title:
Gauss-Bonnet Cosmology Unifying Late and Early-time Acceleration Eras
  with Intermediate Eras

abstract:
  In this paper we demonstrate that with vacuum $F(G)$ gravity it is possible
to describe the unification of late and early-time acceleration eras with the
radiation and matter domination era. The Hubble rate of the unified evolution
contains two mild singularities, so called Type IV singularities, and the
evolution itself has some appealing features, such as the existence of a
deceleration-acceleration transition at late times. We also address
quantitatively a fundamental question related to modified gravity models
description of cosmological evolution: Is it possible for all modified gravity
descriptions of our Universe evolution, to produce a nearly scale invariant
spectrum of primordial curvature perturbations? As we demonstrate, the answer
for the $F(G)$ description is no, since the resulting power spectrum is not
scale invariant, in contrast to the $F(R)$ description studied in the
literature. Therefore, although the cosmological evolution can be realized in
the context of vacuum $F(G)$ gravity, the evolution is not compatible with the
observational data, in contrast to the $F(R)$ gravity description of the same
cosmological evolution.


title: Axioms of adaptivity for separate marking

abstract:
  Mixed finite element methods with flux errors in $H(div)$-norms and
div-least-squares finite element methods require a separate marking strategy in
obligatory adaptive mesh-refining. The refinement indicator $\sigma^2(\mathcal
T,K)=\eta^2(\mathcal T,K)+\mu^2(K)$ of a finite element domain $K$ in an
admissible triangulation $\mathcal T$ consists of some residual-based error
estimator $\eta(\mathcal T,K)$ with some reduction property under local
mesh-refining and some data approximation error $\mu(K)$. Separate marking
means either D\"orfler marking if $\mu^2(\mathcal T) \leq \kappa
\eta^2(\mathcal T)$ or otherwise an optimal data approximation algorithm runs
with controlled accuracy as established in [Carstensen, Rabus, Math.Comp. 2011;
Rabus, J.Numer.Math. 2015].
  The axioms are abstract and sufficient conditions on the estimators
$\eta(\mathcal T,K)$ and data approximation errors $\mu(K)$ for optimal
asymptotic convergence rates. The enfolded set of axioms simplifies
\cite{CFP14} for collective marking, treats separate marking established for
the first time in an abstract framework, generalizes [Carstensen, Park, SIAM
J.Numer.Anal. 2015] for least-squares schemes, and extends [Carstensen, Rabus,
Math.Comp. 2011] to the mixed FEM with flux error control in $H(div)$.


title:
Optimal adaptive control for quantum metrology with time-dependent
  Hamiltonians

abstract:
  Quantum metrology has been studied for a wide range of systems with
time-independent Hamiltonians. For systems with time-dependent Hamiltonians,
however, due to the complexity of dynamics, little has been known about quantum
metrology. Here we investigate quantum metrology with time-dependent
Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher
information for parameters in time-dependent Hamiltonians, and show proper
Hamiltonian control is necessary to optimize the Fisher information. We derive
the optimal Hamiltonian control, which is generally adaptive, and the
measurement scheme to attain the optimal Fisher information. In a minimal
example of a qubit in a rotating magnetic field, we find a surprising result
that the fundamental limit of $T^{2}$ time scaling of quantum Fisher
information can be broken with time-dependent Hamiltonians, which reaches
$T^{4}$ in estimating the rotation frequency of the field. We conclude by
considering level crossings in the derivatives of the Hamiltonians, and point
out additional control is necessary for that case.


title:
Integrative modeling of sprout formation in angiogenesis: coupling the
  VEGFA-Notch signaling in a dynamic stalk-tip cell selection

abstract:
  During angiogenesis, new blood vessels headed by a migrating endothelial tip
cell sprout from pre-existing ones. This process is known to be regulated by
two signaling pathways concurrently, vascular endothelial growth factor A
(VEGFA) and Notch-Delta. Extracellular VEGFA activates the intracellular
Notch-Delta pathway in nearby endothelial cells which results in endothelial
(stalk, tip) differentiation. Retinal astrocytes appear to play a crucial role
in polarizing new sprouts by secreting VEGFA. \emph{In vivo} retinal
angiogenesis experiments in neonatal mouse generated quantitative data on daily
cell counts and morphological data of vascular network expanding over
fibronectin-rich matrix. Based on this set of data and other existing ones, we
developed a cell-based, multiscale mathematical model using the cellular Potts
model framework to investigate the sprout evolution by integrating the VEGFA
and Notch-Delta signaling pathways. The model incorporates three levels of
description: intracellular, intercellular, and extracellular. Starting with a
single astrocyte embedded in a fibronectin-rich matrix, we use the model to
assess different scenarios regarding VEGFA levels and its interaction with
matrix proteins. Simulation results suggest that astrocyte-derived VEGFA
gradients along with heterogeneous ECM reproduces sprouting morphology, and the
extension speed is in agreement with experimental data in 7 days postnatal
mouse retina. Results also reproduce empirical observations in sprouting
angiogenesis, including anastomosis, dynamic tip cell competition, and sprout
regression as a result of Notch blockade.


title:
Constructing perturbation theory kernels for large-scale structure in
  generalized cosmologies

abstract:
  We present a simple numerical scheme for perturbation theory (PT)
calculations of large-scale structure. Solving the evolution equations for
perturbations numerically, we construct the PT kernels as building blocks of
statistical calculations, from which the power spectrum and/or correlation
function can be systematically computed. The scheme is especially applicable to
the generalized structure formation including modified gravity, in which the
analytic construction of PT kernels is intractable. As an illustration, we show
several examples for power spectrum calculations in $f(R)$ gravity and
$\Lambda$CDM models.


title:
A short proof of the deformation property of Bridgeland stability
  conditions

abstract:
  The key result in the theory of Bridgeland stability conditions is the
property that they form a complex manifold. This comes from the fact that given
any small deformation of the central charge, there is a unique way to
correspondingly deform the stability condition.
  We give a short direct proof of a strong version of this deformation
property.


title: Latent Constrained Correlation Filters for Object Localization

abstract:
  There is a neglected fact in the traditional machine learning methods that
the data sampling can actually lead to the solution sampling. We consider this
observation to be important because having the solution sampling available
makes the variable distribution estimation, which is a problem in many
learning-related applications, more tractable. In this paper, we implement this
idea on correlation filter, which has attracted much attention in the past few
years due to its high performance with a low computational cost. More
specifically, we propose a new method, named latent constrained correlation
filters (LCCF) by mapping the correlation filters to a given latent subspace,
in which we establish a new learning framework that embeds distribution-related
constraints into the original problem. We further introduce a subspace based
alternating direction method of multipliers (SADMM) to efficiently solve the
optimization problem, which is proved to converge at the saddle point. Our
approach is successfully applied to two different tasks inclduing eye
localization and car detection. Extensive experiments demonstrate that LCCF
outperforms the state-of-the-art methods when samples are suffered from noise
and occlusion.


title: Three pion nucleon coupling constants

abstract:
  There exist four pion nucleon coupling constants, $f_{\pi^0, pp}$,
$-f_{\pi^0, nn}$, $f_{\pi^+, pn} /\sqrt{2}$ and $ f_{\pi^-, np} /\sqrt{2}$
which coincide when up and down quark masses are identical and the electron
charge is zero. While there is no reason why the pion-nucleon-nucleon coupling
constants should be identical in the real world, one expects that the small
differences might be pinned down from a sufficiently large number of
independent and mutually consistent data. Our discussion provides a rationale
for our recent determination $$f_p^2 = 0.0759(4) \, , \quad f_{0}^2 = 0.079(1)
\,, \quad f_{c}^2 = 0.0763(6) \, , $$ based on a partial wave analysis of the
$3\sigma$ self-consistent nucleon-nucleon Granada-2013 database comprising 6713
published data in the period 1950-2013.


title: An asymptotically exact theory of smart sandwich shells

abstract:
  An asymptotically exact two-dimensional theory of elastic-piezoceramic
sandwich shells is derived by the variational-asymptotic method. The error
estimation of the constructed theory is given in the energetic norm. As an
application, analytical solution to the problem of forced vibration of a
circular elastic plate partially covered by two piezoceramic patches with
thickness polarization excited by a harmonic voltage is found.


title:
Non-markovian mesoscopic dissipative dynamics of open quantum spin
  chains

abstract:
  We study the dissipative dynamics of $N$ quantum spins with Lindblad
generator consisting of operators scaling as fluctuations, namely with the
inverse square-root of $N$. In the large $N$ limit, the microscopic dissipative
time-evolution converges to a non-Markovian unitary dynamics on strictly local
operators, while at the mesoscopic level of fluctuations it gives rise to a
dissipative non-Markovian dynamics. The mesoscopic time-evolution is Gaussian
and exhibits either a stable or an unstable asymptotic character; furthermore,
the mesoscopic dynamics builds correlations among fluctuations that survive in
time even when the original microscopic dynamics is unable to correlate local
observables.


title:
Properties of stationary statistical solutions of the three-dimensional
  Navier-Stokes equations

abstract:
  The stationary version of a modified definition of statistical solution for
the three-dimensional incompressible Navier-Stokes equations introduced in a
previous work is investigated. Particular types of such stationary statistical
solutions and their analytical properties are addressed. Results on the support
and carriers of these stationary statistical solutions are also given, showing
in particular that they are supported on the weak global attractor and are
carried by a more regular part of the weak global attractor containing
Leray-Hopf weak solutions which are locally strong solutions. Two
recurrence-type results related to these measures are also proved.


title: Quasilinear systems with linearizable characteristic webs

abstract:
  We classify quasilinear systems in Riemann invariants whose characteristic
webs are linearizable on every solution. Although the linearizability of an
individual web is a rather nontrivial differential constraint, the requirement
of linearizability of characteristic webs on all solutions imposes simple
second-order constraints for the characteristic speeds of the system. It is
demonstrated that every such system with n>3 components can be transformed by a
reciprocal transformation to n uncoupled Hopf equations. All our considerations
are local.


title: Running of the Running and Entropy Perturbations During Inflation

abstract:
  In single field slow-roll inflation, one expects that the spectral index $n_s
-1$ is first order in slow-roll parameters. Similarly, its running $\alpha_s =
dn_s/d \log k$ and the running of the running $\beta_s = d\alpha_s/d \log k$
are second and third order and therefore expected to be progressively smaller,
and usually negative. Hence, such models of inflation are in considerable
tension with a recent analysis hinting that $\beta_s$ may actually be positive,
and larger than $\alpha_s$. Motivated by this, in this work we ask the question
of what kinds of inflationary models may be useful in achieving such a
hierarchy of runnings, particularly focusing on two--field models of inflation
in which the late-time transfer of power from isocurvature to curvature modes
allows for a much more diverse range of phenomenology. We calculate the
runnings due to this effect and briefly apply our results to assessing the
feasibility of finding $|\beta_s| \gtrsim |\alpha_s|$ in some specific models.


