title:
Measurement of differential cross sections for t-channel
  single-top-quark production at 13 TeV

abstract:
  The production of single top quarks is a cornerstone in understanding the
nature of the heaviest known elementary particle and its involvement in
electroweak interactions. An early differential cross section measurement of
t-channel single-top-quark production is presented. Proton-Proton collision
data at a center-of-mass energy of $13~\mathrm{TeV}$ collected in 2015 were
analyzed, corresponding to $2.3~\mathrm{fb}^{-1}$. The amount of signal events
as a function of the top quark transverse momentum and rapidity is estimated
using a multivariate discriminant. The results are unfolded to parton level and
compared to predictions by various Monte-Carlo generators.


title: On the Coded Caching Delivery Design over Wireless Networks

abstract:
  Coded caching scheme is a promising technique to migrate the network burden
in peak hours, which attains more prominent gains than the uncoded caching. The
coded caching scheme can be classified into two types, namely, the centralized
and the decentralized scheme, according to whether the placement procedures are
carefully designed or operated at random. However, most of the previous
analysis assumes that the connected links between server and users are
error-free. In this paper, we explore the coded caching based delivery design
in wireless networks, where all the connected wireless links are different. For
both centralized and decentralized cases, we proposed two delivery schemes,
namely, the orthogonal delivery scheme and the concurrent delivery scheme. We
focus on the transmission time slots spent on satisfying the system requests,
and prove that for both the centralized and the decentralized cases, the
concurrent delivery always outperforms orthogonal delivery scheme. Furthermore,
for the orthogonal delivery scheme, we derive the gap in terms of transmission
time between the decentralized and centralized case, which is essentially no
more than 1.5.


title:
The quantum CP-violating kaon system reproduced in the electronic
  laboratory (Homage to Nolberto Martinez)

abstract:
  The equivalence between the $\mathrm{Schr\ddot{o}dinger}$ dynamics of a
quantum system with a finite number of basis states and a classical dynamics is
realized in terms of electric networks. The isomorphism that connects in a
univocal way both dynamical systems was applied to the case of neutral mesons,
kaons in particular, and the class of electric networks univocally related to
the quantum system was analyzed. Moreover, under $CPT$ invariance, the relevant
$\epsilon$ parameter that measures $CP$ violation in the kaon system is
reinterpreted in terms of network parameters. All these results were explicitly
shown by means of both a numerical simulation of the implied networks and by
constructing the corresponding circuits.


title:
Violation of probabilistic inequality Clauser-Horne-Shimony-Holt in
  Quantum Mechanics

abstract:
  In 1982, Alain Aspect, and collaborators performed an experiment, in order to
observe the violation of the inequality of Clauser-Horne-Shimony-Holt. After
the experiment, they used the data in the inequality and concluded that the
inequality, obtained through probabilistic arguments, was violated confirming
the conclusions obtained by John S. Bell that was not possible a theory of
hidden variables in the conditions suggested by Einstein, Podolsky and Rosen.
The aim of this work is to verify the validity of the inequalities in the
conditions of the probabilistic theory, in order to hold with the axioms of the
probability.


title: Computing twists of hyperelliptic curves

abstract:
  We give an efficient algorithm to compute equations of twists of
hyperelliptic curves of arbitrary genus over any separable field (of
characteristic different from 2), and we explicitly describe some interesting
examples.


title:
Linear magnetoresistance in a quasi-free two dimensional electron gas in
  an ultra-high mobility GaAs quantum well

abstract:
  We report a magnetotransport study of an ultra-high mobility
($\bar{\mu}\approx 25\times 10^6$\,cm$^2$\,V$^{-1}$\,s$^{-1}$) $n$-type GaAs
quantum well up to 33 T. A strong linear magnetoresistance (LMR) of the order
of 10$^5$ % is observed in a wide temperature range between 0.3 K and 60 K. The
simplicity of our material system with a single sub-band occupation and free
electron dispersion rules out most complicated mechanisms that could give rise
to the observed LMR. At low temperature, quantum oscillations are superimposed
onto the LMR. Both, the featureless LMR at high $T$ and the quantum
oscillations at low $T$ follow the empirical resistance rule which states that
the longitudinal conductance is directly related to the derivative of the
transversal (Hall) conductance multiplied by the magnetic field and a constant
factor $\alpha$ that remains unchanged over the entire temperature range. Only
at low temperatures, small deviations from this resistance rule are observed
beyond $\nu=1$ that likely originate from a different transport mechanism for
the composite fermions.


title:
Starobinsky Inflation and Dark Energy and Dark Matter Effects from
  Quasicrystal Like Spacetime Structures

abstract:
  The goal of this work on mathematical cosmology and geometric methods in
modified gravity theories, MGTs, is to investigate Starobinsky-like inflation
scenarios determined by gravitational and scalar field configurations mimicking
quasicrystal, QC, like structures. Such spacetime aperiodic QCs are different
from those discovered and studied in solid state physics but described by
similar geometric methods. We prove that an inhomogeneous and locally
anisotropic gravitational and matter field effective QC mixed continuous and
discrete "aether" can be modeled by exact cosmological solutions in MGTs and
Einstein gravity. The coefficients of corresponding generic off-diagonal
metrics and generalized connections depend (in general) on all spacetime
coordinates via generating and integration functions and certain smooth and
discrete parameters. Imposing additional nonholonomic constraints, prescribing
symmetries for generating functions and solving the boundary conditions for
integration functions and constants, we can model various nontrivial torsion QC
structures or extract cosmological Levi--Civita configurations with diagonal
metrics reproducing de Sitter (inflationary) like and other types homogeneous
inflation and acceleration phases. Finally, we speculate how various dark
energy and dark matter effects can be modeled by off-diagonal interactions and
deformations of a nontrivial QC like gravitational vacuum structure and
analogous scalar matter fields.


title: Towards a comprehensive knowledge of the open cluster Haffner 9

abstract:
  We turn our attention to Haffner 9, a Milky Way open cluster whose previous
fundamental parameter estimates are far from being in agreement. In order to
provide with accurate estimates we present high-quality Washington CT1 and
Johnson BVI photometry of the cluster field. We put particular care in
statistically clean the colour-magnitude diagrams (CMDs) from field star
contamination, which was found a common source in previous works for the
discordant fundamental parameter estimates. The resulting cluster CMD fiducial
features were confirmed from a proper motion membership analysis. Haffner 9 is
a moderately young object (age ~ 350 Myr), placed in the Perseus arm -at a
heliocentric distance of ~ 3.2 kpc-, with a lower limit for its present mass of
~ 160 Mo and of nearly metal solar content. The combination of the cluster
structural and fundamental parameters suggest that it is in an advanced stage
of internal dynamical evolution, possibly in the phase typical of those with
mass segregation in their core regions. However, the cluster still keeps its
mass function close to that of the Salpeter's law.


title:
Molecular dynamics simulation of the capillary leveling of viscoelastic
  polymer films

abstract:
  Surface tension-driven flow techniques have recently emerged as an efficient
means of shedding light into the rheology of thin polymer films. Motivated by
experimental and theoretical approaches in films bearing a varying surface
topography, we present results on the capillary relaxation of a square pattern
at the free surface of a viscoelastic polymer film, using molecular dynamics
simulations of a coarse-grained polymer model. Height profiles are monitored as
a function of time after heating the system above its glass-transition
temperature and their time dependence is fitted to the theory of capillary
leveling. Results show that the viscosity is not constant, but time dependent.
In addition to providing a complementary insight about the local inner
mechanisms, our simulations of the capillary-leveling process therefore probe
the viscoelasticity of the polymer and not only its viscosity, in contrast to
previous experimental approaches.

