Our
electrochemical studies provided new evidence for charge transfer interactions
that influence ApoA-I unfolding. While the unfolding of ApoA-I on AgNPs did not
significantly modify their cellular uptake and short-term cytotoxicity, we
observed that it strongly altered the ability of only some AgNPs to generate
reactive oxygen species in macrophages. Our results shed new light on the
importance of surface functionality and charge transfer interactions in
biocorona formation.

categories: physics.bio-ph cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.soft


title:
On the sighting of unicorns: a variational approach to computing
  invariant sets in dynamical systems

abstract:
  We propose to compute approximations to general invariant sets in dynamical
systems by minimizing the distance between an appropriately selected finite set
of points and its image under the dynamics. We demonstrate, through
computational experiments that this approach can successfully converge to
approximations of (maximal) invariant sets of arbitrary topology, dimension and
stability as, e.g., saddle type invariant sets with complicated dynamics. We
further propose to extend this approach by adding a Lennard-Jones type
potential term to the objective function which yields more evenly distributed
approximating finite point sets and perform corresponding numerical
experiments.


title:
Complete coverage of space favors modularity of the grid system in the
  brain

abstract:
  Grid cells in the entorhinal cortex fire when animals that are exploring a
certain region of space occupy the vertices of a triangular grid that spans the
environment. Different neurons feature triangular grids that differ in their
properties of periodicity, orientation and ellipticity. Taken together, these
grids allow the animal to maintain an internal, mental representation of
physical space. Experiments show that grid cells are modular, i.e. there are
groups of neurons which have grids with similar periodicity, orientation and
ellipticity. We use statistical physics methods to derive a relation between
variability of the properties of the grids within a module and the range of
space that can be covered completely (i.e. without gaps) by the grid system
with high probability. Larger variability shrinks the range of representation,
providing a functional rationale for the experimentally observed co-modularity
of grid cell periodicity, orientation and ellipticity. We obtain a scaling
relation between the number of neurons and the period of a module, given the
variability and coverage range. Specifically, we predict how many more neurons
are required at smaller grid scales than at larger ones.


title: Characterizations of graded Pr\"ufer $\star$-multiplication domains, II

abstract:
  Let $R=\bigoplus_{\alpha\in\Gamma}R_{\alpha}$ be a graded integral domain and
$\star$ be a semistar operation on $R$. For $a\in R$, denote by $C(a)$ the
ideal of $R$ generated by homogeneous components of $a$ and
for$f=f_0+f_1X+\cdots+f_nX^n\in R[X]$, let $\A_f:=\sum_{i=0}^nC(f_i)$. Let
$N(\star):=\{f\in R[X]\mid f\neq0\text{and}\A_f^{\star}=R^{\star}\}$. In this
paper we study relationships between ideal theoretic properties of
$\NA(R,\star):=R[X]_{N(\star)}$ and the homogeneous ideal theoretic properties
of $R$. For example we show that $R$ is a graded
Pr\"ufer-$\star$-multiplication domain if and only if $\NA(D,\star)$ is a
Pr\"ufer domain if and only if $\NA(R,\star)$ is a B\'ezout domain. We also
determine when $\NA(R,v)$ is a PID.


title:
Restriction and induction for supercharacters of finite groups of
  triangular type

abstract:
  It is proved the the restriction of any supercharacter of a finite group of
triangular type on its subgroup is a sum of supercharacters with nonnegative
integer coefficients. We define superinduction and prove the analog of the
Frobenius formula for supercharacters.


title:
Spin Interaction under the Collision of Two Kerr-(anti-)de Sitter Black
  Holes

abstract:
  We have investigated spin interaction under the collision of Kerr-(anti-)de
Sitter black holes. The potential of a spin interaction is dependent on the
relative rotating directions of the black holes, and this potential can be
released as gravitational radiation under the collision. The radiation depends
on the cosmological constant and corresponds to the potential of the spin
interaction at a limit where one of the black holes is assumed to have small
mass and angular momentum. Then, we have shown, approximately, the overall
behaviors of the upper bounds on the radiation using thermodynamics. From these
bounds, the spin interaction can consistently contribute to the radiation. In
addition, the radiation depends on the stability of the black hole synthesized
from the collision.


title: Renormalized stress-energy tensor of an evaporating spinning black hole

abstract:
  We employ a recently developed mode-sum regularization method to compute the
renormalized stress-energy tensor of a quantum field in the Kerr background
metric (describing a stationary spinning black hole). More specifically, we
consider a minimally-coupled massless scalar field in the Unruh vacuum state,
the quantum state corresponding to an evaporating black hole. The computation
is done here for the case $a=0.7M$, using two different variants of the method:
$t$-splitting and $\varphi$-splitting, yielding good agreement between the two
(in the domain where both are applicable). We briefly discuss possible
implications of the results for computing semiclassical corrections to certain
quantities, and also for simulating dynamical evaporation of a spinning black
hole.