title:
First-principles calculation of the stabilities of LMP/LAMP lithium
  superionic conductors against sodium-ion exchange in seawater

abstract:
  Electronic structure calculations carried out to estimate the free energies
of Na(aq)+ exchange for lithium in LiM2(PO4)3 (LMP, M=Si4+,Ge4+,Ti4+,Sn4+,Zr4+)
and Li1+xAlxM2-x(PO4)3 (LAMP; M=Ge4+,Ti4+, between 0 and 0.5) compounds in
seawater. The calculations show that resistance to sodium-ion exchange
increases with decreasing cell volume. For the pure LMP compounds, only the
hypothetical LiSi2(PO4)3 is predicted to be stable against sodium ion exchange
in aqueous solution. The calculations indicate that increasing the extent of
Al3+ substitution for M4+ in the LAMP compounds increases the resistance to
exchange, and that both LAGP and LATP can be stabilized against sodium exchange
for x greater than or equal to approximately 0.5 Li1+xAlxM2-x(PO4)3.


title:
Measuring anomalous WW$\gamma$ and t$\bar{\text{t}}\gamma$ couplings
  using top+$\gamma$ production at the LHC

abstract:
  We consider the electroweak production of a top quark in association with a
photon at the LHC to probe the electroweak top quark couplings
(t$\bar{\text{t}}\gamma$) as well as the triple gauge boson couplings
(WW$\gamma$). The study is based on the modifications of the
t$\bar{\text{t}}\gamma$ and WW$\gamma$ interactions via heavy degrees of
freedom in the form of dimension-six operators which we add to the standard
model Lagrangian. A binned angular asymmetry in single top quark plus photon
events and cross section ratio are proposed to probe the anomalous
  t$\bar{\text{t}}\gamma$ and WW$\gamma$ couplings. It is shown that the
proposed angular asymmetry can distinguish anomalous t$\bar{\text{t}}\gamma$,
WW$\gamma$ couplings from the standard model prediction and yield a great
sensitivity.


title:
Measurement of the top quark mass in the $t\bar{t}\to$ dilepton channel
  from $\sqrt{s}=8$ TeV ATLAS data

abstract:
  The top quark mass is measured in the $t\bar{t}\to$ dilepton channel (lepton
$= e, \mu$) using ATLAS data recorded in the year 2012 at the LHC. The data
were taken at a proton--proton centre-of-mass energy of $\sqrt{s}=$ 8 TeV and
correspond to an integrated luminosity of about 20.2 fb$^{-1}$. Exploiting the
template method, and using the distribution of invariant masses of
lepton--b-jet pairs, the top quark mass is measured to be $m_{top} =$ 172.99
$\pm$ 0.41 (stat) $\pm$ 0.74 (syst) GeV, with a total uncertainty of 0.84 GeV.
Finally, a combination with previous ATLAS $m_{top}$ measurements from
$\sqrt{s}=$7 TeV data in the $t\bar{t}\to$ dilepton and $t\bar{t}\to$
lepton+jets channels results in $m_{top} =$ 172.84 $\pm$ 0.34 (stat) $\pm$ 0.61
(syst) GeV, with a total uncertainty of 0.70 GeV.


title: Arithmetic Euler Top

abstract:
  The theory of differential equations has an arithmetic analogue in which
derivatives of functions are replaced by Fermat quotients of numbers. Many
classical differential equations (Riccati, Weierstrass, Painlev\'{e}, etc.)
were previously shown to possess arithmetic analogues. The paper introduces an
arithmetic analogue of the Euler differential equations for the rigid body.


title:
Search for the Standard Model Higgs boson produced by vector-boson
  fusion in 8 TeV $pp$ collisions and decaying to bottom quarks with the ATLAS
  detector

abstract:
  A search with the ATLAS detector is presented for the Standard Model Higgs
boson produced by vector-boson fusion and decaying to a pair of bottom quarks,
using 20.2 ${fb}^{-1}$ of LHC proton-proton collision data at $\sqrt{s}$ = 8
TeV. The signal is searched for as a resonance in the invariant mass
distribution of a pair of jets containing $b$-hadrons in vector-boson-fusion
candidate events. The yield is measured to be $-0.8 \pm 2.3$ times the Standard
Model cross-section for a Higgs boson mass of 125 GeV. The upper limit on the
cross-section times the branching ratio is found to be 4.4 times the Standard
Model cross-section at the 95% confidence level, consistent with the expected
limit value of 5.4 (5.7) in the background-only (Standard Model production)
hypothesis.


title: Discrete Calculus of Finite Sequences

abstract:
  The calculus of finite differences is a solid foundation for the development
of operations such as the derivative and the integral for infinite sequences.
Here we showed a way to extend it for finite sequences. We could then define
convexity for finite sequences and some related concepts. To finalize, we
propose a way to go from our extension to the calculus of finite differences.


title: On rational Dyck paths and the enumeration of factor-free Dyck words

abstract:
  Motivated by independent results of Bizley and Duchon, we study rational Dyck
paths and their subset of factor-free elements. On the one hand, we give a
bijection between rational Dyck paths and regular Dyck paths with ascents
colored by factor-free words. This bijection leads to a new statistic based on
the reducibility level of the paths for which we provide a corresponding
formula. On the other hand, we prove an inverse relation for certain sequences
defined via partial Bell polynomials, and we use it to derive a formula for the
enumeration of factor-free words. In addition, we give alternative formulas for
various enumerative sequences that appear in the context of rational Dyck
paths.


title: Integral Cayley Graphs over Dihedral Groups

abstract:
  In this paper, we give a necessary and sufficient condition for the
integrality of Cayley graphs over the dihedral group $D_n=\langle a,b\mid
a^n=b^2=1,bab=a^{-1}\rangle$. Moreover, we also obtain some simple sufficient
conditions for the integrality of Cayley graphs over $D_n$ in terms of the
Boolean algebra of $\langle a\rangle$, from which we find infinite classes of
integral Cayley graphs over $D_n$. In particular, we completely determine all
integral Cayley graphs over the dihedral group $D_p$ for a prime $p$.


title: Towards a Neural Statistician

abstract:
  An efficient learner is one who reuses what they already know to tackle a new
problem. For a machine learner, this means understanding the similarities
amongst datasets. In order to do this, one must take seriously the idea of
working with datasets, rather than datapoints, as the key objects to model.
Towards this goal, we demonstrate an extension of a variational autoencoder
that can learn a method for computing representations, or statistics, of
datasets in an unsupervised fashion. The network is trained to produce
statistics that encapsulate a generative model for each dataset. Hence the
network enables efficient learning from new datasets for both unsupervised and
supervised tasks. We show that we are able to learn statistics that can be used
for: clustering datasets, transferring generative models to new datasets,
selecting representative samples of datasets and classifying previously unseen
classes. We refer to our model as a neural statistician, and by this we mean a
neural network that can learn to compute summary statistics of datasets without
supervision.


title:
Stable and predictive functional domain selection with application to
  brain images

abstract:
  Motivated by increasing trends of relating brain images to a clinical outcome
of interest, we propose a functional domain selection (FuDoS) method that
effectively selects subregions of the brain associated with the outcome. View
each individual's brain as a 3D functional object, the statistical aim is to
distinguish the region where a regression coefficient $\beta(t)=0$ from
$\beta(t)\neq0$, where $t$ denotes spatial location. FuDoS is composed of two
stages of estimation. We first segment the brain into several small parts based
on the correlation structure. Then, potential subsets are built using the
obtained segments and their predictive performance are evaluated to select the
best subset, augmented by a stability selection criterion. We conduct extensive
simulations both for 1D and 3D functional data, and evaluate its effectiveness
in selecting the true subregion. We also investigate predictive ability of the
selected stable regions. To find the brain regions related to cognitive
ability, FuDoS is applied to the ADNI's PET data. Due to the induced
sparseness, the results naturally provide more interpretable information about
the relations between the regions and the outcome. Moreover, the selected
regions from our analysis show high associations with the expected anatomical
brain areas known to have memory-related functions.


title: Laplacians on smooth distributions

abstract:
  Let $M$ be a compact smooth manifold equipped with a positive smooth density
$\mu$ and $H$ be a smooth distribution endowed with a fiberwise inner product
$g$. We define the Laplacian $\Delta_H$ associated with $(H,\mu,g)$ and prove
that it gives rise to an unbounded self-adjoint operator in $L^2(M,\mu)$. Then,
assuming that $H$ generates a singular foliation $\mathcal F$, we prove that,
for any function $\varphi$ from the Schwartz space $\mathcal S(\mathbb R)$, the
operator $\varphi(\Delta_H)$ is a smoothing operator in the scale of
longitudinal Sobolev spaces associated with $\mathcal F$. The proofs are based
on pseudodifferential calculus on singular foliations developed by
Androulidakis and Skandalis and subelliptic estimates for $\Delta_H$.


title: Heisenberg scaling of imaging resolution by coherent enhancement

abstract:
  Classical imaging works by scattering photons from an object to be imaged,
and achieves resolution scaling as $1/\sqrt{t}$, with $t$ the imaging time. By
contrast, the laws of quantum mechanics allow one to utilize quantum coherence
to obtain imaging resolution that can scale as quickly as $1/t$ -- the
so-called "Heisenberg limit." However, ambiguities in the obtained signal often
preclude taking full advantage of this quantum enhancement, while imaging
techniques designed to be unambiguous often lose this optimal Heisenberg
scaling. Here, we demonstrate an imaging technique which combines unambiguous
detection of the target with Heisenberg scaling of the resolution. We also
demonstrate a binary search algorithm which can efficiently locate a coherent
target using the technique, resolving a target trapped ion to within 0.3% of
the $1/e^2$ diameter of the excitation beam.


title:
Resonant Raman scattering theory for Kitaev models and their Majorana
  fermion boundary modes

abstract:
  We study the inelastic light scattering response in two- (2D) and
three-dimensional (3D) Kitaev spin-liquid models with \ms band structures in
the symmetry classes BDI and D leading to protected gapless surface modes. We
present a detailed calculation of the resonant Raman/Brillouin scattering
vertex relevant to iridate and ruthenate compounds whose low-energy physics is
believed to be proximate to these spin-liquid phases. In the symmetry class
BDI, we find that while the resonant scattering on thin films can detect the
gapless boundary modes of spin liquids, the non-resonant processes do not
couple to them. For the symmetry class D, however, we find that the coupling
between both types of light-scattering processes and the low-energy surface
states is strongly suppressed. Additionally, we describe the effect of weak
time-reversal symmetry breaking perturbations on the bulk Raman response of
these systems.