categories: cond-mat.soft cond-mat.mes-hall cond-mat.stat-mech physics.comp-ph physics.flu-dyn


title: Inferring Network Structure from Cascades

abstract:
  Many physical, biological, and social phenomena can be described by cascades
taking place on a network. Often, the activity can be empirically observed, but
not the underlying network of interactions. In this paper we offer three
topological methods to infer the structure of any directed network given a set
of cascade arrival times. Our formulas hold for a very general class of models
where the activation probability of a node is a generic function of its degree
and the number of its active neighbors. We report high success rates for
synthetic and real networks, for several different cascade models.


title: Lagrangian 3D tracking of fluorescent microscopic objects in motion

abstract:
  We describe the development of a tracking device, mounted on an
epi-fluorescent inverted microscope, suited to obtain time resolved 3D
Lagrangian tracks of fluorescent passive or active micro-objects in
micro-fluidic devices. The system is based on real-time image processing,
determining the displacement of a x,y mechanical stage to keep the chosen
object at a fixed position in the observation frame. The z displacement is
based on the refocusing of the fluorescent object determining the displacement
of a piezo mover keeping the moving object in focus. Track coordinates of the
object with respect to the micro-fluidic device, as well as images of the
object are obtained at a frequency of several tenths of Hertz. This device is
particularly well adapted to obtain trajectories of motile micro-organisms in
micro-fluidic devices with or without flow.


title:
Regenerative Soot-IX: C3 as the dominant, stable carbon cluster in high
  pressure sooting discharges

abstract:
  Results are presented that have been obtained while operating the graphite
hollow cathode duoplasmatron ion source in dual mode under constant discharge
current. This dual mode operation enabled us to obtain the mass and emission
spectra simultaneously. In mass spectra C3 is the main feature but C4 and C5
are also prominent, whereas in emission spectra C2 is also there and its
presence shows that it is in an excited state rather than in an ionic state.
These facts provide evidence that C3 is produced due to the regeneration of a
soot forming sequence and leave it in ionic state. C3 is a stable molecule and
the only dominant species among the carbon clusters that survives in a
regenerative sooting environment at high-pressure discharges.


title:
Prospects for an experiment to measure BR($K_L\to\pi^0\nu\bar{\nu}$) at
  the CERN SPS

abstract:
  Precise measurements of the branching ratios for the $K\to\pi\nu\bar{\nu}$
decays can provide unique constraints on CKM unitarity and, potentially,
evidence for new physics. It is important to measure both decay modes,
$K^+\to\pi^+\nu\bar{\nu}$ and $K_L\to\pi^0\nu\bar{\nu}$, since different new
physics models affect the rates for each channel differently. We are
investigating the feasibility of performing a measurement of
BR($K_L\to\pi^0\nu\bar{\nu}$) using a high-energy secondary neutral beam at the
CERN SPS in a successor experiment to NA62. The planned experiment would reuse
some of the NA62 infrastructure, including possibly the NA48 liquid-krypton
calorimeter. The mean momentum of $K_L$ mesons decaying in the fiducial volume
is 70 GeV; the decay products are boosted forward, so that less demanding
performance is required from the large-angle photon veto detectors. On the
other hand, the layout poses particular challenges for the design of the
small-angle vetoes, which must reject photons from $K_L$ decays escaping
through the beam pipe amidst an intense background from soft photons and
neutrons in the beam. We present some preliminary conclusions from our
feasibility studies, summarizing the design challenges faced and the
sensitivity obtainable for the measurement of BR($K_L\to\pi^0\nu\bar{\nu}$).


title:
Investigating the Transition Region in Scanned Probe Images of the
  Cyclotron Orbit in Graphene

abstract:
  A cooled scanning probe microscope (SPM) has been used to image cyclotron
orbits of electrons through high-mobility graphene in a magnetic field.1-5 In a
hBN-graphene-hBN device patterned into a hall bar geometry, the magnetic field
focuses a current Ii injected from one narrow contact into another narrow
contact located an integer number of cyclotron diameters away, creating a
voltage Vc. The degree of focusing is measured by the transresistance Rm =
Vc/Ii. In SPM, the tip can either enhance or decrease conductance in the sample
by deflecting electrons into or away from the second contact, respectively.3,4
Our SPM images of magnetic focusing feature a region in which the tip
transitions from enhancing to decreasing the conductance in the sample where
the change in transresistance caused by the tip is equal to zero. In this
paper, we investigate how the location of this region in the graphene sample
changes as we modulate the electron density n and magnetic field B. By plotting
line-cuts of the change in trans-resistance for different electron densities
and magnetic fields, we identify trends in the inflection point where the tip
changes from enhancing to decreasing the conductance in the sample. From the
location of each transition region, we show that the cyclotron diameter of the
electron trajectories can be obtained, and explain the trends in inflection
point location for different electron densities and magnetic fields.


title:
Interpreting the strongly lensed supernova iPTF16geu: time delay
  predictions, microlensing, and lensing rates

abstract:
  We present predictions for time delays between multiple images of the
gravitationally lensed supernova, iPTF16geu, which was recently discovered from
the intermediate Palomar Transient Factory (iPTF). As the supernova is of Type
Ia where the intrinsic luminosity is usually well-known, accurately measured
time delays of the multiple images could provide tight constraints on the
Hubble constant. According to our lens mass models constrained by the {\it
Hubble Space Telescope} F814W image, we expect the maximum relative time delay
to be less than a day, which is consistent with the maximum of 100 hours
reported by Goobar et al. but places a stringent upper limit. Furthermore, the
fluxes of most of the supernova images depart from expected values suggesting
that they are affected by microlensing. The microlensing timescales are small
enough that they may pose significant problems to measure the time delays
reliably. Our lensing rate calculation indicates that the occurrence of a
lensed SN in iPTF is likely. However, the observed total magnification of
iPTF16geu is larger than expected, given its redshift. This may be a further
indication of ongoing microlensing in this system.


title:
Encapsulated Nanowires: Boosting Electronic Transport in Carbon
  Nanotubes

abstract:
  The electrical conductivity of metallic carbon nanotubes (CNTs) quickly
saturates with respect to bias voltage due to scattering from a large
population of optical phonons. Decay of these dominant scatterers in pristine
CNTs is too slow to offset an increased generation rate at high voltage bias.
We demonstrate from first principles that encapsulation of 1D atomic chains
within a single-walled CNT can enhance decay of "hot" phonons by providing
additional channels for thermalisation. Pacification of the phonon population
growth reduces electrical resistivity of metallic CNTs by 51% for an example
system with encapsulated beryllium.


title: N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$

abstract:
  We construct 4D $\mathcal{N}=2$ theories on an infinite family of 4D toric
manifolds with the topology of connected sums of $S^2 \times S^2$. These
theories are constructed through the dimensional reduction along a non-trivial
$U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the
conditions under which such reductions can be carried out and give a partial
classification result of the resulting 4D manifolds. We calculate the partition
functions of these 4D theories and they involve both instanton and
anti-instanton contributions, thus generalizing Pestun's famous result on
$S^4$.


title: Spectral theory for random Poincar\'e maps

abstract:
  We consider stochastic differential equations, obtained by adding weak
Gaussian white noise to ordinary differential equations admitting $N$
asymptotically stable periodic orbits. We construct a discrete-time,
continuous-space Markov chain, called a random Poincar\'e map, which encodes
the metastable behaviour of the system. We show that this process admits
exactly $N$ eigenvalues which are exponentially close to $1$, and provide
expressions for these eigenvalues and their left and right eigenfunctions in
terms of committor functions of neighbourhoods of periodic orbits. The
eigenvalues and eigenfunctions are well-approximated by principal eigenvalues
and quasistationary distributions of processes killed upon hitting some of
these neighbourhoods. The proofs rely on Feynman--Kac-type representation
formulas for eigenfunctions, Doob's $h$-transform, spectral theory of compact
operators, and a recently discovered detailed-balance property satisfied by
committor functions.