title:
Long-range spin correlations in a honeycomb spin model with magnetic
  field

abstract:
  We consider spin-$\frac{1}{2}$ model on the honeycomb lattice in the presence
of weak magnetic field $h\ll J$. Such a perturbation treated in the second
order over $h$ leads to the power-law decay of irreducible spin correlation
function $S(\mathbf{r},t)=\left\langle \left\langle
s^{z}_r(t)s^{z}_0(0)\right\rangle \right\rangle \propto
h_{z}^{2}f(t,\mathbf{r})$, where $f(t,\mathbf{r})\propto \lbrack \max
(t,Jr)]^{-4}$ is an oscillating function of $\mathbf{r}$, with a wavelength
equal to 3 lattice constants. In the present Letter we sum main terms in all
orders of the perturbation theory for the correlation function
$S(\mathbf{r},t)$ in the limit of large $r,t$. Our results can be understood in
terms of the effective low-energy Hamiltonian written in terms of Majorana
fermions, which in the presence of magnetic field acquire vector potential $A_x
\propto h_z^2$. Correspondingly, the wave vector of the oscillations in
$S(\mathbf{r},t)$ changes according to $\delta k \propto h_z^2$. We also
compute the dynamic structure factor $S(\mathbf{p},\omega)$; in the vicinity of
$\mathbf{p}_K$ corresponding to the inter-conical points excitations it reads
as
$S(\mathbf{p},\omega)-S(\mathbf{p}_K,\omega)\propto\sqrt{\omega^2-3J^2(\mathbf{p}-\mathbf{p}_K)^2}$.


title:
Efficient Rectangular Maximal-Volume Algorithm for Rating Elicitation in
  Collaborative Filtering

abstract:
  Cold start problem in Collaborative Filtering can be solved by asking new
users to rate a small seed set of representative items or by asking
representative users to rate a new item. The question is how to build a seed
set that can give enough preference information for making good
recommendations. One of the most successful approaches, called Representative
Based Matrix Factorization, is based on Maxvol algorithm. Unfortunately, this
approach has one important limitation --- a seed set of a particular size
requires a rating matrix factorization of fixed rank that should coincide with
that size. This is not necessarily optimal in the general case. In the current
paper, we introduce a fast algorithm for an analytical generalization of this
approach that we call Rectangular Maxvol. It allows the rank of factorization
to be lower than the required size of the seed set. Moreover, the paper
includes the theoretical analysis of the method's error, the complexity
analysis of the existing methods and the comparison to the state-of-the-art
approaches.


title:
Joint Multiuser Downlink Beamforming and Admission Control for Green
  Cloud-RANs with Limited Fronthaul Based on Mixed Integer Semi-definite
  Program

abstract:
  With the dense deployment of the remote radio heads (RRHs), the huge network
power consumption has become a great challenge for green cloud radio access
networks (Cloud-RANs), and multiuser downlink beamforming has been proposed as
a promising solution. Moreover, the increasing number of mobile users (MUs)
causes that admission control is essential for Cloud-RAN with limited fronthaul
capacity and predefined power budget. In this paper, we consider the problem of
joint multiuser downlink beamforming and admission control (JBAC) to enhance
the admitted MUs in the network and reduce the network power consumption, while
taking into account the Quality of Service requirements of the MUs, the power
budget constraints and fronthaul limitation. It is shown that the JBAC problem
is a mixed integer nonlinear problem, and still non-convex even though the
continuous relaxation is adopted. Therefore, we first transform the JBAC
problem into a Mixed-Integer Semidefinite Program. Then, we propose a bound
improving Branch and Bound algorithm to yield the near-optimal solution. For
practical application, a polynomial-time heuristic algorithm is proposed to
derive the sub-optimal solution. Extensive simulations are conducted with
different system configurations to show the effectiveness of the proposed two
schemes.


title:
One more recursive-theoretic characterization of the Topological Vaught
  Conjecture

abstract:
  We prove in ZF a recursive-theoretic characterization of the Topological
Vaught Conjecture by revisiting the fact that orbits in Polish $G$-spaces are
Borel sets.


title:
Dynamical analysis of NGC 110: cluster of fainter stars or data
  fluctuation?

abstract:
  The stellar enhancement of the cluster NGC 110 is investigated in various
optical and infrared (IR) bands. The radial density profile of the IR region
does not show a stellar enhancement in the central region of the cluster. This
stellar deficiency may be occurring by undetected fainter stars due to the
contamination effect of massive stars. Since, our analysis is not indicating
the stellar enhancement below 16.5 mag of I band, therefore the cluster is
assumed to be a group of fainter stars. The proposed magnitude scatter factor
would be an excellent tool to understand the characteristic of
colour-scattering of stars. The most probable members do not coincide with the
model isochronic fitting in the optical bands due to poor data quality of P P
MXL catalogue. The different values of the mean proper motions are found for
the fainter stars of the cluster and field regions, whereas similar values are
obtained for radial zones of the cluster. The symmetrical distribution of
fainter stars of the core are found around the best solution of isochrone. The
mass function and mass segregation studies are not possible due to higher
uncertainty of the photometric data. The number of the massive stars of the
cluster region is low in comparison with the field region due to completed
evolution life of the massive stars.