title:
Optimality conditions applied to free-time multi-burn optimal orbital
  transfers

abstract:
  While the Pontryagin Maximum Principle can be used to calculate candidate
extremals for optimal orbital transfer problems, these candidates cannot be
guaranteed to be at least locally optimal unless sufficient optimality
conditions are satisfied. In this paper, through constructing a parameterized
family of extremals around a reference extremal, some second-order necessary
and sufficient conditions for the strong-local optimality of the free-time
multi-burn fuel-optimal transfer are established under certain regularity
assumptions. Moreover, the numerical procedure for computing these optimality
conditions is presented. Finally, two medium-thrust fuel-optimal trajectories
with different number of burn arcs for a typical orbital transfer problem are
computed and the local optimality of the two computed trajectories are tested
thanks to the second-order optimality conditions established in this paper.


title: Run-and-pause dynamics of cytoskeletal motor proteins

abstract:
  Cytoskeletal motor proteins are involved in major intracellular transport
processes which are vital for maintaining appropriate cellular function. The
motor exhibits distinct states of motility: active motion along filaments, and
effectively stationary phase in which it detaches from the filaments and
performs passive diffusion in the vicinity of the detachment point due to
cytoplasmic crowding. The transition rates between motion and pause phases are
asymmetric in general, and considerably affected by changes in environmental
conditions which influences the efficiency of cargo delivery to specific
targets. By considering the motion of molecular motor on a single filament as
well as a dynamic filamentous network, we present an analytical model for the
dynamics of self-propelled particles which undergo frequent pause phases. The
interplay between motor processivity, structural properties of filamentous
network, and transition rates between the two states of motility drastically
changes the dynamics: multiple transitions between different types of anomalous
diffusive dynamics occur and the crossover time to the asymptotic diffusive or
ballistic motion varies by several orders of magnitude. We map out the phase
diagrams in the space of transition rates, and address the role of initial
conditions of motion on the resulting dynamics.


title: Degree-inverting involutions on matrix algebras

abstract:
  Let $F$ be an algebraically closed field of characteristic zero, and $G$ be a
finite abelian group. If $A=\oplus_{g\in G} A_g$ is a $G$-graded algebra, we
study degree-inverting involutions on $A$, i.e., involutions $*$ on $A$
satisfying $(A_g)^*\subseteq A_{g^{-1}}$, for all $g\in G$. We describe such
involutions for the full $n\times n$ matrix algebra over $F$ and for the
algebra of $n\times n$ upper triangular matrices.


title:
Adapting Sampling Interval of Sensor Networks Using On-Line
  Reinforcement Learning

abstract:
  Monitoring Wireless Sensor Networks (WSNs) are composed of sensor nodes that
report temperature, relative humidity, and other environmental parameters. The
time between two successive measurements is a critical parameter to set during
the WSN configuration because it can impact the WSN's lifetime, the wireless
medium contention and the quality of the reported data. As trends in monitored
parameters can significantly vary between scenarios and within time,
identifying a sampling interval suitable for several cases is also challenging.
In this work, we propose a dynamic sampling rate adaptation scheme based on
reinforcement learning, able to tune sensors' sampling interval on-the-fly,
according to environmental conditions and application requirements. The primary
goal is to set the sampling interval to the best value possible so as to avoid
oversampling and save energy, while not missing environmental changes that can
be relevant for the application. In simulations, our mechanism could reduce up
to 73% the total number of transmissions compared to a fixed strategy and,
simultaneously, keep the average quality of information provided by the WSN.
The inherent flexibility of the reinforcement learning algorithm facilitates
its use in several scenarios, so as to exploit the broad scope of the Internet
of Things.


title:
The Price of Anarchy in Transportation Networks: Data-Driven Evaluation
  and Reduction Strategies

abstract:
  Among the many functions a Smart City must support, transportation dominates
in terms of resource consumption, strain on the environment, and frustration of
its citizens. We study transportation networks under two different routing
policies, the commonly assumed selfish user-centric routing policy and a
socially-optimal system-centric one. We consider a performance metric of
efficiency - the Price of Anarchy (PoA) - defined as the ratio of the total
travel latency cost under selfish routing over the corresponding quantity under
socially-optimal routing. We develop a data-driven approach to estimate the
PoA, which we subsequently use to conduct a case study using extensive actual
traffic data from the Eastern Massachusetts road network. To estimate the PoA,
our approach learns from data a complete model of the transportation network,
including origin-destination demand and user preferences. We leverage this
model to propose possible strategies to reduce the PoA and increase efficiency.


title:
Some isoperimetric inequalities on $\mathbb{R} ^N$ with respect to
  weights $|x|^\alpha $

abstract:
  We solve a class of isoperimetric problems on $\mathbb{R}^N $ with respect to
weights that are powers of the distance to the origin. For instance we show
that if $k\in [0,1]$, then among all smooth sets $\Omega$ in $\mathbb{R} ^N$
with fixed Lebesgue measure, $\int_{\partial \Omega } |x|^k \,
\mathscr{H}_{N-1} (dx)$ achieves its minimum for a ball centered at the origin.
Our results also imply a weighted Polya-Sz\"ego principle. In turn, we
establish radiality of optimizers in some Caffarelli-Kohn-Nirenberg
inequalities, and we obtain sharp bounds for eigenvalues of some nonlinear
problems.


title: On a diffusion model with absorption and production

abstract:
  We discuss the structure of radial solutions of some superlinear elliptic
equations which model diffusion phenomena when both absorption and production
are present. We focus our attention on solutions defined in R (regular) or in R
\ {0} (singular) which are infinitesimal at infinity, discussing also their
asymptotic behavior. The phenomena we find are present only if absorption and
production coexist, i.e., if the reaction term changes sign. Our results are
then generalized to include the case where Hardy potentials are considered.


title:
Two-qubit correlations revisited: average mutual information, relevant
  (and useful) observables and an application to remote state preparation

abstract:
  Understanding how correlations can be used for quantum communication
protocols is a central goal of quantum information science. While many authors
have linked global measures of correlations such as entanglement or discord to
the performance of specific protocols, in general the latter may require only
correlations between specific observables. In this work, we first introduce a
general measure of correlations for two-qubit states based on the classical
mutual information between local observables. We then discuss the role of the
symmetry in the state's correlations distribution and accordingly provide a
classification of maximally mixed marginals states (MMMS). We discuss the
complementarity relation between correlations and coherence. By focusing on a
simple yet paradigmatic example, i.e., the remote state preparation protocol,
we introduce a method to systematically define proper protocol-tailored
measures of correlations. The method is based on the identification of those
correlations that are relevant (useful) for the protocol. The approach allows
on one hand to discuss the role of the symmetry of the correlations
distribution in determining the efficiency of the protocol, both for MMMS and
general two-qubit quantum states, and on the other hand to devise an optimized
protocol for non-MMMS that can have a better efficiency with respect to the
standard one. The scheme we propose can be extended to other communication
protocols and more general bipartite settings. Overall our findings clarify how
the key resources in simple communication protocols are the purity of the state
used and the symmetry of correlations distribution.


title:
Band structure reconstruction across nematic order in high quality FeSe
  single crystal as revealed by optical spectroscopy study

abstract:
  We perform an in-plane optical spectroscopy measurement on high quality FeSe
single crystals grown by a vapor transport technique. Below the structural
transition at $T_{\rm s}\sim$90 K, the reflectivity spectrum clearly shows a
gradual suppression around 400 cm$^{-1}$ and the conductivity spectrum shows a
peak at higher frequency. The energy scale of this gap-like feature is
comparable to the width of the band splitting observed by ARPES. The
low-frequency conductivity consists of two Drude components and the overall
plasma frequency is smaller than that of the FeAs based compounds, suggesting a
lower carrier density or stronger correlation effect. The plasma frequency
becomes even smaller below $T_{\rm s}$ which agrees with the very small Fermi
energy estimated by other experiments. Similar to iron pnictides, a clear
temperature-induced spectral weight transfer is observed for FeSe, being
indicative of strong correlation effect.


title:
Strong-Field S-Matrix Theory With Coulomb-Volkov Final State in All
  Orders

abstract:
  Despite its long standing usefulness for the analysis of various processes in
intense laser fields, it is well-known that the so-called strong-field KFR or
SFA ansatz does not account for the final-state Coulomb interaction. Due to its
importance for the ubiquitous ionisation process, numerous heuristic attempts
have been made during the last several decades to account for the final state
Coulomb interaction with in the SFA. Also to this end an ad hoc model with the
so-called Coulomb-Volkov final state was introduced a long time ago. However,
till now, no systematic strong-field S-matrix expansion using the
Coulomb-Volkov final state could be found. Here we solve this long standing
problem by determining the Coulomb-Volkov Hamiltonian, identifying the
rest-interaction in the final state, and explicitly constructng the
Coulomb-Volkov propagator (or Green's function). We employ them to derive the
complete S-matrix series for the ionisation amplitude governed by the
Coulomb-Volkov final state in all orders. The results are given in both
"velocity" and "length" gauges. We also present a gauge independent version of
the Coulomb-Volkov S-matrix series.


title:
Electronic and photonic counting statistics as probes of non-equilibrium
  quantum dynamics

abstract:
  When a mesoscopic conductor is coupled to a high-quality electromagnetic
cavity the flow of charges and the flux of photons leaking out of the cavity
can both depend strongly on the coupled quantum dynamics of the system. Using a
voltage-biased Josephson junction as a model system, we demonstrate that there
is a simple connection between the full counting statistics of the charges and
the photons in the long time limit. We then reveal the intimate relation
between the counting statistics and the nonlinear dynamics of the system,
uncovering novel regimes of coherent charge and photon transport associated
with bifurcations in the classical dynamics of the system.


title:
Searching for galactic axions through magnetized media: the QUAX
  proposal

abstract:
  We present a proposal to search for QCD axions with mass in the 200 $\mu$eV
range, assuming that they make a dominant component of dark matter. Due to the
axion-electron spin coupling, their effect is equivalent to the application of
an oscillating rf field with frequency and amplitude fixed by the axion mass
and coupling respectively. This equivalent magnetic field would produce spin
flips in a magnetic sample placed inside a static magnetic field, which
determines the resonant interaction at the Larmor frequency. Spin flips would
subsequently emit radio frequency photons that can be detected by a suitable
quantum counter in an ultra-cryogenic environment. This new detection technique
is crucial to keep under control the thermal photon background which would
otherwise produce a too large noise.