title: Constrained Low-Rank Learning Using Least Squares-Based Regularization

abstract:
  Low-rank learning has attracted much attention recently due to its efficacy
in a rich variety of real-world tasks, e.g., subspace segmentation and image
categorization. Most low-rank methods are incapable of capturing
low-dimensional subspace for supervised learning tasks, e.g., classification
and regression. This paper aims to learn both the discriminant low-rank
representation (LRR) and the robust projecting subspace in a supervised manner.
To achieve this goal, we cast the problem into a constrained rank minimization
framework by adopting the least squares regularization. Naturally, the data
label structure tends to resemble that of the corresponding low-dimensional
representation, which is derived from the robust subspace projection of clean
data by low-rank learning. Moreover, the low-dimensional representation of
original data can be paired with some informative structure by imposing an
appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a
novel constrained LRR method. The objective function is formulated as a
constrained nuclear norm minimization problem, which can be solved by the
inexact augmented Lagrange multiplier algorithm. Extensive experiments on image
classification, human pose estimation, and robust face recovery have confirmed
the superiority of our method.


title:
Audio Event and Scene Recognition: A Unified Approach using Strongly and
  Weakly Labeled Data

abstract:
  In this paper we propose a novel learning framework called Supervised and
Weakly Supervised Learning where the goal is to learn simultaneously from
weakly and strongly labeled data. Strongly labeled data can be simply
understood as fully supervised data where all labeled instances are available.
In weakly supervised learning only data is weakly labeled which prevents one
from directly applying supervised learning methods. Our proposed framework is
motivated by the fact that a small amount of strongly labeled data can give
considerable improvement over only weakly supervised learning. The primary
problem domain focus of this paper is acoustic event and scene detection in
audio recordings. We first propose a naive formulation for leveraging labeled
data in both forms. We then propose a more general framework for Supervised and
Weakly Supervised Learning (SWSL). Based on this general framework, we propose
a graph based approach for SWSL. Our main method is based on manifold
regularization on graphs in which we show that the unified learning can be
formulated as a constraint optimization problem which can be solved by
iterative concave-convex procedure (CCCP). Our experiments show that our
proposed framework can address several concerns of audio content analysis using
weakly labeled data.


title: Topological classifier for detecting the emergence of epileptic seizures

abstract:
  In this work we study how to apply topological data analysis to create a
method suitable to classify EEGs of patients affected by epilepsy. The
topological space constructed from the collection of EEGs signals is analyzed
by Persistent Entropy acting as a global topological feature for discriminating
between healthy and epileptic signals. The Physionet data-set has been used for
testing the classifier.


title:
Numerical study of magnetization plateaux in the spin-1/2 Heisenberg
  antiferromagnet on the checkerboard lattice

abstract:
  We present numerical evidence that the spin-1/2 Heisenberg model on the
two-dimensional checkerboard lattice exhibits several magnetization plateaux
for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its
saturation value. These incompressible states correspond to somehow similar
valence-bond crystal phases that break lattice symmetries, though they are
different from the already established plaquette phase for m=0. Our results are
based on Exact Diagonalization as well as Density Matrix Renormalization Group
large-scale simulations, and interpreted in terms of simple trial
wavefunctions.


title: The damped stochastic wave equation on p.c.f. fractals

abstract:
  A p.c.f. fractal with a regular harmonic structure admits an associated
Dirichlet form, which is itself associated with a Laplacian. This Laplacian
enables us to give an analogue of the damped stochastic wave equation on the
fractal. We show that a unique function-valued solution exists, which has an
explicit formulation in terms of the spectral decomposition of the Laplacian.
We then use a Kolmogorov-type continuity theorem to derive the spatial and
temporal H\"older exponents of the solution. Our results extend the analogous
results on the stochastic wave equation in one-dimensional Euclidean space. It
is known that no function-valued solution to the stochastic wave equation can
exist in Euclidean dimension two or higher. The fractal spaces that we work
with always have spectral dimension less than two, and show that this is the
right analogue of dimension to express the "curse of dimensionality" of the
stochastic wave equation. Finally we prove some results on the convergence to
equilibrium of the solutions.


title:
Light-by-light scattering in the Lamb shift and the bound electron g
  factor

abstract:
  We compute an $\mathcal{O}\left(\alpha^2(Z\alpha)^6\right)$ contribution to
the hydrogen-atom Lamb shift arising from the light-by-light scattering.
Analogous diagrams, with one atomic electric field insertion replaced by an
external magnetic field, contribute to the gyromagnetic factor of the bound
electron at $\mathcal{O}\left(\alpha^2(Z\alpha)^4\right)$. We also calculate
the contribution to the gyromagnetic factor from the muon magnetic loop.


title: A Superradiant Topological Peierls Insulator inside an Optical Cavity

abstract:
  We consider a spinless ultracold Fermi gas tightly trapped along the axis of
an optical resonator and transversely illuminated by a laser closely tuned to a
resonator mode. At a certain threshold pump intensity the homogeneous gas
density breaks a $\mathbf{Z}_2$ symmetry towards a spatially periodic order,
which collectively scatters pump photons into the cavity. We show that this
known self-ordering transition also occurs for low field seeking fermionic
particles when the laser light is blue-detuned to an atomic transition. The
emergent superradiant optical lattice in this case is homopolar and possesses
two distinct dimerizations. Depending on the spontaneously chosen dimerization
the resulting Bloch bands can have a non-trivial topological structure
characterized by a non-vanishing Zak phase. In the case the Fermi momentum is
close to half the cavity-mode wavenumber, a Peierls-like instability here
creates a topoloical insulator with a gap at the Fermi surface, which hosts a
pair of edge states. The topological features of the system can be
non-destructively observed via the cavity output: the Zak phase of the bulk
coincides with the relative phase between laser and cavity field, while the
fingerprint of edge states can be observed as additional broadening in a well
defined frequency window of the cavity spectrum.


title:
The Asset Liability Management problem of a nuclear operator : a
  numerical stochastic optimization approach

abstract:
  We numerically study an Asset Liability Management problem linked to the
decommissioning of French nuclear power plants. We link the risk aversion of
practitioners to an optimization problem. Using different price models we show
that the optimal solution is linked to a de-risking management strategy similar
to a concave strategy and we propose an effective heuristic to simulate the
underlying optimal strategy. Besides we show that the strategy is stable with
respect to the main parameters involved in the liability problem.


title:
A Data Quality Metric (DQM): How to Estimate The Number of Undetected
  Errors in Data Sets

abstract:
  Data cleaning, whether manual or algorithmic, is rarely perfect leaving a
dataset with an unknown number of false positives and false negatives after
cleaning. In many scenarios, quantifying the number of remaining errors is
challenging because our data integrity rules themselves may be incomplete, or
the available gold-standard datasets may be too small to extrapolate. As the
use of inherently fallible crowds becomes more prevalent in data cleaning
problems, it is important to have estimators to quantify the extent of such
errors. We propose novel species estimators to estimate the number of distinct
remaining errors in a dataset after it has been cleaned by a set of crowd
workers -- essentially, quantifying the utility of hiring additional workers to
clean the dataset. This problem requires new estimators that are robust to
false positives and false negatives, and we empirically show on three
real-world datasets that existing species estimators are unstable for this
problem, while our proposed techniques quickly converge.