title: Theory of plasmonic effects in nonlinear optics: the case of graphene

abstract:
  We develop a microscopic large-$N$ theory of electron-electron interaction
corrections to multi-legged Feynman diagrams describing second- and third-order
nonlinear response functions. Our theory, which reduces to the well-known
random phase approximation in the linear-response limit, is completely general
and is useful to understand all second- and third-order nonlinear effects,
including harmonic generation, wave mixing, and photon drag. We apply our
theoretical framework to the case of graphene, by carrying out microscopic
calculations of the second- and third-order nonlinear response functions of an
interacting two-dimensional (2D) gas of massless Dirac fermions. We compare our
results with recent measurements, where all-optical launching of graphene
plasmons has been achieved by virtue of the finiteness of the quasi-homogeneous
second-order nonlinear response of this inversion-symmetric 2D material.


title:
Bio-Soliton Model that predicts Non-Thermal Electromagnetic Radiation
  Frequency Bands, that either Stabilize or Destabilize Life Conditions

abstract:
  Solitons, as self-reinforcing solitary waves, interact with complex
biological phenomena such as cellular self-organisation. Soliton models are
able to describe a spectrum of electromagnetism modalities that can be applied
to understand the physical principles of biological effects in living cells, as
caused by electromagnetic radiation. A bio-soliton model is proposed, that
enables to predict which eigen-frequencies of non-thermal electromagnetic waves
are life-sustaining and which are, in contrast, detrimental for living cells.
The particular effects are exerted by a range of electromagnetic wave
frequencies of one-tenth of a Hertz till Peta Hertz, that show a pattern of
twelve bands, if positioned on an acoustic frequency scale. The model was
substantiated by a meta-analysis of 240 published papers of biological
radiation experiments, in which a spectrum of non-thermal electromagnetic waves
were exposed to living cells and intact organisms. These data support the
concept of coherent quantized electromagnetic states in living organisms and
the theories of Davydov, Fr\"ohlich and Pang. A spin-off strategy from our
study is discussed in order to design bio-compatibility promoting
semi-conducting materials and to counteract potential detrimental effects due
to specific types of electromagnetic radiation produced by man-made
electromagnetic technologies.


title:
Origins and control of the polarization splitting in exciton-polaritons
  microwires

abstract:
  We report on the experimental investigation of the polarization-dependent
energy splitting in the lower exciton-polariton branches of a 1D microcavity.
The splitting observed for the lowest branch can reach up to 1 meV. It does not
result from low temperature thermal constraints but from anisotropic mechanical
internal strains induced by etching. Those strains remove the degeneracy both
in the photonic ($\delta E_{\mathrm{ph}}$) and excitonic ($\delta
E_{\mathrm{exc}}$) components of the polariton but also in the photon-exciton
coupling ($\delta\Omega$). Those three contributions are accurately infered
from experimental data. It appears that the sign and magnitude of the
polarization splitting as well as the linear polarization of the corresponding
polariton eigenstates can be tuned through the bare exciton-photon detuning.
Moreover, no dependence on the width of the wire (from 3 to 7 $\mathrm{\mu}$m)
is observed. We propose a mechanical model explaining the universality of those
observations paving the way to the engineering of polarization eigenstates in
microwires exciton-polaritons.


title:
Search for top quark decays via Higgs-boson-mediated flavor-changing
  neutral currents in pp collisions at sqrt(s) = 8 TeV

abstract:
  A search is performed for Higgs-boson-mediated flavor-changing neutral
currents in the decays of top quarks. The search is based on proton-proton
collision data corresponding to an integrated luminosity of 19.7 inverse
femtobarns at a center-of-mass energy of 8 TeV collected with the CMS detector
at the LHC. Events in which a top quark pair is produced with one top quark
decaying into a charm or up quark and a Higgs boson (H), and the other top
quark decaying into a bottom quark and a W boson are selected. The Higgs boson
in these events is assumed to subsequently decay into either dibosons or
difermions. No significant excess is observed above the expected standard model
background, and an upper limit at the 95% confidence level is set on the
branching fraction B(t to Hc) of 0.40% and B(t to Hu) of 0.55%, where the
expected upper limits are 0.43% and 0.40%, respectively. These results
correspond to upper limits on the square of the flavor-changing Higgs boson
Yukawa couplings |lambda[tc]^H|^2 < 6.9E-3 and |lambda[tu]^H|^2 < 9.8E-3.


title:
Almost global asymptotic stability of a grid-connected synchronous
  generator

abstract:
  We study the global asymptotic behavior of a grid-connected constant field
current synchronous generator (SG). The grid is regarded as an "infinite bus",
i.e. a three-phase AC voltage source. The generator does not include any
controller other than the frequency droop loop. This means that the mechanical
torque applied to this generator is an affine function of its angular velocity.
The negative slope of this function is the frequency droop constant. We derive
sufficient conditions on the SG parameters under which there exist exactly two
periodic state trajectories for the SG, one stable and another unstable, and
for almost all initial states, the state trajectory of the SG converges to the
stable periodic trajectory (all the angles are measured modulo $2\pi$). Along
both periodic state trajectories, the angular velocity of the SG is equal to
the grid frequency. Our sufficient conditions are easy to check
computationally. An important tool in our analysis is an integro-differential
equation called the {\em exact swing equation}, which resembles a forced
pendulum equation and is equivalent to our fourth order model of the
grid-connected SG. Apart from our objective of providing an analytical proof
for a global asymptotic behavior observed in a classical dynamical system, a
key motivation for this work is the development of synchronverters which are
inverters that mimic the behavior of SGs. Understanding the global dynamics of
SGs can guide the choice of synchronverter parameters and operation. As an
application we find a set of stable nominal parameters for a 500 kW
synchronverter.