title:
Higgs Inflation, Reheating and Gravitino Production in No-Scale
  Supersymmetric GUTs

abstract:
  We extend our previous study of supersymmetric Higgs inflation in the context
of no-scale supergravity and grand unification, to include models based on the
flipped SU(5) and the Pati-Salam group. Like the previous SU(5) GUT model,
these yield a class of inflation models whose inflation predictions interpolate
between those of the quadratic chaotic inflation and Starobinsky-like
inflation, while avoiding tension with proton decay limits. We further analyse
the reheating process in these models, and derive the number of e-folds, which
is independent of the reheating temperature. We derive the corresponding
predictions for the scalar tilt and the tensor-to-scalar ratio in cosmic
microwave background perturbations, as well as discussing the gravitino
production following inflation.


title:
Poisson equation for the three loop ladder diagram in string theory at
  genus one

abstract:
  The three loop ladder diagram is a graph with six links and four cubic
vertices that contributes to the D^{12} R^4 amplitude at genus one in type II
string theory. The vertices represent the insertion points of vertex operators
on the toroidal worldsheet and the links represent scalar Green functions
connecting them. By using the properties of the Green function and manipulating
the various expressions, we obtain a modular invariant Poisson equation
satisfied by this diagram, with source terms involving one, two and three loop
diagrams. Unlike the source terms in the Poisson equations for diagrams at
lower orders in the momentum expansion or the Mercedes diagram, a particular
source term involves a five point function containing a holomorphic and a
antiholomorphic worldsheet derivative acting on different Green functions. We
also obtain simple equalities between topologically distinct diagrams, and
consider some elementary examples.


title:
Upholding the Unified Model for Active Galactic Nuclei: VLT/FORS2
  Spectropolarimetry of Seyfert 2 galaxies

abstract:
  The origin of the unification model for Active Galactic Nuclei (AGN) was the
detection of broad hydrogen recombination lines in the optical polarized
spectrum of the Seyfert 2 galaxy (Sy2) NGC 1068. Since then, a search for the
hidden broad-line region (HBLR) of nearby Sy2s started, but polarized broad
lines have only been detected in 30-40% of the nearby Sy2s observed to date.
Here we present new VLT/FORS2 optical spectropolarimetry of a sample of 15
Sy2s, including Compton-thin and Compton-thick sources. The sample includes six
galaxies without previously published spectropolarimetry, some of them normally
treated as non-hidden BLR (NHBLR) objects in the literature, four classified as
NHBLR, and five as HBLR based on previous data. We report >=4{\sigma}
detections of a HBLR in 11 of these galaxies (73% of the sample) and a
tentative detection in NGC 5793, which is Compton-thick according to the
analysis of X-ray data performed here. Our results confirm that at least some
NHBLRs are misclassified, bringing previous publications reporting differences
between HBLR and NHBLR objects into question. We detect broad H{\alpha} and
H{\beta} components in polarized light for 10 targets, and just broad H{\alpha}
for NGC 5793 and NGC 6300, with line widths ranging between 2100 and 9600 km/s.
High bolometric luminosities and low column densities are associated with
higher polarization degrees, but not necessarily with the detection of the
scattered broad components.


title:
Applying Gaussian distributed constraints to Gaussian distributed
  variables

abstract:
  This paper develops an analytical method of truncating inequality constrained
Gaussian distributed variables where the constraints are themselves described
by Gaussian distributions. Existing truncation methods either assume hard
constraints, or use numerical methods to handle uncertain constraints. The
proposed approach introduces moment-based Gaussian approximations of the
truncated distribution. This method can be applied to numerous problems, with
the motivating problem being Kalman filtering with uncertain constraints. In a
simulation example, the developed method is shown to outperform unconstrained
Kalman filtering by over 40% and hard-constrained Kalman filtering by over 17%.


title: A Minimax Approach to Supervised Learning

abstract:
  Given a task of predicting $Y$ from $X$, a loss function $L$, and a set of
probability distributions $\Gamma$ on $(X,Y)$, what is the optimal decision
rule minimizing the worst-case expected loss over $\Gamma$? In this paper, we
address this question by introducing a generalization of the principle of
maximum entropy. Applying this principle to sets of distributions with marginal
on $X$ constrained to be the empirical marginal from the data, we develop a
general minimax approach for supervised learning problems. While for some loss
functions such as squared-error and log loss, the minimax approach rederives
well-knwon regression models, for the 0-1 loss it results in a new linear
classifier which we call the maximum entropy machine. The maximum entropy
machine minimizes the worst-case 0-1 loss over the structured set of
distribution, and by our numerical experiments can outperform other well-known
linear classifiers such as SVM. We also prove a bound on the generalization
worst-case error in the minimax approach.


title: Decay modes of the excited pseudoscalar glueball

abstract:
  We study three different chiral Lagrangians that describe the two- and
three-body decays of an excited pseudoscalar glueball, $J^{PC}=0^{*-+}$, into
light mesons and charmonium states as well as into a scalar and pseudoscalar
glueball. We compute the decay channels for an excited pseudoscalar glueball
with a mass of $3.7$ GeV and consider a ground state pseudoscalar glueball of
mass $2.6$ GeV, following predictions from lattice QCD simulations. These
states and channels are in reach of the ongoing BESIII experiment and the PANDA
experiments at the upcoming FAIR facility experiment. We present the resulting
decay branching ratios with a parameter-free prediction.


title: Initialization Errors in Quantum Data Base Recall

abstract:
  This paper analyzes the relationship between initialization error and recall
of a specific memory in the Grover algorithm for quantum database search. It is
shown that the correct memory is obtained with high probability even when the
initial state is far removed from the correct one. The analysis is done by
relating the variance of error in the initial state to the recovery of the
correct memory and the surprising result is obtained that the relationship
between the two is essentially linear.


title: On irreducibility of Oseledets subspaces

abstract:
  For a cocycle of invertible real $n$-by-$n$ matrices, the Multiplicative
Ergodic Theorem gives an Oseledets subspace decomposition of $\mathbb{R}^n$;
that is, above each point in the base space, $\mathbb{R}^n$ is written as a
direct sum of equivariant subspaces, one for each Lyapunov exponent of the
cocycle. It is natural to ask if these summands may be further decomposed into
equivariant subspaces; that is, if the Oseledets subspaces are reducible. We
prove a theorem yielding sufficient conditions for irreducibility of the
trivial equivariant subspaces $\mathbb{R}^2$ and $\mathbb{C}^2$ for
$O_2(\mathbb{R})$-valued cocycles and give explicit examples where the
conditions are satisfied.


title:
Selective Unsupervised Feature Learning with Convolutional Neural
  Network (S-CNN)

abstract:
  Supervised learning of convolutional neural networks (CNNs) can require very
large amounts of labeled data. Labeling thousands or millions of training
examples can be extremely time consuming and costly. One direction towards
addressing this problem is to create features from unlabeled data. In this
paper we propose a new method for training a CNN, with no need for labeled
instances. This method for unsupervised feature learning is then successfully
applied to a challenging object recognition task. The proposed algorithm is
relatively simple, but attains accuracy comparable to that of more
sophisticated methods. The proposed method is significantly easier to train,
compared to existing CNN methods, making fewer requirements on manually labeled
training data. It is also shown to be resistant to overfitting. We provide
results on some well-known datasets, namely STL-10, CIFAR-10, and CIFAR-100.
The results show that our method provides competitive performance compared with
existing alternative methods. Selective Convolutional Neural Network (S-CNN) is
a simple and fast algorithm, it introduces a new way to do unsupervised feature
learning, and it provides discriminative features which generalize well.


title: Acoustic confinement in superlattice cavities

abstract:
  The large coupling rate between the acoustic and optical fields confined in
GaAs/AlAs superlattice cavities makes them appealing systems for cavity
optomechanics. We have developed a mathematical model based on the scattering
matrix that allows the acoustic guided modes to be predicted in nano and
micropillar superlattice cavities. We demonstrate here that the reflection at
the surface boundary considerably modifies the acoustic quality factor and
leads to significant confinement at the micropillar center. Our mathematical
model also predicts unprecedented acoustic Fano resonances on nanopillars
featuring small mode volumes and very high mechanical quality factors, making
them attractive systems for optomechanical applications.


title: Strong energy condition and the repulsive character of f(R) gravity

abstract:
  The Raychaudhuri equation enables to examine the whole spacetime structure
without specific solutions of Einstein's equations, playing a central role for
the understanding of the gravitational interaction in Cosmology. In General
Relativity, without considering a cosmological constant, a non-positive
contribution in the Raychaudhuri equation is usually interpreted as the
manifestation of the attractive character of gravity. In this case, particular
energy conditions -- indeed the strong energy condition -- must be assumed in
order to guarantee the attractive character. In the context of f(R) gravity,
however, even assuming the standard energy conditions one may have a positive
contribution to the Raychaudhuri equation. Besides providing a simple way to
explain the observed cosmic acceleration, this fact opens the possibility of a
repulsive character of this kind of gravity. In order to discuss physical
bounds on f(R) models, we address the attractive/non-attractive character of
f(R) gravity considering the Raychaudhuri equation and assuming the strong
energy condition along with recent estimates of the cosmographic parameters.


title:
Energy-Aware Relay Selection and Power Allocation for Multiple-User
  Cooperative Networks

abstract:
  This paper investigates the relay assignment and power allocation problem for
two different network power management policies: group lifetime maximization
(GLM) and minimum weighted total power (MWTP), with the aim of lifetime
maximization in symbol error rate (SER) constrained multipleuser cooperative
network. With optimal power allocation solution obtained for each policy, we
show that the optimal relay assignment can be obtained using bottleneck
matching (BM) algorithm and minimum weighted matching (MWM) algorithm for GLM
and MWTP policies, respectively. Since relay assignment with BM algorithm is
not power efficient, we propose a novel minimum bottleneck matching (MBM)
algorithm to solve the relay assignment problem optimally for GLM policy. To
further reduce the complexity of the relay assignment, we propose suboptimal
relay selection (SRS) algorithm which has linear complexity in number of source
and relay nodes. Simulation results demonstrate that the proposed relay
selection and power allocation strategies based on GLM policy have better
network lifetime performance over the strategies based on MWTP policy. Compared
to the MBM and SRS algorithm, relay assignment based on BM algorithm for GLM
policy has inferior network lifetime performance at low update interval. We
show that relay assignment based on MBM algorithm achieves maximum network
lifetime performance and relay assignment with SRS algorithm has performance
very close to it.