title:
Evaluating the bulk Lorentz factors of outflow material: lessons learned
  from the extremely-energetic outburst GRB 160625B

abstract:
  GRB 160625B is an extremely-bright outburst with well-monitored afterglow
emission. The geometry-corrected energy is high up to $\sim 5.2\times10^{52}$
erg or even $\sim 8\times 10^{52}$ erg, rendering it the most energetic GRB
prompt emission recorded so far. We analyzed the time-resolved spectra of the
prompt emission and found that in some intervals there were likely
thermal-radiation components and the high energy emission were characterized by
significant cutoff. The bulk Lorentz factors of the outflow material are
estimated accordingly. We found out that the Lorentz factors derived in the
thermal-radiation model are consistent with the luminosity-Lorentz factor
correlation found in other bursts as well as in GRB 090902B for the
time-resolved thermal-radiation components. While the spectral cutoff model
yields much lower Lorentz factors that are in tension with the constraints set
by the electron pair Compoton scattering process. We then suggest that these
spectral cutoffs are more likely related to the particle acceleration process
and that one should be careful in estimating the Lorentz factors if the
spectrum cuts at a rather low energy (e.g., $\sim$ tens MeV). The nature of the
central engine has also been discussed and a stellar-mass black hole is likely
favored.


title:
IoT Sentinel: Automated Device-Type Identification for Security
  Enforcement in IoT

abstract:
  With the rapid growth of the Internet-of-Things (IoT), concerns about the
security of IoT devices have become prominent. Several vendors are producing
IP-connected devices for home and small office networks that often suffer from
flawed security designs and implementations. They also tend to lack mechanisms
for firmware updates or patches that can help eliminate security
vulnerabilities. Securing networks where the presence of such vulnerable
devices is given, requires a brownfield approach: applying necessary protection
measures within the network so that potentially vulnerable devices can coexist
without endangering the security of other devices in the same network. In this
paper, we present IOT SENTINEL, a system capable of automatically identifying
the types of devices being connected to an IoT network and enabling enforcement
of rules for constraining the communications of vulnerable devices so as to
minimize damage resulting from their compromise. We show that IOT SENTINEL is
effective in identifying device types and has minimal performance overhead.


title:
Broadband, Lensless and Optomechanically Stabilised Coupling into
  Microfluidic Hollow-Core Photonic Crystal Fiber Using Glass Nanospike

abstract:
  We report a novel technique for launching broadband laser light into
liquid-filled hollow-core photonic crystal fiber (HC-PCF). It uniquely offers
self-alignment and self-stabilization via optomechanical trapping of a fused
silica nanospike, fabricated by thermally tapering and chemically etching a
single mode fiber into a tip diameter of 350 nm. We show that a trapping laser,
delivering ~300 mW at 1064 nm, can be used to optically align and stably
maintain the nanospike at the core center. Once this is done, a broadband
supercontinuum beam (~575 to 1064 nm) can be efficiently and close to
achromatically launched in the HC-PCF. The system is robust against liquid-flow
in either direction inside the HC-PCF and the Fresnel back-reflections are
reduced to negligible levels compared to free-space launching or butt-coupling.
The results are of potential relevance for any application where the efficient
delivery of broadband light into liquid-core waveguides is desired.


title:
Anisotropic Raman Scattering and Mobility in Monolayer 1Td-ReS2
  Controlled by Strain Engineering

abstract:
  Regulation of electronic structure and mobility cut-on rate in
two-dimensional transition metal dichalcogenides (TMDs) has attracted much
attention because of its potential in electronic device design. The anisotropic
Raman scattering and mobility cut-on rate of monolayer unique distorted-1T(1Td)
ReS2 with external strain are determined theoretically based on the density
function theory. The angle-dependent Raman spectrum of Ag-like, Eg-like and Cp
models are used to discriminate and analysis structural anisotropy; the strain
is exploited to adjust the structural symmetry and electronic structure of ReS2
so as to enhance mobility cut-on rate to almost 6 times of the original value.
Our results suggest the use of the strain engineering in high-quality
semiconductor switch device.


title: String theory and the 4D/3D reduction of Seiberg duality. A Review

abstract:
  We review the reduction of four-dimensional N=1 Seiberg duality to three
dimensions focusing on the D brane engineering approach. We start with an
overview of four-dimensional Seiberg duality for theories with various types of
gauge groups and matter content both from a field-theoretic and a brane
engineering point of view. Then we describe two families of N=2
three-dimensional dualities, namely Giveon-Kutasov-like and Aharony-like
dualities. The last part of our discussion is devoted to the 4D/3D reduction of
the dualities studied above. We discuss both the analysis at finite radius,
crucial for preserving the duality in the dimensional reduction, and the
zero-size limit that must be supported by a real mass flow and a Higgsing,
which can differ case by case. We show that this mechanism is reproduced in the
brane description by T-duality, supplying a unified picture for all the
different cases. As a bonus we show that this analysis provides a brane
description for Aharony-like dualities.


title:
Randomized Dynamic Mode Decomposition for Non-Intrusive Reduced Order
  Modelling

abstract:
  This paper focuses on a new framework for reduced order modelling of
non-intrusive data with application to 2D flows. To overcome the shortcomings
of intrusive model order reduction usually derived by combining the POD and the
Galerkin projection methods, we developed a novel technique based on Randomized
Dynamic Mode Decomposition as a fast and accurate option in model order
reduction of non-intrusive data originating from Saint-Venant systems.
Combining efficiently the Randomized Dynamic Mode Decomposition algorithm with
Radial Basis Function interpolation, we produced an efficient tool in
developing the linear model of a complex flow field described by non-intrusive
(or experimental) data. The rank of the reduced DMD model is given as the
unique solution of a constrained optimization problem. We emphasize the
excellent behavior of the non-intrusive reduced order models by performing a
qualitative analysis. In addition, we gain a significantly reduction of CPU
time in computation of the reduced order models (ROMs) for non-intrusive
numerical data.


title: On singular stochastic differential equations and Dirichlet forms

abstract:
  This survey paper is a structured concise summary of four of our recent
papers on the stochastic regularity of diffusions that are associated to
regular strongly local (but not necessarily symmetric) Dirichlet forms. Here by
stochastic regularity we mean the question whether a diffusion associated to a
Dirichlet form as mentioned above can be started and identified as a solution
to an explicit stochastic differential equation for explicitly given starting
points. Beyond the stochastic regularity, we consider its applications to
strong existence and pathwise uniqueness of singular stochastic differential
equations.


title:
An alternative approach to Michaelis-Menten kinetics that is based on
  the Renormalization Group: Comparison with the perturbation expansion beyond
  the sQSSA

abstract:
  We recall the perturbation expansion for Michaelis-Menten kinetics, beyond
the standard quasi-steady-state approximation (sQSSA). Against this background,
we are able to appropriately apply the alternative approach to the study of
singularly perturbed differential equations that is based on the
renormalization group (SPDERG), by clarifying similarities and differences. In
the present demanding situation, we directly renormalize the bare initial
condition value for the substrate. Our main results are: i) the 2nd order
SPDERG uniform approximations to the correct solutions contain, up to 1st
order, the same outer components as the known perturbation expansion ones; ii)
the differential equation to be solved for the derivation of the 1st order
outer substrate component is simpler within the SPDERG approach; iii) the
approximations better reproduce the numerical solutions of the original problem
in a region encompassing the matching one, because of the 2nd order terms in
the inner components, calculated here for the first time to our knowledge: iv)
the refined SPDERG uniform approximations, that we propose, give the correct
asymptotically vanishing solutions, too, and allow to obtain results nearly
indistinguishable from the solutions of the original problem in a large part of
the whole relevant time window, even in the studied unfavourable kinetic
constant case, for an expansion parameter value as large as {\epsilon} = 0.5.