title:
Classification of all alternatives to the Born rule in terms of
  informational properties

abstract:
  The standard postulates of quantum theory can be divided into two groups: the
first one characterizes the structure and dynamics of pure states, while the
second one specifies the structure of measurements and the corresponding
probabilities. In this work we keep the first group of postulates and
characterize all alternatives to the second group that give rise to
finite-dimensional sets of mixed states. We prove a correspondence between all
these alternatives and a class of representations of the unitary group. Some
features of these probabilistic theories are identical to quantum theory, but
there are important differences in others. For example, some theories have
three perfectly distinguishable states in a two-dimensional Hilbert space.
Others have exotic properties such as lack of "bit symmetry", the violation of
"no simultaneous encoding" (a property similar to information causality) and
the existence of maximal measurements without phase groups. We also analyze
which of these properties single out the Born rule.


title:
Dip-hump temperature dependence of Specific Heat and Effects of Pairing
  Fluctuations in the Weak-coupling Side of a $p$-wave Interacting Fermi Gas

abstract:
  We investigate the specific heat $C_V$ at constant volume in the normal state
of a $p$-wave interacting Fermi gas. Including $p$-wave pairing fluctuations
within the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we
show that, in the weak-coupling side, $C_V$ exhibits a dip-hump behavior as a
function of the temperature. While the dip is associated with the pseudogap
phenomenon near $T_{\rm c}$, the hump structure is found to come from the
suppression of Fermi quasiparticle scattering into a $p$-wave molecular state
in the Fermi degenerate regime. Since the latter phenomenon does not occur in
the ordinary $s$-wave interacting Fermi gas, it may be viewed as a
characteristic phenomenon associated with a $p$-wave pairing interaction.


title: Digital Makeup from Internet Images

abstract:
  We present a novel approach of color transfer between images by exploring
their high-level semantic information. First, we set up a database which
consists of the collection of downloaded images from the internet, which are
segmented automatically by using matting techniques. We then, extract image
foregrounds from both source and multiple target images. Then by using image
matting algorithms, the system extracts the semantic information such as faces,
lips, teeth, eyes, eyebrows, etc., from the extracted foregrounds of the source
image. And, then the color is transferred between corresponding parts with the
same semantic information. Next we get the color transferred result by
seamlessly compositing different parts together using alpha blending. In the
final step, we present an efficient method of color consistency to optimize the
color of a collection of images showing the common scene. The main advantage of
our method over existing techniques is that it does not need face matching, as
one could use more than one target images. It is not restricted to head shot
images as we can also change the color style in the wild. Moreover, our
algorithm does not require to choose the same color style, same pose and image
size between source and target images. Our algorithm is not restricted to
one-to-one image color transfer and can make use of more than one target images
to transfer the color in different parts in the source image. Comparing with
other approaches, our algorithm is much better in color blending in the input
data.


title:
The Effect of Corner Modes in the Initial Conditions of Cosmological
  Simulations

abstract:
  In view of future high-precision large-scale structure surveys, it is
important to quantify the percent and subpercent level effects in cosmological
$N$-body simulations from which theoretical predictions are drawn. One such
effect involves deciding whether to zero all modes above the one-dimensional
Nyquist frequency, the so-called "corner" modes, in the initial conditions. We
investigate this effect by comparing power spectra, density distribution
functions, halo mass functions, and halo profiles in simulations with and
without these modes. For a simulation with a mass resolution of $m_p \sim
10^{11}\,h^{-1}\,M_{\odot}$, we find that at $z>6$, the difference in the
matter power spectrum is large at wavenumbers above $\sim 80$\% of
$k_{\rm{Ny}}$, reducing to below 2\% at all scales by $z\sim 3$. Including
corner modes results in a better match between low- and high-resolution
simulations at wavenumbers around the Nyquist frequency of the low-resolution
simulation, but the effect of the corner modes is smaller than the effect of
particle discreteness. The differences in mass functions are 3\% for the
smallest halos at $z=6$ for the $m_p \sim 10^{11}\,h^{-1}\,M_{\odot}$
simulation, but we find no significant difference in the stacked profiles of
well-resolved halos at $z \leq 6$. Thus removing power at
$|\mathbf{k}|>k_{\rm{Ny}}$ in the initial conditions of cosmological
simulations has a small effect on small scales and high redshifts, typically
below a few percent.