title:
Chiral-symmetry breaking and pion structure in the Covariant Spectator
  Theory

abstract:
  We introduce a covariant approach in Minkowski space for the description of
quarks and mesons that exhibits both chiral-symmetry breaking and confinement.
In a simple model for the interquark interaction the quark mass function is
obtained and used in the calculation of the pion form factor. We study the
effects of the mass function and of the different quark pole contributions on
the pion form factor.


title: Entanglement without hidden nonlocality

abstract:
  We consider Bell tests in which the distant observers can perform local
filtering before testing a Bell inequality. Notably, in this setup, certain
entangled states admitting a local hidden variable model in the standard Bell
scenario can nevertheless violate a Bell inequality after filtering, displaying
so-called hidden nonlocality. Here we ask whether all entangled states can
violate a Bell inequality after well-chosen local filtering. We answer this
question in the negative by showing that there exist entangled states without
hidden nonlocality. Specifically, we prove that some two-qubit Werner states
still admit a local hidden variable model after any possible local filtering on
a single copy of the state.


title: Nambu-Goldstone modes in the random phase approximation

abstract:
  I show that the kernel of the random phase approximation (RPA) matrix based
on a stable Hartree, Hartree-Fock, Hartree-Bogolyubov or
Hartree-Fock-Bogolyubov mean field solution is decomposed into a subspace with
a basis whose vectors are associated, in the equivalent formalism of a
classical Hamiltonian homogeneous of second degree in canonical coordinates,
with conjugate momenta of cyclic coordinates (Nambu-Goldstone modes) and a
subspace with a basis whose vectors are associated with pairs of a coordinate
and its conjugate momentum neither of which enters the Hamiltonian at all. In a
subspace complementary to the one spanned by all these coordinates including
the conjugate coordinates of the Nambu-Goldstone momenta, the RPA matrix
behaves as in the case of a zerodimensional kernel. This result was derived
very recently by Nakada as a corollary to a general analysis of RPA matrices
based on both stable and unstable mean field solutions. The present proof does
not rest on Nakada's general results.


title: AdS3/CFT2 and q-Poincare' superalgebras

abstract:
  We discover that a certain deformation of the 1+1 dimensional Poincare'
superalgebra is exactly realised in the massless sector of the AdS3/CFT2
integrable scattering problem. Deformed Poincar\'e superalgebras were
previously noticed to appear in the AdS5/CFT4 correspondence - which displays
only massive excitations -, but they were there only a partial symmetry. We
obtain a representation of the boost operator and its coproduct, and show that
the comultiplication exactly satisfies the homomorphism property. We present a
classical limit, and finally speculate on an analogy with the physics of
phonons.


title: Spectral Hirzebruch-Milnor classes of singular hypersurfaces

abstract:
  We introduce spectral Hirzebruch-Milnor classes for singular hypersurfaces.
These can be identified with Steenbrink spectra in the isolated singularity
case, and may be viewed as their global analogues in general. Their definition
uses vanishing cycles of mixed Hodge modules and the Todd class transformation.
These are compatible with the pushforward by proper morphisms, and the classes
can be calculated by using resolutions of singularities. Formulas for
Hirzebruch-Milnor classes of projective hypersurfaces in terms of these classes
are given in the case where the multiplicity of a generic hyperplane section is
not 1. These formulas using hyperplane sections instead of hypersurface ones
are easier to calculate in certain cases. Here we use the Thom-Sebastiani
theorem for the underlying filtered $D$-modules of vanishing cycles, from which
we can deduce the Thom-Sebastiani type theorem for spectral Hirzebruch-Milnor
classes. For the Chern classes after specializing to $y=-1$, we can give a
relatively simple formula for the localized Milnor classes, which implies a new
formula for the Euler numbers of projective hypersurfaces, using iterated
hyperplane sections. Applications to log canonical thresholds and Du Bois
singularities are also explained; for instance, the latter can be detected by
using Hirzebruch-Milnor classes in the projective hypersurface case.


title:
A translation invariant bipolaron in the Holstein model and
  superconductivity

abstract:
  Large-radius translation invariant (TI) bipolarons are considered in a
one-dimensional Holstein molecular chain. Criteria of their stability are
obtained. The energy of a translation invariant bipolaron is shown to be lower
than that of a bipolaron with broken symmetry. The results obtained are applied
to the problem of superconductivity in 1D-systems. It is shown that
TI-bipolaron mechanism of Bose-Einstein condensation can support
superconductivity even for infinite chain.


title: Non-aligned drawings of planar graphs

abstract:
  A non-aligned drawing of a graph is a drawing where no two vertices are in
the same row or column. Auber et al. showed that not all planar graphs have
non-aligned drawings that are straight-line, planar, and in the
minimal-possible $n\times n$-grid. They also showed that such drawings exist if
up to $n-3$ edges may have a bend. In this paper, we give algorithms for
non-aligned planar drawings that improve on the results by Auber et al. In
particular, we give such drawings in an $n\times n$-grid with significantly
fewer bends, and we study what grid-size can be achieved if we insist on having
straight-line drawings.


title:
Multi-resource defensive strategies for patrolling games with alarm
  systems

abstract:
  Security Games employ game theoretical tools to derive resource allocation
strategies in security domains. Recent works considered the presence of alarm
systems, even suffering various forms of uncertainty, and showed that
disregarding alarm signals may lead to arbitrarily bad strategies. The central
problem with an alarm system, unexplored in other Security Games, is finding
the best strategy to respond to alarm signals for each mobile defensive
resource. The literature provides results for the basic single-resource case,
showing that even in that case the problem is computationally hard. In this
paper, we focus on the challenging problem of designing algorithms scaling with
multiple resources. First, we focus on finding the minimum number of resources
assuring non-null protection to every target. Then, we deal with the
computation of multi-resource strategies with different degrees of coordination
among resources. For each considered problem, we provide a computational
analysis and propose algorithmic methods.


title:
Codes arising from incidence matrices of points and hyperplanes in
  $PG(n,q)$

abstract:
  In this paper we completely characterize the words with second minimum weight
in the $p-$ary linear code generated by the rows of the incidence matrix of
points and hyperplanes of $PG(n,q)$, with $q=p^h$ and $p$ prime, proving that
they are the scalar multiples of the difference of the incidence vectors of two
distinct hyperplanes of $PG(n,q)$.


title: CAD model simplification error estimation for electrostatics problems

abstract:
  Simplifying the geometry of a CAD model using defeaturing techniques enables
more efficient discretisation and subsequent simulation for engineering
analysis problems. Understanding the effect this simplification has on the
solution helps to decide whether the simplification is suitable for a specific
simulation problem. It can also help to understand the functional effect of a
geometry feature. The effect of the simplification is quantified by a
user-defined quantity of interest which is assumed to be (approximately) linear
in the solution. A bound on the difference between the quantity of interest of
the original and simplified solutions based on the energy norm is derived. The
approach is presented in the context of electrostatics problems, but can be
applied in general to a range of elliptic partial differential equations.
Numerical results on the efficiency of the bound are provided for
electrostatics problems with simplifications involving changes inside the
problem domain as well as changes to the boundaries.


title:
Distributed Model Predictive Control of Spatially Interconnected Systems
  Using Switched Cost Functions

abstract:
  This note proposes a distributed model predictive control (DMPC) scheme with
switched cost functions for a class of spatially interconnected systems with
communication constraints. Non-iterative and parallel communication strategy is
considered to ensure that all distributed controllers complete input updates at
each single information exchange step. The proposed DMPC scheme switches the
optimization index on a switching surface generated by control invariant sets.
With the index-switching strategy, stability of the origin is ensured by a
terminal control law. Convergence conditions of the optimal cost to zero are
established taking into account the causal link between the presumed trajectory
and the optimized trajectory of the previous step. The compatibility
constraints preserve the quadratic program property that is desired in
practical applications. It is also observed that the proposed DMPC scheme has
benefits dealing with systems that need to take into account safety-related
spatial constraints.


title:
Nuclear Reactions and Superfluid Time Dependent Density Functional
  Theory

abstract:
  The extension of Time Dependent Density Functional Theory (TDDFT) to
superfluid systems is discussed in the context of nuclear reactions and large
amplitude collective motion.


title: Spaces of quasi-invariant measures and convergence in them

abstract:
  Spaces of quasi-invariant measures supplied with different topologies are
studied. Their embeddings, projective decompositions, conditions for their
metrizability are investigated. Theorems about convergence of nets of
quasi-invariant measures and their extensions are proved as well. Moreover,
associated with them uniform spaces are studied.


title: A cohomological criterion for $p$-solvability

abstract:
  Let $G$ be a finite group, $p$ a prime and $P$ a Sylow $p$-subgroup of $G$.
In this note we give a cohomological criterion for the $p$-solvability of $G$
depending on the cohomology in degree $1$ with coefficients in $\mathbb F_p$ of
both the normal subgroups of $G$ and $P$. As a byproduct we bound the minimal
number of quotients of order a power of $p$ appearing in any normal series of
$G$ by the number of generators of $P$.


title: Systematic evaluation of CNN advances on the ImageNet

abstract:
  The paper systematically studies the impact of a range of recent advances in
CNN architectures and learning methods on the object categorization (ILSVRC)
problem. The evalution tests the influence of the following choices of the
architecture: non-linearity (ReLU, ELU, maxout, compatibility with batch
normalization), pooling variants (stochastic, max, average, mixed), network
width, classifier design (convolutional, fully-connected, SPP), image
pre-processing, and of learning parameters: learning rate, batch size,
cleanliness of the data, etc.
  The performance gains of the proposed modifications are first tested
individually and then in combination. The sum of individual gains is bigger
than the observed improvement when all modifications are introduced, but the
"deficit" is small suggesting independence of their benefits. We show that the
use of 128x128 pixel images is sufficient to make qualitative conclusions about
optimal network structure that hold for the full size Caffe and VGG nets. The
results are obtained an order of magnitude faster than with the standard 224
pixel images.