title:
Interpreting the Syntactic and Social Elements of the Tweet
  Representations via Elementary Property Prediction Tasks

abstract:
  Research in social media analysis is experiencing a recent surge with a large
number of works applying representation learning models to solve high-level
syntactico-semantic tasks such as sentiment analysis, semantic textual
similarity computation, hashtag prediction and so on. Although the performance
of the representation learning models are better than the traditional baselines
for the tasks, little is known about the core properties of a tweet encoded
within the representations. Understanding these core properties would empower
us in making generalizable conclusions about the quality of representations.
Our work presented here constitutes the first step in opening the black-box of
vector embedding for social media posts, with emphasis on tweets in particular.
  In order to understand the core properties encoded in a tweet representation,
we evaluate the representations to estimate the extent to which it can model
each of those properties such as tweet length, presence of words, hashtags,
mentions, capitalization, and so on. This is done with the help of multiple
classifiers which take the representation as input. Essentially, each
classifier evaluates one of the syntactic or social properties which are
arguably salient for a tweet. This is also the first holistic study on
extensively analysing the ability to encode these properties for a wide variety
of tweet representation models including the traditional unsupervised methods
(BOW, LDA), unsupervised representation learning methods (Siamese CBOW,
Tweet2Vec) as well as supervised methods (CNN, BLSTM).


title: On the Weyl symbol of the resolvent of the harmonic oscillator

abstract:
  We compute the Weyl symbol of the resolvent of the harmonic oscillator and
study its properties.


title:
Pfaffians and nonintersecting paths in graphs with cycles: Grassmann
  algebra methods

abstract:
  After recalling the definition of Grassmann algebra and elements of
Grassmann--Berezin calculus, we use the expression of Pfaffians as Grassmann
integrals to generalize a series of formulas relating generating functions of
paths in digraphs to Pfaffians. We start with the celebrated
Lindstr\"om-Gessel-Viennot formula, which we derive in the general case of a
graph with cycles. We then make further use of Grassmann algebraic tools to
prove a generalization of the results of (Stembridge 1990). Our results, which
are applicable to graphs with cycles, are formulated in terms of systems of
nonintersecting paths and nonintersecting cycles in digraphs.


title:
Enhancement of the d-wave pairing correlations by charge and spin
  ordering in the spin-one-half Falicov-Kimball model with Hund and
  Hubbard~coupling

abstract:
  Projector Quantum-Monte-Carlo Method is used to examine effects of the
spin-independent $U_{fd}$ as well as spin-dependent $J_z$ Coulomb interaction
between the localized $f$ and itinerant $d$ electrons on the stability of
various types of charge/spin ordering and superconducting correlations in the
spin-one-half Falicov-Kimball model with Hund and Hubbard coupling. The model
is studied for a wide range of $f$ and $d$-electron concentrations and it is
found that the interband interactions $U_{fd}$ and $J_z$ stabilize three basic
types of charge/spin ordering, and namely, (i) the axial striped phases, (ii)
the regular $n$-molecular phases and (iii) the phase separated states. It is
shown that the d-wave pairing correlations are enhanced within the axial
striped and phase separated states, but not in the regular phases. Moreover, it
was found that the antiferromagnetic spin arrangement within the chains further
enhances the d-wave paring correlations, while the ferromagnetic one has a
fully opposite effect.


title: Structures induced by companions in galactic discs

abstract:
  Using N-body simulations we study the structures induced on a galactic disc
by repeated flybys of a companion in decaying eccentric orbit around the disc.
Our system is composed by a stellar disc, bulge and live dark matter halo, and
we study the system's dynamical response to a sequence of a companion's flybys,
when we vary i) the disc's temperature (parameterized by Toomre's Q-parameter)
and ii) the companion's mass and initial orbit. We use a new 3D Cartesian grid
code: MAIN (Mesh-adaptive Approximate Inverse N-body solver). The main features
of MAIN are reviewed, with emphasis on the use of a new Symmetric Factored
Approximate Sparse Inverse (SFASI) matrix in conjunction with the multigrid
method that allows the efficient solution of Poisson's equation in three space
variables. We find that: i) companions need to be assigned initial masses in a
rather narrow window of values in order to produce significant and more
long-standing non-axisymmetric structures (bars and spirals) in the main
galaxy's disc by the repeated flyby mechanism. ii) a crucial phenomenon is the
antagonism between companion-excited and self-excited modes on the disc. Values
of $Q >1.5$ are needed in order to allow for the growth of the
companion-excited modes to prevail over the the growth of the disc's
self-excited modes. iii) We give evidence that the companion-induced spiral
structure is best represented by a density wave with pattern speed nearly
constant in a region extending from the ILR to a radius close to, but inside,
corotation.


title:
Regulation of oxygen vacancy types on SnO2 (110) surface by external
  strain

abstract:
  In tin dioxide nanostructures, oxygen vacancies (OVs) play an important role
in their optical properties and thus regulation of both OV concentration and
type via external strain is crucial to exploration of more applications.
First-principle calculations of SnO2 (110) surface disclose that asymmetric
deformations induced by external strain not only lead to its intrinsic surface
elastic changes, but also result in different OV formation energy. In the
absence of external strain, the energetically favorable oxygen vacancies (EFOV)
appear in the bridging site of second layer. When -3.5% external strain is
applied along y direction, the EFOV moves into plane site. This can be ascribed
that the compressed deformation gives rise to redistribution of electronic wave
function near OVs, therefore, formation of newly bond structures. Our results
suggest that different type OVs in SnO2 surface can be controlled by strain
engineering.


title:
Universal phase diagrams with superconducting domes for electronic flat
  bands

abstract:
  Condensed matter systems with flat bands close to the Fermi level generally
exhibit, due to their very large density of states, extraordinary high critical
ordering temperatures of symmetry breaking orders, such as superconductivity
and magnetism. Here we show that the critical temperatures follow one of two
universal curves with doping away from a flat band depending on the ordering
channel, which completely dictates both the general order competition and the
phase diagram. Notably, we find that orders in the particle-particle channel
(superconducting orders) survive decisively further than orders in the
particle-hole channel (magnetic or charge orders) because the channels have
fundamentally different polarizabilities. Thus, even if a magnetic or charge
order initially dominates, superconducting domes are still likely to exist on
the flanks of flat bands. We apply these general results to both the
topological surface flat bands of rhombohedral ABC-stacked graphite and to the
van Hove singularity of graphene.


title: Meromorphic continuation approach to noncommutative geometry

abstract:
  Following an idea of Nigel Higson, we develop a method for proving the
existence of a meromor-phic continuation for some spectral zeta functions. The
method is based on algebras of generalized differential operators. The main
theorem states, under some conditions, the existence of a meromor-phic
continuation, a localization of the poles in supports of arithmetic sequences
and an upper bound of their order. We give an application in relation with a
class of nilpotent Lie algebras.


title: The Planckonions

abstract:
  We consider a spherically symmetric stellar configuration with a density
profile $\rho(r)=\frac{c^2}{8\pi G r^2} $. This configuration satisfies the
Schwarzchild black hole condition $\frac {2GM}{c^2 R}=~1$ for every $ r =R $.
We refer it as "Planckonion". The interesting thing about the Plankonion is
that it has an onion like structure. The central sphere with radius of the
Plank-lenght $ L_p=\sqrt{(\frac {2\hbar G}{c^3})}$ has one unit of the
Planck-mass $M_p=\sqrt {(\frac {c\hbar}{2G})}$. Subsequent spherical shells of
radial width $L_p$ contain exactly one unit of $M_p$. We study this stellar
configuration using Tolman-Oppenheimer-Volkoff equation and show that the
equation is satisfied if pressure $P(r)=-\rho(r)$. On the geometrical side, the
space component of the metric blows up at every point. The time component of
the metric is zero inside the star but only in the sense of a distribution
(generalized function). The Planckonions mimic some features of black holes but
avoid appearance of central singularity because of the violation of null energy
conditions.