title:
Curious case of gravitational lensing by binary black holes: a tale of
  two photon spheres, new relativistic images and caustics

abstract:
  Binary black holes have been in limelight off late due to the detection of
gravitational waves from coalescing compact binaries in the events GW150914 and
GW151226. In this paper we study gravitational lensing by the binary black
holes modeled as equal mass Majumdar-Papapetrou dihole metric and show that
this system displays features that are quite unprecedented and absent in any
other lensing configuration investigated so far. We restrict our attention to
the light rays which move on the plane midway between the two identical black
holes, which allows us to employ techniques developed for the equatorial
lensing in spherically symmetric spacetimes. If distance between the two black
holes is below a certain threshold value, the system admits two photon spheres.
As in the case of single black hole, infinitely many relativistic images are
formed due to the light rays which turn back from the region outside the outer
(unstable) photon sphere, all of which lie beyond a critical angular radius
with respect to the lens. However in the presence of the inner (stable) photon
sphere, the effective potential now increases again and the light rays that
enter the outer photon sphere can turn back, leading to the formation of a new
set of infinitely many relativistic images, all of which lie below the critical
radius from the lens mentioned above. As the distance between the two black
hole increases, two photon spheres approach each other, merge and eventually
disappear. In the absence of photon sphere, apart from the formation of a
finite number of discrete relativistic images, the system remarkably admits a
radial caustic, which has never been observed in the context of relativistic
lensing before. Thus the system of binary black hole admits novel features both
in the presence and absence of photon spheres. We discuss possible
observational signatures and implications of binary black hole lensing.


title: How square ice helps lubrication

abstract:
  In the context of friction we use atomistic molecular-dynamics simulations to
investigate water confined between graphene sheets over a wide range of
pressures. We find that thermal equilibration of the confined water is hindered
at high pressures. We demonstrate that, under the right conditions, square ice
can form in an asperity, and that it is similar to cubic ice VII and ice X. We
simulate sliding of atomically flat graphite on the square ice and find
extremely low friction due to structural superlubricity. The conditions needed
for square ice to form correspond to low sliding speeds, and we suggest that
the ice observed in experiments of friction on wet graphite is of this type.


title:
Toroidal Compactifications and Dimension Formulas for Spaces of Modular
  Forms for Orthogonal Shimura Varieties

abstract:
  In this paper we describe the general theory of constructing toroidal
compactifications of locally symmetric spaces and using these to compute
dimension formulas for spaces of modular forms. We focus explicitly on the case
of the orthogonal locally symmetric spaces arising from quadratic forms of
signature $(2,n)$, giving explicit details of the constructions, structures and
results in these cases. This article does not give explicit cone
decompositions, compute explicit intersection pairings, or count cusps and thus
does not give any complete formulas for the dimensions.
  This article is still `in preparation'.


title: Delayed collapses of BECs in relation to AdS gravity

abstract:
  We numerically investigate spherically symmetric collapses in the
Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential.
Even below threshold for direct collapse, the wave function bounces off from
the origin and may eventually become singular after a number of oscilla- tions
in the trapping potential. This is reminiscent of the evolution of Einstein
gravity sourced by a scalar field in Anti-de Sitter space where collapse
corresponds to black hole formation. We carefully examine the long time
evolution of the wave function for continuous families of initial states in
order to sharpen out this qualitative coincidence which may bring new insights
in both directions. On one hand, we comment on possible implications for the
so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the
other hand, Gross-Pitaevskii provides a toy model to study the relevance of
either the resonance conditions or the nonlinearity for the problem of Anti-de
Sitter instability.


title:
High-Energy Non-Thermal and Thermal Emission from GRB141207A detected by
  Fermi

abstract:
  The bright long gamma-ray burst GRB 141207A was observed by the {\it Fermi
Gamma-ray Space Telescope} and detected by both instruments onboard. The
observations show that the spectrum in the prompt phase is not well described
by the canonical empirical Band function alone, and that an additional
power-law component is needed. In the early phase of the prompt emission, a
modified blackbody with a hard low-energy photon index ($\alpha$ = +0.2 --
+0.4) is detected, which suggests a photospheric origin. In a finely
time-resolved analysis, the spectra are also well fitted by the modified
blackbody combined with a power-law function. We discuss the physical
parameters of the photosphere such as the bulk Lorentz factor of the
relativistic flow and the radius. We also discuss the physical origin of the
extra power-law component observed during the prompt phase in the context of
different models such as leptonic and hadronic scenarios in the internal shock
regime and synchrotron emission in the external forward shock. In the afterglow
phase, the temporal and spectral behaviors of the temporally extended
high-energy emission and the fading X-ray emission detected by XRT on-board
{\it Swift} are consistent with synchrotron emission in a radiative external
forward shock.


title: Stability of the integral control of stable nonlinear systems

abstract:
  PI controllers are the most widespread type of controllers and there is an
intuitive understanding that if their gains are sufficiently small and of the
correct sign, then they always work. In this paper we try to give some rigorous
backing to this claim, under specific assumptions. Let $\bf P$ be a nonlinear
system described by $\dot x=f(x,u)$, $y=g(x)$, where the state trajectory $x$
takes values in $R^n$, $u$ and $y$ are scalar and $f,g$ are of class $C^1$. We
assume that there is a Lipschitz function $\Xi:[u_{min},u_{max}]\rightarrow
R^n$ such that for every constant input $u_0\in[u_{min},u_{max}]$, $\Xi(u_0)$
is an exponentially stable equilibrium point of $\bf P$. We also assume that
$G(u)=g(\Xi(u))$, which is the steady state input-output map of $\bf P$, is
strictly increasing. Denoting $y_{min}=G(u_{min})$ and $y_{max}=G(u_{max})$, we
assume that the reference value $r$ is in $(y_{min},y_{max})$. Our aim is that
$y$ should track $r$, i.e., $y\rightarrow r$ as $t\rightarrow\infty$, while the
input of $P$ is only allowed to be in $[u_{min},u_{max}]$. For this, we
introduce a variation of the integrator, called the saturating integrator, and
connect it in feedback with $\bf P$ in the standard way, with gain $k>0$. We
show that for any small enough $k$, the closed-loop system is (locally)
exponentially stable around an equilibrium point $(Xi(u_r),u_r)$, with a large
region of attraction $X_T\subset R^n\times[u_{min},u_{max}]$. When the state
$(x(t),u(t))$ of the closed-loop system converges to $(\Xi(u_r),u_r)$, then the
tracking error $r-y$ tends to zero. The compact set $X_T$ can be made larger by
choosing a larger parameter $T>0$, resulting in smaller $k$.