title:
Adiabatic Perturbation Theory and Geometry of Periodically-Driven
  Systems

abstract:
  We give a systematic review of the adiabatic theorem and the leading
non-adiabatic corrections in periodically-driven (Floquet) systems. These
corrections have a two-fold origin: (i) conventional ones originating from the
gradually changing Floquet Hamiltonian and (ii) corrections originating from
changing the micro-motion operator. These corrections conspire to give a
Hall-type linear response for non-stroboscopic (time-averaged) observables
allowing one to measure the Berry curvature and the Chern number related to the
Floquet Hamiltonian, thus extending these concepts to periodically-driven
many-body systems. The non-zero Floquet Chern number allows one to realize a
Thouless energy pump, where one can adiabatically add energy to the system in
discrete units of the driving frequency. We discuss the validity of Floquet
Adiabatic Perturbation Theory (FAPT) using five different models covering
linear and non-linear few and many-particle systems. We argue that in
interacting systems, even in the stable high-frequency regimes, FAPT breaks
down at ultra slow ramp rates due to avoided crossings of photon resonances,
not captured by the inverse-frequency expansion, leading to a counter-intuitive
stronger heating at slower ramp rates. Nevertheless, large windows in the ramp
rate are shown to exist for which the physics of interacting driven systems is
well captured by FAPT.

categories: cond-mat.quant-gas cond-mat.other cond-mat.str-el quant-ph


title:
The Politics of Routing: Investigating the Relationship Between AS
  Connectivity and Internet Freedom

abstract:
  The Internet's importance for promoting free and open communication has led
to widespread crackdowns on its use in countries around the world. In this
study, we investigate the relationship between national policies around freedom
of speech and Internet topology in countries around the world. We combine
techniques from network measurement and machine learning to identify features
of Internet structure at the national level that are the best indicators of a
country's level of freedom. We find that IP density and path lengths to other
countries are the best indicators of a country's freedom. We also find that our
methods predict freedom categories for countries with 91% accuracy.


title: Emotional Intensity analysis in Bipolar subjects

abstract:
  The massive availability of digital repositories of human thought opens
radical novel way of studying the human mind. Natural language processing tools
and computational models have evolved such that many mental conditions are
predicted by analysing speech. Transcription of interviews and discourses are
analyzed using syntactic, grammatical or sentiment analysis to infer the mental
state. Here we set to investigate if classification of Bipolar and control
subjects is possible. We develop the Emotion Intensity Index based on the
Dictionary of Affect, and find that subjects categories are distinguishable.
Using classical classification techniques we get more than 75\% of labeling
performance. These results sumed to previous studies show that current
automated speech analysis is capable of identifying altered mental states
towards a quantitative psychiatry.


title: On the $S_n$-invariant F-conjecture

abstract:
  By using classical invariant theory, we reduce the $S_{n}$-invariant
F-conjecture to a feasibility problem in polyhedral geometry. We show by
computer that for $n \le 19$, every integral $S_{n}$-invariant F-nef divisor on
the moduli space of genus zero stable pointed curves is semi-ample, over
arbitrary characteristic. Furthermore, for $n \le 16$, we show that for every
integral $S_{n}$-invariant nef (resp. ample) divisor $D$ on the moduli space,
$2D$ is base-point-free (resp. very ample). As applications, we obtain the nef
cone of the moduli space of stable curves without marked points, and the
semi-ample cone that of the moduli space of genus 0 stable maps to Grassmannian
for small numerical values.


title:
Order-preserving drawings of trees with approximately optimal height
  (and small width)

abstract:
  In this paper, we study how to draw trees so that they are planar,
straight-line and respect a given order of edges around each node. We focus on
minimizing the height, and show that we can always achieve a height of at most
2pw(T)+1, where pw(T) (the so-called pathwidth) is a known lower bound on the
height. Hence we give an asymptotic 2-approximation algorithm. We also create a
drawing whose height is at most 3pw(T ), but where the width can be bounded by
the number of nodes. Finally we construct trees that require height 2pw(T)+1 in
all planar order-preserving straight-line drawings.


title: Robust bent line regression

abstract:
  We introduce a rank-based bent linear regression with an unknown change
point. Using a linear reparameterization technique, we propose a rank-based
estimate that can make simultaneous inference on all model parameters,
including the location of the change point, in a computationally efficient
manner. We also develop a score-like test for the existence of a change point,
based on a weighted CUSUM process. This test only requires fitting the model
under the null hypothesis in absence of a change point, thus it is
computationally more efficient than likelihood-ratio type tests. The asymptotic
properties of the test are derived under both the null and the local
alternative models. Simulation studies and two real data examples show that the
proposed methods are robust against outliers and heavy-tailed errors in both
parameter estimation and hypothesis testing.


title:
Estimating the observable population size from biased samples: a new
  approach to population estimation with capture heterogeneity

abstract:
  Capture-recapture methods aim to estimate the size of a closed population on
the basis of multiple incomplete enumerations of individuals. In many
applications, the individual probability of being recorded is heterogeneous in
the population. Previous studies have suggested that it is not possible to
reliably estimate the total population size when capture heterogeneity exists.
Here we approach population estimation in the presence of capture heterogeneity
as a latent length biased nonparametric density estimation problem on the unit
interval. We show that in this setting it is generally impossible to estimate
the density on the entire unit interval in finite samples, and that estimators
of the population size have high and sometimes unbounded risk when the density
has significant mass near zero. As an alternative, we propose estimating the
population of individuals with capture probability exceeding some threshold. We
provide methods for selecting an appropriate threshold, and show that this
approach results in estimators with substantially lower risk than estimators of
the total population size, with correspondingly smaller uncertainty, even when
the parameter of interest is the total population. The alternative paradigm is
demonstrated in extensive simulation studies and an application to snowshoe
hare multiple recapture data.


title:
Electromagnetic polarization controlled perfect switching effect with
  high refractive index dimers. the beam-splitter configuration

abstract:
  High Refractive Index (HRI) dielectric particles smaller than the wavelength,
isolated or forming a designed ensemble are ideal candidates as new
multifunctional elements for building optical devices. Their directionality
effects are traditionally analyzed through forward and backward measurements,
even if these directions are not suitable for practical purposes. Here we
present unambiguous experimental evidence in the microwave range that, for a
dimer of HRI spherical particles, a perfect switching effect (perfect means off
= null intensity) is observed out of those directions as a consequence of the
mutual particle electric/magnetic interaction. The binary state depends on the
excitation polarization (polarization switching). Its analysis is performed
through the linear polarization degree of scattered radiation at a detection
direction perpendicular to the incident direction: the beam-splitter
configuration. The scaling property of Maxwell equations allows generalizing
our results to other frequency range and dimension scales, for instance, the
visible and the nanometric scale.


title: Concept-Oriented Model: the Functional View

abstract:
  The plethora of existing data models and specific data modeling techniques is
not only confusing but leads to complex, eclectic and inefficient designs of
systems for data management and analytics. The main goal of this paper is to
describe a unified approach to data modeling, called the concept-oriented model
(COM), by using functions as a basis for its formalization. COM tries to answer
the question what is data and to rethink basic assumptions underlying this and
related notions. Its main goal is to unify major existing views on data
(generality), using only a few main notions (simplicity) which are very close
to how data is used in real life (naturalness).


title: Recognizing cyclic matrices and a conjecture of J.G. Thompson

abstract:
  In 2006 J.G. Thompson conjectured: "If F is a field and A is in GL(n,F), then
there is a permutation matrix P such that AP is cyclic, that is, the minimal
polynomial of AP is also its characteristic polynomial" (open problem 16.95 in
the Kourovka Notebook). The present note provides a simple criterion for a
matrix to be cyclic and uses this to prove Thompson's conjecture.
  ERRATA
  I am indebted to Alexander Stasinski (Durham University) for the following
observations. Suppose n > 2 and J is the n x n all 1's matrix over a field of
characteristic not 2. Then A := J - I has the minimal polynomial (X + 1)(X - n
+ 1). Thus A is invertible and not cyclic even though A satisfies condition
(iv) of the Proposition. The error lies in the claim towards the end of the
proof that "these particular row and column errors do not change the
determinants ...".


title: A Formal Calculus for International Relations Computation and Evaluation

abstract:
  This publication presents a relation computation or calculus for
international relations using a mathematical modeling. It examined trust for
international relations and its calculus, which related to Bayesian inference,
Dempster-Shafer theory and subjective logic. Based on an observation in the
literature, we found no literature discussing the calculus method for the
international relations. To bridge this research gap, we propose a relation
algebra method for international relations computation. The proposed method
will allow a relation computation which is previously subjective and
incomputable. We also present three international relations as case studies to
demonstrate the proposed method is a real-world scenario. The method will
deliver the relation computation for the international relations that to
support decision makers in a government such as foreign ministry, defense
ministry, presidential or prime minister office. The Department of Defense
(DoD) may use our method to determine a nation that can be identified as a
friendly, neutral or hostile nation.


title: Spectral Gap of Random Hyperbolic Graphs and Related Parameters

abstract:
  Random hyperbolic graphs have been suggested as a promising model of social
networks. A few of their fundamental parameters have been studied. However,
none of them concerns their spectra. We consider the random hyperbolic graph
model as formalized by [GPP12] and essentially determine the spectral gap of
their normalized Laplacian. Specifically, we establish that with high
probability the second smallest eigenvalue of the normalized Laplacian of the
giant component of and $n$-vertex random hyperbolic graph is
$\Omega(n^{-(2\alpha-1)}/D)$, where $\frac12<\alpha<1$ is a model parameter and
$D$ is the network diameter (which is known to be at most polylogarithmic in
$n$). We also show a matching (up to a polylogarithmic factor) upper bound of
$n^{-(2\alpha-1)}(\log n)^{1+o(1)}$. As a byproduct we conclude that the
conductance upper bound on the eigenvalue gap obtained via Cheeger's inequality
is essentially tight. We also provide a more detailed picture of the collection
of vertices on which the bound on the conductance is attained, in particular
showing that for all subsets whose volume is $O(n^{1-\varepsilon})$ the
obtained conductance is with high probability
$\Omega(n^{-(2\alpha-1)\varepsilon+o(1)})$. Finally, we also show consequences
of our result for the minimum and maximum bisection of the giant component.


title:
Anisotropic magnetoresistance and upper critical fields up to 63 T in
  CaKFe$_4$As$_4$ single crystals

abstract:
  We report the temperature dependencies of the upper critical fields
$H_{c\text{2}}^{\text{c}}(T)$ parallel to the c-axis and
$H_{c\text{2}}^{\text{ab}}(T)$ parallel to the ab-plane of single crystalline
CaKFe$_4$As$_4$ inferred from the measurements of the temperature-dependent
resistance in static magnetic fields up to 14 T and magnetoresistance in pulsed
fields up to 63 T. We show that the observed decrease of the anisotropy
parameter $\gamma(T)=H_{c\text{2}}^{\text{ab}}/H_{c\text{2}}^{\text{c}}$ from
$\simeq 2.5$ at $T_c$ to $\simeq 1.5$ at 25 K can be explained by interplay of
paramagnetic pairbreaking and orbital effects in a multiband theory of
$H_{c2}$. The slopes of $dH_{c\text{2}}^{\text{c}}/dT\simeq-4.4$ T/K and
$dH_{c\text{2}}^{\text{ab}}/dT \simeq-10.9$ T/K at $T_c$ yield an electron mass
anisotropy of $m_{ab}/m_c\simeq 1/6$ and short coherence lengths $\xi_c\simeq
5.8\,\text{\AA}$ and $\xi_{ab}\simeq 14.3\,\text{\AA}$. The behavior of
$H_{c\text{2}}(T)$ turns out to be similar to that of the optimal doped
(Ba,K)Fe$_2$As$_2$, with $H_{c\text{2}}^{\text{ab}}(0)$ extrapolating to
$\simeq 92$ T, well above the BCS paramagnetic limit.