title: Boundary Layer Analysis for the Fast Horizontal Rotating Fluids

abstract:
  It is well known that, for fast rotating fluids with the axis of rotation
being perpendicular to the boundary, the boundary layer is of Ekman-type,
described by a linear ODE system. In this paper we consider fast rotating
fluids, with the axis of rotation being parallel to the boundary. We show that
the corresponding boundary layer is describe by a nonlinear, degenerated PDE
system which is similar to the 2-D Prandtl system. Finally, we prove the
well-posedness of the governing system of the boundary layer in the space of
analytic functions with respect to tangential variable.


title:
Tur\'an type converse Markov inequalities in $L^q$ on a generalized
  Er\H{o}d class of convex domains

abstract:
  P. Tur\'an was the first to derive lower estimations on the uniform norm of
the derivatives of polynomials $p$ of uniform norm $1$ on the interval
I:=[-1,1] and the disk D:=$\{z \in C~:~|z| \le 1\}$, under the normalization
condition that the zeroes of the polynomial p in question all lie in I or D,
resp. Namely, in 1939 he proved that with n:=deg p tending to infinity, the
precise growth order of the minimal possible derivative norm is $\sqrt{n}$ for
I and n for D.
  Already the same year J. Er\H{o}d considered the problem on other domains. In
his most general formulation, he extended Tur\'an's order n result on D to a
certain general class of piecewise smooth convex domains. Finally, a decade ago
the growth order of the minimal possible norm of the derivative was proved to
be n for all compact convex domains.
  Tur\'an himself gave comments about the above oscillation question in $L^q$
norm on D. Nevertheless, till recently results were known only for I, D and
so-called R-circular domains.
  Continuing our recent work, also here we investigate the Tur\'an-Er\H{o}d
problem on general classes of domains.


title:
Gyrokinetic turbulence: between idealized estimates and a detailed
  analysis of nonlinear energy transfers

abstract:
  Using large resolution numerical simulations of GK turbulence, spanning an
interval ranging from the end of the fluid scales to the electron gyroradius,
we study the energy transfers in the perpendicular direction for a
proton-electron plasma in a slab magnetic geometry. In addition, to aid our
understanding of the nonlinear cascade, we use an idealized test representation
for the energy transfers between two scales, mimicking the dynamics of
turbulence in an infinite inertial range. For GK turbulence, a detailed
analysis of nonlinear energy transfers that account for the separation of
energy exchanging scales is performed. We show that locality functions
associated with the energy cascade across dyadic (i.e. multiple of two)
separated scales achieve an asymptotic state, recovering clear values for the
locality exponents. We relate these exponents to the energy exchange between
two scales, diagnostics that are less computationally intensive than the
locality functions. It is the first time asymptotic locality is shown to exist
for GK turbulence and the contributions made by highly non-local interactions,
previously reported in the literature, are explained as very local transfers of
energy that occur between wavenumbers within the same dyadic signal. The
results presented here and their implications are discussed from the
perspective of previous findings reported in the literature and the idea of
universality of GK turbulence.


title:
Diversity encouraged learning of unsupervised LSTM ensemble for neural
  activity video prediction

abstract:
  Being able to predict the neural signal in the near future from the current
and previous observations has the potential to enable real-time responsive
brain stimulation to suppress seizures. We have investigated how to use an
auto-encoder model consisting of LSTM cells for such prediction. Recog- nizing
that there exist multiple activity pattern clusters, we have further explored
to train an ensemble of LSTM mod- els so that each model can specialize in
modeling certain neural activities, without explicitly clustering the training
data. We train the ensemble using an ensemble-awareness loss, which jointly
solves the model assignment problem and the error minimization problem. During
training, for each training sequence, only the model that has the lowest recon-
struction and prediction error is updated. Intrinsically such a loss function
enables each LTSM model to be adapted to a subset of the training sequences
that share similar dynamic behavior. We demonstrate this can be trained in an
end- to-end manner and achieve significant accuracy in neural activity
prediction.


title:
Surface plasmon amplification by stimulated emission of radiation in
  hyperbolic metamaterials

abstract:
  We study theoretically and numerically spasing conditions and optical
dynamics of a composite hyperbolic metamaterial interacting with gain
molecules. By combining Maxwell-Bloch equations with Green's function approach,
we calculate lasing frequency and threshold population inversion for various
gain density in the gain layer. We demonstrate high level of enhancement for
photonic density of states in spacious spectral range provided by hyperbolic
metastructures. We find that direct dipole-dipole interactions between
molecules in the gain layer has a negligible effect on spasing conditions. We
identify a region of parameters in which spasing can occur considering these
effects.


title:
Verifying the consistency relation for the scale-dependent bias from
  local primordial non-Gaussianity

abstract:
  We measure the large-scale bias of dark matter halos in simulations with
non-Gaussian initial conditions of the local type, and compare this bias to the
response of the mass function to a change in the primordial amplitude of
fluctuations. The two are found to be consistent, as expected from physical
arguments, for three halo-finder algorithms which use different Spherical
Overdensity (SO) and Friends-of-Friends (FoF) methods. On the other hand, we
find that the commonly used prediction for universal mass functions, that the
scale-dependent bias is proportional to the first-order Gaussian Lagrangian
bias, does not yield a good agreement with the measurements. For all halo
finders, high-mass halos show a non-Gaussian bias suppressed by 10-15% relative
to the universal mass function prediction. For SO halos, this deviation changes
sign at low masses, where the non-Gaussian bias becomes larger than the
universal prediction.


title: p-th Kazdan-Warner equation on graph

abstract:
  Let $G=(V,E)$ be a connected finite graph and $C(V)$ be the set of functions
defined on $V$. Let $\Delta_p$ be the discrete $p$-Laplacian on $G$ with $p>1$
and $L=\Delta_p-k$, where $k\in C(V)$ is positive everywhere. Consider the
operator $L:C(V)\rightarrow C(V)$. We prove that $-L$ is one to one, onto and
preserves order. So it implies that there exists a unique solution to the
equation $Lu=f$ for any given $f\in C(V)$. We also prove that the equation
$\Delta_pu=\overline{f}-f$ has a solution which is unique up to a constant,
where $\overline{f}$ is the average of $f$. With the help of these results, we
finally give various conditions such that the $p$-th Kazdan-Warner equation
$\Delta_pu=c-he^u$ has a solution on $V$ for given $h\in C(V)$ and $c\in
\mathds{R}$. Thus we generalize Grigor'yan, Lin and Yang's work \cite{GLY} for
$p=2$ to any $p>1$.


title: Topology of a class of $p2$-crystallographic replication tiles

abstract:
  We study the topological properties of a class of planar crystallographic
replication tiles. Let $M\in\mathbb{Z}^{2\times2}$ be an expanding matrix with
characteristic polynomial $x^2+Ax+B$ ($A,B\in\mathbb{Z}$, $B\geq 2$) and ${\bf
v}\in\mathbb{Z}^2$ such that $({\bf v},M{\bf v})$ are linearly independent.
Then the equation $$MT+\frac{B-1}{2}{\bf v} =T\cup(T+{\bf v})\cup (T+2{\bf
v})\cup \cdots\cup(T+(B-2){\bf v})\cup(-T) $$ defines a unique nonempty compact
set $T$ satisfying $\overline{T^o}=T$. Moreover, $T$ tiles the plane by the
crystallographic group $p2$ generated by the $\pi$-rotation and the
translations by integer vectors. It was proved by Leung and Lau in the context
of self-affine lattice tiles with collinear digit set that $T\cup (-T)$ is
homeomorphic to a closed disk if and only if $2|A|<B+3$. However, this
characterization does not hold anymore for $T$ itself. In this paper, we
completely characterize the tiles $T$ of this class that are homeomorphic to a
closed disk.