title: Noise-induced transport in the motion of trapped ions

abstract:
  The interplay of noise and quantum coherence in transport gives rise to rich
dynamics relevant for a variety of systems. In this work, we put forward a
proposal for an experiment testing noise-induced transport in the vibrational
modes of a chain of trapped ions. We focus on the case of transverse modes,
considering multiple-isotope chains and an "angle trap", where the transverse
trapping varies along the chain. This variation induces localization of the
motional modes and therefore suppresses transport. By suitably choosing the
action of laser fields that couple to the internal and external degrees of
freedom of the ions, we show how to implement effective local dephasing on the
modes, broadening the vibrational resonances. This leads to an overlap of the
local mode frequencies, giving rise to a pronounced increase in the transport
of excitations along the chain. We propose an implementation and measurement
scheme which require neither ground-state cooling nor low heating rates, and we
illustrate our results with a simulation of the dynamics for a chain of three
ions.


title:
Search for electroweak production of charginos in final states with two
  tau leptons in pp collisions at sqrt(s) = 8 TeV

abstract:
  Results are presented from a search for the electroweak production of
supersymmetric particles in pp collisions in final states with two tau leptons.
The data sample corresponds to an integrated luminosity between 18.1 inverse
femtobarns and 19.6 inverse femtobarns depending on the final state of tau
lepton decays, at sqrt(s) = 8 TeV, collected by the CMS experiment at the LHC.
The observed event yields in the signal regions are consistent with the
expected standard model backgrounds. The results are interpreted using
simplified models describing the pair production and decays of charginos or tau
sleptons. For models describing the pair production of the lightest chargino,
exclusion limits are obtained in the plane of chargino mass vs. neutralino mass
under the following assumptions: the chargino decays into third-generation
sleptons, which are taken as the lightest sleptons, and the slepton masses lie
midway between those of the chargino and the neutralino. Chargino masses below
420 GeV are excluded at a 95% confidence level in the limit of a massless
neutralino, and for neutralino masses up to 100 GeV, chargino masses up to 325
GeV are excluded at 95% confidence level. Constraints are also placed on the
cross section for pair production of tau sleptons as a function of mass,
assuming a massless neutralino.


title: Probabilistic Articulated Real-Time Tracking for Robot Manipulation

abstract:
  We propose a probabilistic filtering method which fuses joint measurements
with depth images to yield a precise, real-time estimate of the end-effector
pose in the camera frame. This avoids the need for frame transformations when
using it in combination with visual object tracking methods.
  Precision is achieved by modeling and correcting biases in the joint
measurements as well as inaccuracies in the robot model, such as poor extrinsic
camera calibration. We make our method computationally efficient through a
principled combination of Kalman filtering of the joint measurements and
asynchronous depth-image updates based on the Coordinate Particle Filter.
  We quantitatively evaluate our approach on a dataset recorded from a real
robotic platform, annotated with ground truth from a motion capture system. We
show that our approach is robust and accurate even under challenging conditions
such as fast motion, significant and long-term occlusions, and time-varying
biases. We release the dataset along with open-source code of our approach to
allow for quantitative comparison with alternative approaches.


title:
Fault Detection Engine in Intelligent Predictive Analytics Platform for
  DCIM

abstract:
  With the advancement of huge data generation and data handling capability,
Machine Learning and Probabilistic modelling enables an immense opportunity to
employ predictive analytics platform in high security critical industries
namely data centers, electricity grids, utilities, airport etc. where downtime
minimization is one of the primary objectives. This paper proposes a novel,
complete architecture of an intelligent predictive analytics platform, Fault
Engine, for huge device network connected with electrical/information flow.
Three unique modules, here proposed, seamlessly integrate with available
technology stack of data handling and connect with middleware to produce online
intelligent prediction in critical failure scenarios. The Markov Failure module
predicts the severity of a failure along with survival probability of a device
at any given instances. The Root Cause Analysis model indicates probable
devices as potential root cause employing Bayesian probability assignment and
topological sort. Finally, a community detection algorithm produces correlated
clusters of device in terms of failure probability which will further narrow
down the search space of finding route cause. The whole Engine has been tested
with different size of network with simulated failure environments and shows
its potential to be scalable in real-time implementation.