title: The Importance of Computation in Astronomy Education

abstract:
  Computational skills are required across all astronomy disciplines. Many
students enter degree programs without sufficient skills to solve computational
problems in their core classes or contribute immediately to research. We
recommend advocacy for computational literacy, familiarity with fundamental
software carpentry skills, and mastery of basic numerical methods by the
completion of an undergraduate degree in Astronomy.
  We recommend the AAS Education Task Force advocate for a significant increase
in computational literacy.
  We encourage the AAS to modestly fund efforts aimed at providing Open
Education Resources (OER) that will significantly impact computational literacy
in astronomy education.


title:
Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator
  Transition

abstract:
  We consider the orthogonality catastrophe at the Anderson Metal-Insulator
transition (AMIT). The typical overlap $F$ between the ground state of a Fermi
liquid and the one of the same system with an added potential impurity is found
to decay at the AMIT exponentially with system size $L$ as $F \sim \exp (-
\langle I_A\rangle /2)= \exp(-c L^{\eta})$, where $I_A$ is the so called
Anderson integral, $\eta $ is the power of multifractal intensity correlations
and $\langle ... \rangle$ denotes the ensemble average. Thus, strong disorder
typically increases the sensitivity of a system to an additional impurity
exponentially. We recover on the metallic side of the transition Anderson's
result that fidelity $F$ decays with a power law $F \sim L^{-q (E_F)}$ with
system size $L$. This power increases as Fermi energy $E_F$ approaches mobility
edge $E_M$ as $q (E_F) \sim (\frac{E_F-E_M}{E_M})^{-\nu \eta},$ where $\nu$ is
the critical exponent of correlation length $\xi_c$. On the insulating side of
the transition $F$ is constant for system sizes exceeding localization length
$\xi$. While these results are obtained from the mean value of $I_A,$ giving
the typical fidelity $F$, we find that $I_A$ is widely, log normally,
distributed with a width diverging at the AMIT. As a consequence, the mean
value of fidelity $F$ converges to one at the AMIT, in strong contrast to its
typical value which converges to zero exponentially fast with system size $L$.
This counterintuitive behavior is explained as a manifestation of
multifractality at the AMIT.


title: Local integrands for two-loop all-plus Yang-Mills amplitudes

abstract:
  We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with
all positive helicities in compact analytic form using D-dimensional local
integrands that are free of spurious singularities. The integrand is fixed from
on-shell tree amplitudes in six dimensions using D-dimensional generalised
unitarity cuts. The resulting expressions are shown to have manifest infrared
behaviour at the integrand level. We also find simple representations of the
rational terms obtained after integration in 4-2epsilon dimensions.


title: Iterative Alternating Neural Attention for Machine Reading

abstract:
  We propose a novel neural attention architecture to tackle machine
comprehension tasks, such as answering Cloze-style queries with respect to a
document. Unlike previous models, we do not collapse the query into a single
vector, instead we deploy an iterative alternating attention mechanism that
allows a fine-grained exploration of both the query and the document. Our model
outperforms state-of-the-art baselines in standard machine comprehension
benchmarks such as CNN news articles and the Children's Book Test (CBT)
dataset.


title: Rigidity and Frobenius Structure

abstract:
  We show that an irreducible ordinary differential equation on the projective
line has a Frobenius structure for a power of some prime p if it is rigid in
the sense of Katz and satisfies some other reasonable (and necessary)
conditions relative to the prime p.


title: On the dimension of matrix embeddings of torsion-free nilpotent groups

abstract:
  Since the work of Jennings (1955), it is well-known that any finitely
generated torsion-free nilpotent group can be embedded into unitriangular
integer matrices $UT_N(Z)$ for some $N$. In 2006, Nickel proposed an algorithm
to calculate such embeddings. In this work, we show that if $UT_n(Z)$ is
embedded into $UT_N(Z)$ using Nickel's algorithm, then $N \geq 2^{n/2 -2}$ if
the standard ordering of the Mal'cev basis (as in Nickel's original paper) is
used. In particular, we establish an exponential worst-case running time of
Nickel's algorithm.
  On the other hand, we also prove a general exponential upper bound on the
dimension of the embedding by showing that for any torsion free, finitely
generated nilpotent group the matrix representation produced by Nickel's
algorithm has never larger dimension than Jennings' embedding. Moreover, when
starting with a special Mal'cev basis, Nickel's embedding for $UT_n(Z)$ has
only quadratic size. Finally, we consider some special cases like free
nilpotent groups and Heisenberg groups and compare the sizes of the embeddings.


title: An independent pair-link model of simple fluids

abstract:
  A new approach to thermodynamics of simple fluids is presented. The partition
function is first expressed in the reciprocal space, it is argued that the
links (p,q) between 2 molecules can reasonably in the thermodynamical limit be
considered as a set nearly independent objects characterized by the dynamical
variables . It is then possible to derive an expression of the pair correlation
function. The results, which are independent of the exact shape of the
intermolecular potential, are applied to the simple case of hard sphere fluids.


title: Complementary weak-value amplification with concatenated postselections

abstract:
  We measure a transverse momentum kick in a Sagnac interferometer using
weak-value amplification with two postselections. The first postselection is
controlled by a polarization dependent phase mismatch between both paths of a
Sagnac interferometer and the second postselection is controlled by a polarizer
at the exit port. By monitoring the darkport of the interferometer, we study
the complementary amplification of the concatenated postselections, where the
polarization extinction ratio is greater than the contrast of the spatial
interference. In this case, we find an improvement in the amplification of the
signal of interest by introducing a second postselection to the system.


title: Communicating Data Quality in On-Demand Curation

abstract:
  On-demand curation (ODC) tools like Paygo, KATARA, and Mimir allow users to
defer expensive curation effort until it is necessary. In contrast to classical
databases that do not respond to queries over potentially erroneous data, ODC
systems instead answer with guesses or approximations. The quality and scope of
these guesses may vary and it is critical that an ODC system be able to
communicate this information to an end-user. The central contribution of this
paper is a preliminary user study evaluating the cognitive burden and
expressiveness of four representations of "attribute-level" uncertainty. The
study shows (1) insignificant differences in time taken for users to interpret
the four types of uncertainty tested, and (2) that different presentations of
uncertainty change the way people interpret and react to data. Ultimately, we
show that a set of UI design guidelines and best practices for conveying
uncertainty will be necessary for ODC tools to be effective. This paper
represents the first step towards establishing such guidelines.


title:
On Photon Spin and the Electrodynamic Origin of the charge of the
  Electron

abstract:
  We recently performed experiments on the transfer of photon spin to electron
orbital angular momentum. For an interpretation of the experimental results we
used a classical electrodynamic model of the photon as a propagating
electromagnetic solitary wave which is developed in detail here. A linearly
polarized monochromatic photon is considered as a propagating solitary
electromagnetic wave of finite energy hf which carries an angular momentum
h/2pi with the frequency f and Plancks constant h. This model has, apart from
being a tool for an interpretation of our experimental results, far reaching
consequences of fundamental relevance and guides us to an outline to a unified
quantum theory of electromagnetism and gravitation including an explanation of
the electrodynamic origin of the quantized charge of an electron.


title: DNA-to-go: A portable smartphone-enabled PCR assay platform

abstract:
  We address the need for affordable, rapid, and easy to use diagnostic
technologies by coupling an innovative thermocycling system that harnesses
natural convection to perform rapid DNA amplification via the polymerase chain
reaction (PCR) with smartphone-based detection. Our approach offers an
inherently simple design that enables PCR to be completed in 10-20 minutes.
Electrical power requirements are dramatically reduced by harnessing natural
convection to actuate the reaction, allowing the entire system to be operated
from a standard USB connection (5 V) via solar battery packs. Instantaneous
detection and analysis are enabled using an ordinary smartphone camera and
dedicated app interface.


title: How to flatten a soccer ball

abstract:
  This is an experimental case study in real algebraic geometry, aimed at
computing the image of a semialgebraic subset of 3-space under a polynomial map
into the plane. For general instances, the boundary of the image is given by
two highly singular curves. We determine these curves and show how they
demarcate the "flattened soccer ball". We explore cylindrical algebraic
decompositions, by working through concrete examples. Maps onto convex polygons
and connections to convex optimization are also discussed.


title:
Longitudinal Face Modeling via Temporal Deep Restricted Boltzmann
  Machines

abstract:
  Modeling the face aging process is a challenging task due to large and
non-linear variations present in different stages of face development. This
paper presents a deep model approach for face age progression that can
efficiently capture the non-linear aging process and automatically synthesize a
series of age-progressed faces in various age ranges. In this approach, we
first decompose the long-term age progress into a sequence of short-term
changes and model it as a face sequence. The Temporal Deep Restricted Boltzmann
Machines based age progression model together with the prototype faces are then
constructed to learn the aging transformation between faces in the sequence. In
addition, to enhance the wrinkles of faces in the later age ranges, the wrinkle
models are further constructed using Restricted Boltzmann Machines to capture
their variations in different facial regions. The geometry constraints are also
taken into account in the last step for more consistent age-progressed results.
The proposed approach is evaluated using various face aging databases, i.e.
FG-NET, Cross-Age Celebrity Dataset (CACD) and MORPH, and our collected
large-scale aging database named AginG Faces in the Wild (AGFW). In addition,
when ground-truth age is not available for input image, our proposed system is
able to automatically estimate the age of the input face before aging process
is employed.


title:
Comment on "$Z_{2}$ spin liquid phase on the kagome lattice: a new
  saddle point", by Tao Li [arXiv:1601.02165 (2016)]

abstract:
  In a recent paper [arXiv:1601.02165], Tao Li claimed that a gapped
$\mathbb{Z}_2$ spin liquid, obtained using projected Gutzwiller fermionic wave
functions, can be stabilized in the Heisenberg model on the kagome lattice. We
perform very accurate variational calculations and confirm with unprecedented
accuracy the fact, that the $\mathbb{Z}_{2}$ spin liquid is a local energy
minimum that goes away with system size, thus reaffirming the scenario of a
gapless $U(1)$ Dirac spin liquid ground state.