title:
Transit Clairvoyance: Enhancing TESS follow-up using artificial neural
  networks

abstract:
  The upcoming TESS mission is expected to find thousands of transiting planets
around bright stars, yet for three-quarters of the fields observed the temporal
coverage will limit discoveries to planets with orbital periods below 13.7
days. From the Kepler catalog, the mean probability of these short-period
transiting planets having additional longer period transiters (which would be
missed by TESS) is 18%, a value ten times higher than the average star. In this
work, we show how this probability is not uniform but functionally dependent
upon the properties of the observed short-period transiters, ranging from less
than 1% up to over 50%. Using artificial neural networks (ANNs) trained on the
Kepler catalog and making careful feature selection to account for the
differing sensitivity of TESS, we are able to predict the most likely
short-period transiters to be accompanied by additional transiters. Through
cross-validation, we predict that a targeted, optimized TESS transit and/or
radial velocity follow-up program using our trained ANN would have a discovery
yield improved by a factor of two. Our work enables a near-optimal follow-up
strategy for surveys following TESS targets for additional planets, improving
the science yield derived from TESS and particularly beneficial in the search
for habitable-zone transiting worlds.


title: CIFAR-10: KNN-based Ensemble of Classifiers

abstract:
  In this paper, we study the performance of different classifiers on the
CIFAR-10 dataset, and build an ensemble of classifiers to reach a better
performance. We show that, on CIFAR-10, K-Nearest Neighbors (KNN) and
Convolutional Neural Network (CNN), on some classes, are mutually exclusive,
thus yield in higher accuracy when combined. We reduce KNN overfitting using
Principal Component Analysis (PCA), and ensemble it with a CNN to increase its
accuracy. Our approach improves our best CNN model from 93.33% to 94.03%.


title: A p-th Yamabe equations on graph

abstract:
  Assume $\alpha\geq p>1$. Consider the following $p$-th Yamabe equation on a
connected finite graph $G$: $$\Delta_p\varphi+h\varphi^{p-1}=\lambda
f\varphi^{\alpha-1},$$ where $\Delta_p$ is the discrete $p$-Laplacian, $h$ and
$f>0$ are fixed real functions defined on all vertices. We show that the above
equation always has a positive solution $\varphi$ for some constant
$\lambda\in\mathds{R}$.


title: Fitting MA(q) Models in the Closed Invertible Region

abstract:
  The use of reparameterization in the maximization of the likelihood function
of the MA(q) model is discussed. A general method for testing for the presence
of a parameter estimate on the boundary of an MA(q) model is presented. This
test is illustrated with a brief simulation experiment for the MA(q) for
q=1,2,3,4 in which it is shown that the probability of an estimate being on the
boundary increases with q.


title: Asymptotic and bootstrap tests for subspace dimension

abstract:
  Most linear dimension reduction methods proposed in the literature can be
formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss
(2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo
and Li (2016). The eigen-decomposition of one scatter matrix with respect to
another is then often used to determine the dimension of the signal subspace
and to separate signal and noise parts of the data. Three popular dimension
reduction methods, namely principal component analysis (PCA), fourth order
blind identification (FOBI) and sliced inverse regression (SIR) are considered
in detail and the first two moments of subsets of the eigenvalues are used to
test for the dimension of the signal space. The limiting null distributions of
the test statistics are discussed and novel bootstrap strategies are suggested
for the small sample cases. In all three cases, consistent test-based estimates
of the signal subspace dimension are introduced as well. The asymptotic and
bootstrap tests are compared in simulations and illustrated in real data
examples.


title:
Canonical quantum observables for molecular systems approximated by ab
  initio molecular dynamics

abstract:
  It is known that ab initio molecular dynamics based on the electron ground
state eigenvalue can be used to approximate quantum observables in the
canonical ensemble when the temperature is low compared to the first electron
eigenvalue gap. This work proves that a certain weighted average of the
different ab initio dynamics, corresponding to each electron eigenvalue,
approximates quantum observables for any temperature. The proof uses the
semiclassical Weyl law to show that canonical quantum observables of
nuclei-electron systems, based on matrix valued Hamiltonian symbols, can be
approximated by ab initio molecular dynamics with the error proportional to the
electron-nuclei mass ratio. The result covers observables that depend on
time-correlations. A combination of the Hilbert-Schmidt inner product for
quantum operators and Weyl's law shows that the error estimate holds for
observables and Hamiltonian symbols that have three and five bounded
derivatives, respectively, provided the electron eigenvalues are distinct for
any nuclei position and the observables are in the diagonal form with respect
to the electron eigenstates.


title: Asymptotic density of Motzkin numbers modulo small primes

abstract:
  We establish the asymptotic density of the Motzkin numbers modulo small
primes.


title: The K-band luminosity functions of cluster galaxies

abstract:
  We derive the galaxy luminosity function in the $K_s$ band for galaxies in 24
clusters to provide a local reference for higher redshift studies and to
analyse how and if the luminosity function varies according to environment and
cluster properties. We use new, deep $K$ band imaging and match the photometry
to available redshift information and to optical photometry from the SDSS or
the UKST/POSS: $>80\%$ of the galaxies to $K \sim 14.5$ have measured
redshifts. We derive composite luminosity functions, for the entire sample and
for cluster subsamples . We consider the luminosity functions for red sequence
and blue cloud galaxies. The full composite luminosity function has $K^*=12.79
\pm 0.14$ ($M_K=-24.81$) and $\alpha=-1.41 \pm 0.10$. We find that $K^*$ is
largely unaffected by the environment but that the slope $\alpha$ increases
towards lower mass clusters and clusters with Bautz-Morgan type $<$ II. The red
sequence luminosity function seems to be approximately universal (within
errors) in all environments: it has parameters $K^*=13.16 \pm 0.15$
($M_K=-24.44$) and $\alpha=-1.00 \pm 0.12$ (for all galaxies). Blue galaxies do
not show a good fit to a Schechter function, but the best values for its
parameters are $K^*=13.51 \pm 0.41$ ($M_K=-24.09$) and $\alpha=-1.60 \pm 0.29$:
we do not have enough statistics to consider environmental variations for these
galaxies. We find some evidence that $K^*$ in clusters is brighter than in the
field and $\alpha$ is steeper, but note this comparison is based (for the
field) on 2MASS photometry, while our data are considerably deeper.


title: Metastability on the hierarchical lattice

abstract:
  We study metastability for Glauber spin-flip dynamics on the $N$-dimensional
hierarchical lattice with $n$ hierarchical levels. Each vertex carries an Ising
spin that can take the values $-1$ or $+1$. Spins interact with an external
magnetic field $h>0$. Pairs of spins interact with each other according to a
ferromagnetic pair potential $\vec{J}=\{J_i\}_{i=1}^n$, where $J_i>0$ is the
strength of the interaction between spins at hierarchical distance $i$. Spins
flip according to a Metropolis dynamics at inverse temperature $\beta$. In the
limit as $\beta\to\infty$, we analyse the crossover time from the metastable
state $\boxminus$ (all spins $-1$) to the stable state $\boxplus$ (all spins
$+1$). Under the assumption that $\vec{J}$ is non-increasing, we identify the
mean transition time up to a multiplicative factor $1+o_\beta(1)$. On the scale
of its mean, the transition time is exponentially distributed. We also identify
the set of configurations representing the gate for the transition. For the
special case where $J_i = \tilde{J}/N^i$, $1 \leq i \leq n$, with $\tilde{J}>0$
the relevant formulas simplify considerably. Also the hierarchical mean-field
limit $N\to\infty$ can be analysed in detail.