title: Gibbard-Satterthwaite Success Stories and Obvious Strategyproofness

abstract:
  The Gibbard-Satterthwaite Impossibility Theorem holds that dictatorship is
the only Pareto optimal and strategyproof social choice function on the full
domain of preferences. Much of the work in mechanism design aims at getting
around this impossibility theorem. Three grand success stories stand out. On
the domains of single peaked preferences, of house matching, and of quasilinear
preferences, there are appealing Pareto optimal and strategyproof social choice
functions. We investigate whether these success stories are robust to
strengthening strategyproofness to obvious strategyproofness (OSP), recently
introduced by Li (2015).
  For single peaked preferences, we characterize the class of OSP-implementable
and unanimous social choice functions as dictatorships with safeguards against
extremism - mechanisms (which turn out to also be Pareto optimal) in which the
dictator can choose the outcome, but other agents may prevent the dictator from
choosing an outcome that is too extreme. Median voting is consequently not
OSP-implementable. Indeed, the only OSP-implementable quantile rules choose
either the minimal or the maximal ideal point. For house matching, we
characterize the class of OSP-implementable and Pareto optimal matching rules
as sequential barter with lurkers - a significant generalization over bossy
variants of bipolar serially dictatorial rules. While Li (2015) shows that
second-price auctions are OSP-implementable when only one good is sold, we show
that this positive result does not extend to the case of multiple goods. Even
when all agents' preferences over goods are quasilinear and additive, no
welfare-maximizing auction where losers pay nothing is OSP-implementable when
more than one good is sold. Our analysis makes use of a gradual revelation
principle, an analog of the (direct) revelation principle for OSP mechanisms
that we present and prove.


title: Coloring Graphs to Produce Properly Colored Walks

abstract:
  For a connected graph, we define the proper-walk connection number as the
minimum number of colors needed to color the edges of a graph so that there is
a walk between every pair of vertices without two consecutive edges having the
same color. We show that the proper-walk connection number is at most three for
all cyclic graphs, and at most two for bridgeless graphs. We also characterize
the bipartite graphs that have proper-walk connection number equal to two, and
show that this characterization also holds for the analogous problem where one
is restricted to properly colored paths.


title:
Product states and Schmidt rank of mutually unbiased bases in dimension
  six

abstract:
  We show that if a set of four mutually unbiased bases (MUBs) in
$\mathbb{C}^6$ exists and contains the identity, then any other basis in the
set contains at most two product states and at the same time has Schmidt rank
at least three. Here both the product states and the Schmidt rank are defined
over the bipartite space $\mathbb{C}^2\otimes\mathbb{C}^3$. We also investigate
the connection of the Sinkhorn normal form of unitary matrices to the fact that
there is at least one vector unbiased to any two orthonormal bases in any
dimension.


title:
Topological Phase Transitions and a Two-Dimensional Weyl Superconductor
  in a Half-Metal/Superconductor Heterostructure

abstract:
  We find a series of topological phase transitions in a
half-metal/superconductor heterostructure, by tuning the direction of the
magnetization of the half-metal film. These include transitions between a
topological superconducting phase with a bulk gap and another phase without a
bulk gap but has a ubiquitous local gap. At the same time, the edge states
change from counter-propagating Majorana edge modes to unidirectional Majorana
edge modes. In addition, we find transitions between the second phase and a
nodal phase which turns out to be a two-dimensional Weyl superconductor with
Fermi line edge states. We identify the topological invariants relevant to each
phase and the symmetry that protects the Weyl superconductivity phase.


title:
Bipolar Anodization Enables the Fabrication of Controlled Arrays of TiO2
  Nanotube Gradients

abstract:
  We report here a new concept, the use of bipolar electrochemistry, which
allows the rapid and wireless growth of self-assembled TiO2 NT layers that
consist of highly defined and controllable gradients in NT length and diameter.
The gradient height and slope can be easily tailored with the time of
electrolysis and the applied electric field, respectively. As this technique
allows obtaining in one run a wide range of self-ordered TiO2 NT dimensions, it
provides the basis for rapid screening of TiO2 NT properties. In two examples,
we show how these gradient arrays can be used to screen for an optimized
photocurrent response from TiO2 NT based devices such as dye-sensitized solar
cells.


title:
Enhanced valley splitting in monolayer WSe2 due to magnetic exchange
  field

abstract:
  Exploiting the valley degree of freedom to store and manipulate information
provides a novel paradigm for future electronics. A monolayer transition metal
dichalcogenide (TMDC) with broken inversion symmetry possesses two degenerate
yet inequivalent valleys, offering unique opportunities for valley control
through helicity of light. Lifting the valley degeneracy by Zeeman splitting
has been demonstrated recently, which may enable valley control by a magnetic
field. However, the realized valley splitting is modest, (~ 0.2 meV/T). Here we
show greatly enhanced valley spitting in monolayer WSe2, utilizing the
interfacial magnetic exchange field (MEF) from a ferromagnetic EuS substrate. A
valley splitting of 2.5 meV is demonstrated at 1 T by magneto-reflectance
measurements. Moreover, the splitting follows the magnetization of EuS, a
hallmark of the MEF. Utilizing MEF of a magnetic insulator can induce magnetic
order, and valley and spin polarization in TMDCs, which may enable valleytronic
and quantum computing applications.