title:
Enhancing Perovskite Electrocatalysis through Strain Tuning of the
  Oxygen Deficiency

abstract:
  Oxygen vacancies in transition metal oxides facilitate catalysis critical for
energy storage and generation. However, it has proven elusive to promote
vacancies at the lower temperatures required for operation in devices such as
metal-air batteries and portable fuel cells. Here, we use thin films of the
perovskite-based strontium cobaltite (SrCoOx) to show that epitaxial strain is
a powerful tool towards manipulating the oxygen content under conditions
consistent with the oxygen evolution reaction, yielding increasingly oxygen
deficient states in an environment where the cobaltite would normally be fully
oxidized. The additional oxygen vacancies created through tensile strain
enhance the cobaltite catalytic activity towards this important reaction by
over an order of magnitude, equaling that of precious metal catalysts,
including IrO2. Our findings demonstrate that strain in these oxides can
dictate oxygen stoichiometry independent of ambient conditions, allowing
unprecedented control over oxygen vacancies essential in catalysis near room
temperature.


title: 44 GHz Class I Methanol (CH$_{3}$OH) Maser Survey in the Galactic Center

abstract:
  We report on a large 44 GHz ($7_0-6_1$ A$^+$) methanol (CH$_3$OH) maser
survey of the Galactic Center (GC). The Karl G. Jansky Very Large Array was
used to search for CH$_3$OH maser emission covering a large fraction of the
region around Sgr A. In 25 pointings, over 300 CH$_3$OH maser sources
($>10\sigma$) were detected. The majority of the maser sources have a single
peak emission spectrum with line of sight velocities that range from about
$-$13 km\,s$^{-1}$ to 72 km\,s$^{-1}$. Most maser sources were found to have
velocities around 35$-$55 km\,s$^{-1}$, closely following velocities of
neighboring interacting molecular clouds. The full width half maximum of each
individual spectral feature is very narrow ($\sim$0.85 km\,s$^{-1}$ on
average). In the north, where Sgr A East is known to be interacting with the 50
km\,s$^{-1}$ molecular cloud, more than 100 44 GHz CH$_3$OH masers were
detected. In addition, three other distinct concentrations of masers were
found, which appear to be located closer to the interior of the interacting
molecular clouds. Possibly a subset of masers are associated with star
formation, although conclusive evidence is lacking.


title: Young Differential Equations with Power Type Nonlinearities

abstract:
  In this note we give several methods to construct nontrivial solutions to the
equation $dy_{t}=\sigma(y_{t}) \, dx_{t}$, where $x$ is a $\gamma$-H\"older
$R^{d}$-valued signal with $\gamma\in(1/2,1)$ and $\sigma$ is a function
behaving like a power function $|\xi|^{\kappa}$, with $\kappa\in(0,1)$. In this
situation, classical Young integration techniques allow to get existence and
uniqueness results whenever $\gamma(\kappa+1)>1$, while we focus on cases where
$\gamma(\kappa+1)\le 1$. Our analysis then relies on some extensions of Young's
integral allowing to cover the situation at hand.


title:
Three-body scattering problem in the fixed center approximation: the
  case of attraction

abstract:
  We study the scattering of a light particle on a bound pair of heavy
particles (e.g., the deuteron) within the fixed center approximation in the
case of light-heavy attraction, solving the integral equation for the
three-body Green's function both in the coordinate and in the momentum space.
The results for the three-body scattering amplitude appear to be ambiguous --
they depend on a single real parameter. This parameter may be fixed by a
three-body input, e.g., the three-body scattering length. We also solve the
integral equation for the three-body Green function in the momentum space,
introducing a finite cut-off. We show that all three approaches are equivalent.
We also discuss how our approach to the problem matches with the introduction
of three-body contact interaction as done by other authors.


title: Gaussian free field light cones and SLE$_\kappa(\rho)$

abstract:
  We derive a surprising correspondence between SLE$_{\kappa}(\rho)$ processes
and light cones of the Gaussian free field (GFF).
  Recall that (one-sided, chordal, origin-seeded) SLE$_\kappa(\rho)$ processes
are in some sense the simplest and most natural variants of the Schramm-Loewner
evolution. They were originally defined only for $\rho > -2$, but one can use
L\'evy compensation to extend the definition to any $\rho >
-2-\tfrac{\kappa}{2}$ and to obtain qualitatively different curves. The
triangle $T = \{(\kappa, \rho): (-2-\tfrac{\kappa}{2})\vee
(\tfrac{\kappa}{2}-4) < \rho < -2 \}$ is the primary focus of this paper. When
$(\kappa, \rho) \in T$, the SLE$_\kappa(\rho)$ curves are highly non-simple
(and double points are dense) even though $\kappa < 4$.
  Let $h$ be an instance of the GFF. Fix $\kappa\in (0,4)$ and $\chi =
2/\sqrt{\kappa} - \sqrt{\kappa}/2$. Recall that an imaginary geometry ray is a
flow line of $e^{i(h/\chi +\theta)}$ that looks locally like SLE$_\kappa$. The
light cone with parameter $\theta \in [0, \pi]$ is the set of points reachable
from the origin by a sequence of rays with angles in $[-\theta/2, \theta/2]$.
When $\theta=0$, the light cone looks like SLE$_\kappa$, and when $\theta =
\pi$ it looks like the range of an SLE$_{16/\kappa}$. We find that when $\theta
\in (0, \pi)$ the light cones are either fractal carpets with a dense set of
holes or space-filling regions with no holes.
  We show that every non-space-filling light cone (with $\theta \in (0,\pi]$
and $\kappa \in (0,4)$) agrees in law with the range of an SLE$_\kappa(\rho)$
process with $(\kappa, \rho) \in T$. Conversely, the range of any
SLE$_\kappa(\rho)$ with $(\kappa,\rho) \in T$ agrees in law with a
non-space-filling light cone. As a consequence, we obtain the first proof that
these SLE$_\kappa(\rho)$ processes are continuous and show that they are
natural path-valued functions of the GFF.


title:
Reducing the error of Monte Carlo Algorithms by Learning Control
  Variates

abstract:
  Monte Carlo (MC) sampling algorithms are an extremely widely-used technique
to estimate expectations of functions f(x), especially in high dimensions.
Control variates are a very powerful technique to reduce the error of such
estimates, but in their conventional form rely on having an accurate
approximation of f, a priori. Stacked Monte Carlo (StackMC) is a recently
introduced technique designed to overcome this limitation by fitting a control
variate to the data samples themselves. Done naively, forming a control variate
to the data would result in overfitting, typically worsening the MC algorithm's
performance. StackMC uses in-sample / out-sample techniques to remove this
overfitting. Crucially, it is a post-processing technique, requiring no
additional samples, and can be applied to data generated by any MC estimator.
Our preliminary experiments demonstrated that StackMC improved the estimates of
expectations when it was used to post-process samples produces by a "simple
sampling" MC estimator. Here we substantially extend this earlier work. We
provide an in-depth analysis of the StackMC algorithm, which we use to
construct an improved version of the original algorithm, with lower estimation
error. We then perform experiments of StackMC on several additional kinds of MC
estimators, demonstrating improved performance when the samples are generated
via importance sampling, Latin-hypercube sampling and quasi-Monte Carlo
sampling. We also show how to extend StackMC to combine multiple fitting
functions, and how to apply it to discrete input spaces x.


title: On commuting varieties of parabolic subalgebras

abstract:
  Let $G$ be a connected reductive algebraic group over an algebraically closed
field $k$, and assume that the characteristic of $k$ is zero or a pretty good
prime for $G$. Let $P$ be a parabolic subgroup of $G$ and let $\mathfrak p$ be
the Lie algebra of $P$. We consider the commuting variety $\mathcal C(\mathfrak
p) = \{(X,Y) \in \mathfrak p \times \mathfrak p \mid [X,Y] = 0\}$. Our main
theorem gives a necessary and sufficient condition for irreducibility of
$\mathcal C(\mathfrak p)$ in terms of the modality of the adjoint action of $P$
on the nilpotent variety of $\mathfrak p$. As a consequence, for the case $P =
B$ a Borel subgroup of $G$, we give a classification of when $\mathcal
C(\mathfrak b)$ is irreducible; this builds on a partial classification given
by Keeton. Further, in cases where $\mathcal C(\mathfrak p)$ is irreducible, we
consider whether $\mathcal C(\mathfrak p)$ is a normal variety. In particular,
this leads to a classification of when $\mathcal C(\mathfrak b)$ is normal.


title: Correlation Plenoptic Imaging With Entangled Photons

abstract:
  Plenoptic imaging is a novel optical technique for three-dimensional imaging
in a single shot. It is enabled by the simultaneous measurement of both the
location and the propagation direction of light in a given scene. In the
standard approach, the maximum spatial and angular resolutions are inversely
proportional, and so are the resolution and the maximum achievable depth of
focus of the 3D image. We have recently proposed a method to overcome such
fundamental limits by combining plenoptic imaging with an intriguing
correlation remote-imaging technique: ghost imaging. Here, we theoretically
demonstrate that correlation plenoptic imaging can be effectively achieved by
exploiting the position-momentum entanglement characterizing spontaneous
parametric down-conversion (SPDC) photon pairs. As a proof-of-principle
demonstration, we shall show that correlation plenoptic imaging with entangled
photons may enable the refocusing of an out-of-focus image at the same depth of
focus of a standard plenoptic device, but without sacrificing
diffraction-limited image resolution.


title: Perfect state transfer is poly-time

abstract:
  We show that deciding whether a graph admits perfect state transfer can be
done in polynomial time with respect to the size of the graph on a classical
computer.


title:
Search for TeV-scale gravity signatures in high-mass final states with
  leptons and jets with the ATLAS detector at $\sqrt{s}=13$ TeV

abstract:
  A search for physics beyond the Standard Model, in final states with at least
one high transverse momentum charged lepton (electron or muon) and two
additional high transverse momentum leptons or jets, is performed using 3.2
fb$^{-1}$ of proton--proton collision data recorded by the ATLAS detector at
the Large Hadron Collider in 2015 at $\sqrt{s}=13$ TeV. The upper end of the
distribution of the scalar sum of the transverse momenta of leptons and jets is
sensitive to the production of high-mass objects. No excess of events beyond
Standard Model predictions is observed. Exclusion limits are set for models of
microscopic black holes with two to six extra dimensions.