title:
When can a formality quasi-isomorphism over rationals be constructed
  recursively?

abstract:
  Let $O$ be a differential graded (possibly colored) operad defined over
rationals. Let us assume that there exists a zig-zag of quasi-isomorphisms
connecting $O \otimes K$ to its cohomology, where $K$ is any field extension of
rationals. We show that for a large class of such dg operads, a formality
quasi-isomorphism for $O$ exists and can be constructed recursively. Every step
of our recursive procedure involves a solution of a finite dimensional linear
system and it requires no explicit knowledge about the zig-zag of
quasi-isomorphisms connecting $O \otimes K$ to its cohomology.


title: Discrete-time trawl processes with long memory

abstract:
  We introduce a class of discrete time stationary trawl processes taking real
or integer values and written as sums of past values of independent `seed'
processes on shrinking intervals (`trawl heights'). Related trawl processes in
continuous time were studied in Barndorff-Nielsen (2011) and Barndorff-Nielsen
et al. (2014), however in our case, the i.i.d. seed processes can be very
general and need not be infinitely divisible. In the case when the trawl height
decays with the lag as $j^{-\alpha}$ for some $1< \alpha < 2 $, the trawl
process exhibits long memory and its covariance decays as $j^{1-\alpha}$. We
show that under general conditions on generic seed process, the normalized
partial sums of such trawl process may tend either to a fractional Brownian
motion or to an $\alpha$-stable L\'evy process.


title: H2 Mapping on Pt-loaded TiO2 Nanotube Gradient Arrays

abstract:
  We describe a rapid screening technique for determining the optimal
characteristics of nano- photocatalysts for the production of H2 on a single
surface. Arrays of TiO2 nanotubes (NTs) with a gradient in length and diameter
were fabricated by bipolar anodization and a perpendicular gradient of Pt
nanoparticles (NPs) was generated by the toposelective decoration of the TiO2
NTs. Photocatalytic hydrogen evolution was locally triggered with a UV laser
beam and the arrays were screened in x- and y-direction for spatially resolved
kinetic measurements and the mapping of the optimal hydrogen production. By
using this technique, we demonstrate the time-efficient and straightforward
determination of the tube dimensions and the Pt amount for an optimized H2
production. The concept holds promise to generally improve the study of many
photoreactions as a function of the physicochemical characteristic of
nano-photocatalysts, which renders it highly attractive for the optimization of
various important chemical processes.


title: Chalcogenide Perovskites- an Emerging Class of Ionic Semiconductors

abstract:
  We report the synthesis and characterization of a novel class of ionic
semiconductor materials- inorganic chalcogenide perovskites. Several different
compounds including BaZrS3, CaZrS3, SrTiS3 and SrZrS3 were synthesized by high
temperature sulfurization of their oxide counterparts. Their crystal structures
were identified by XRD and composition by EDX. UV-vis and photoluminescence
measurements confirmed that they are direct gap semiconductors with band gap
values consistent with theoretical predictions. By adopting an anion alloying
approach, we demonstrate widely tunable band gap from 1.73 eV to 2.87 eV. These
strongly ionic semiconductors provide a new avenue for engineering the
semiconducting properties for applications such as energy harvesting, solid
state lighting and sensing.


title:
A Comparison of Anodic TiO2 Nanotube Membranes used for Front-side
  Illuminated Dye-Sensitized Solar Cells

abstract:
  In the present work we compare TiO2 nanotube lift-off strategies for the
construction of front-side illuminated dye-sensitized solar cells (DSSCs).
Anodic nanotube layers were detached from the metallic back contact by using
different techniques and transferred onto an FTO substrate. We show that if we
use an optimized potential step treatment to fabricate membranes, DSSC cell
efficiencies can be significantly increased (>8%). This improved efficiency is
ascribed to higher specific dye-loading and enhanced electron transport
properties of optimally fabricated TiO2 nanotube membranes.


title: Unveiling Extreme Anisotropy in Elastic Structured Media

abstract:
  Periodic structures can be engineered to exhibit unique properties observed
at symmetry points, such as zero group velocity, Dirac cones and saddle points;
identifying these, and the nature of the associated modes, from a direct
reading of the dispersion surfaces is not straightforward, especially in
three-dimensions or at high frequencies when several dispersion surfaces fold
back in the Brillouin zone. A recently proposed asymptotic high frequency
homogenisation theory is applied to a challenging time-domain experiment with
elastic waves in a pinned metallic plate. The prediction of a narrow
high-frequency spectral region where the effective medium tensor dramatically
switches from positive definite to indefinite is confirmed experimentally; a
small frequency shift of the pulse carrier results in two distinct types of
highly anisotropic modes. The underlying effective equation mirrors this
behaviour with a change in form from elliptic to hyperbolic exemplifying the
high degree of wave control available and the importance of a simple and
effective predictive model.


title: Set avoiding squares in $\mathbb{Z}_m$

abstract:
  We prove that for all squarefree $m$ and any set $A\subset\mathbb{Z}_m$ such
that $A-A$ does not contain non-zero squares the bound $|A|\leq
m^{1/2}(3n)^{1.5n}$ holds, where $n$ denotes the number of odd prime divisors
of $m$.