title: Total Variation Depth for Functional Data

abstract:
  There has been extensive work on data depth-based methods for robust
multivariate data analysis. Recent developments have moved to
infinite-dimensional objects such as functional data. In this work, we propose
a new notion of depth, the total variation depth, for functional data. As a
measure of depth, its properties are studied theoretically, and the associated
outlier detection performance is investigated through simulations. Compared to
magnitude outliers, shape outliers are often masked among the rest of samples
and harder to identify. We show that the proposed total variation depth has
many desirable features and is well suited for outlier detection. In
particular, we propose to decompose the total variation depth into two
components that are associated with shape and magnitude outlyingness,
respectively. This decomposition allows us to develop an effective procedure
for outlier detection and useful visualization tools, while naturally
accounting for the correlation in functional data. Finally, the proposed
methodology is demonstrated using real datasets of curves, images, and video
frames.


title: Long time evolution of concentrated Euler flows with planar symmetry

abstract:
  We study the time evolution of an incompressible Euler fluid with planar
symmetry when the vorticity is initially concentrated in small disks. We
discuss how long this concentration persists, showing that in some cases this
happens for quite long times. Moreover, we analyze a toy model that shows a
similar behavior and gives some hints on the original problem.


title: Dark-bright soliton interactions beyond the integrable limit

abstract:
  In this work we present a systematic theoretical analysis regarding
dark-bright solitons and their interactions, motivated by recent advances in
atomic two-component repulsively interacting Bose-Einstein condensates. In
particular, we study analytically via a two-soliton ansatz adopted within a
variational formulation the interaction between two dark-bright solitons in a
homogeneous environment beyond the integrable regime, by considering general
inter/intra-atomic interaction coefficients. We retrieve the possibility of a
fixed point in the case where the bright solitons are out of phase. As the
inter-component interaction is increased, we also identify an exponential
instability of the two-soliton state, associated with a subcritical pitchfork
bifurcation. The latter gives rise to an asymmetric partition of the bright
soliton mass and dynamically leads to spontaneous splitting of the bound pair.
In the case of the in-phase bright solitons, we explain via parsing the
analytical approximations and monitoring the direct dynamics why no such pair
is identified, despite its prediction by the variational analysis.


title: Marcinkiewicz multipliers and Lipschitz spaces on Heisenberg groups

abstract:
  The Marcinkiewicz multipliers are $L^{p}$ bounded for $1<p<\infty $ on the
Heisenberg group $\mathbb{H}^{n}\simeq \mathbb{C}^{n}\times \mathbb{R}$
(M\"uller, Ricci and Stein \cite{MRS}). This is surprising in the sense that
these multipliers are invariant under a two parameter group of dilations on
$\mathbb{C}^{n}\times \mathbb{R}$, while there is \emph{no} two parameter group
of \emph{automorphic} dilations on $\mathbb{H} ^{n}$. The purpose of this paper
is to establish a theory of the flag Lipschitz space on the Heisenberg group
$\mathbb{H}^{n}\simeq \mathbb{C}^{n}\times \mathbb{R}$ in the sense
`intermediate' between the classical Lipschitz space on the Heisenberg group
$\mathbb{H}^{n}$ and the product Lipschitz space on $\mathbb{C}^{n}\times
\mathbb{R}$. We characterize this flag Lipschitz space via the
Littelewood-Paley theory and prove that flag singular integral operators, which
include the Marcinkiewicz multipliers, are bounded on these flag Lipschitz
spaces.


title: A BRITE view on delta Scuti and gamma Doradus stars

abstract:
  BRITE-Constellation has obtained data for a few delta Scuti and gamma Doradus
type stars. A short overview of the pulsational content found in five stars -
beta Cassiopeiae, epsilon Cephei, M Velorum, beta Pictoris and QW Puppis - is
given and the potential of BRITE-Constellation observations of delta Scuti and
gamma Doradus pulsators is discussed.


title:
Ultrametricity of optimal transport substates for multiple interacting
  paths over a square lattice network

abstract:
  We model a set of point-to-point transports on a network as a system of
polydisperse interacting self-avoiding walks (SAWs) over a finite square
lattice. The ends of each SAW may be located both at random, uniformly
distributed, positions or with one end fixed at a lattice corner. The total
energy of the system is computed as the sum over all SAWs, which may represent
either the time needed to complete the transport over the network, or the
resources needed to build the networking infrastructure. We focus especially on
the second aspect by assigning a concave cost function to each site to
encourage path overlap. A Simulated Annealing optimization, based on a modified
BFACF Montecarlo algorithm developed for polymers, is used to probe the complex
conformational substates structure. We characterize the average cost gains (and
path-length variation) for increasing polymer density with respect to a
Dijkstra routing and find a non-monotonic behavior as previously found in
random networks. We observe the expected phase transition when switching from a
convex to a concave cost function (e.g., $x^\gamma$, where $x$ represents the
node overlap) and the emergence of ergodicity breaking, finally we show that
the space of ground states for $\gamma<1$ is compatible with an ultrametric
structure as seen in many complex systems such as some spin glasses.


title:
The potential of space observations for pulsating pre-main sequence
  stars

abstract:
  The first asteroseismic studies of pre-main sequence (pre-MS) pulsators have
been conducted based on data from the space telescopes MOST and CoRoT with
typical time bases of less than 40 days. With these data, a relation between
the pulsational properties of pre-MS delta Scuti stars and their relative
evolutionary phase on their way from the birthline to the zero-age main
sequence was revealed. But it is evident from comparison with the more evolved
pulsators in their main sequence or post-main sequence stages observed by the
main Kepler mission, that many more questions could be addressed with
significantly longer time bases and ultra-high precision. Here, I will discuss
the observational status of pre-MS asteroseismology and the potential of future
space observations for this research field.


title: Unsupervised Learning with Truncated Gaussian Graphical Models

abstract:
  Gaussian graphical models (GGMs) are widely used for statistical modeling,
because of ease of inference and the ubiquitous use of the normal distribution
in practical approximations. However, they are also known for their limited
modeling abilities, due to the Gaussian assumption. In this paper, we introduce
a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits
efficient inference. Specifically, we impose a bipartite structure on the GGM
and govern the hidden variables by truncated normal distributions. The
nonlinearity of the model is revealed by its connection to rectified linear
unit (ReLU) neural networks. Meanwhile, thanks to the bipartite structure and
appealing properties of truncated normals, we are able to train the models
efficiently using contrastive divergence. We consider three output constructs,
accounting for real-valued, binary and count data. We further extend the model
to deep constructions and show that deep models can be used for unsupervised
pre-training of rectifier neural networks. Extensive experimental results are
provided to validate the proposed models and demonstrate their superiority over
competing models.


title: Gaussian mixtures: entropy and geometric inequalities

abstract:
  A symmetric random variable is called a Gaussian mixture if it has the same
distribution as the product of two independent random variables, one being
positive and the other a standard Gaussian random variable. Examples of
Gaussian mixtures include random variables with densities proportional to
$e^{-|t|^p}$ and symmetric $p$-stable random variables, where $p\in(0,2]$. We
obtain various sharp moment and entropy comparison estimates for weighted sums
of independent Gaussian mixtures and investigate extensions of the B-inequality
and the Gaussian correlation inequality in the context of Gaussian mixtures. We
also obtain a correlation inequality for symmetric geodesically convex sets in
the unit sphere equipped with the normalized surface area measure. We then
apply these results to derive sharp constants in Khintchine inequalities for
vectors uniformly distributed on the unit balls with respect to $p$-norms and
provide short proofs to new and old comparison estimates for geometric
parameters of sections and projections of such balls.


title: 43 Cygni observed with BRITE-Constellation

abstract:
  The gamma Doradus star 43 Cygni was observed by BRITE-Toronto for 156 days in
2015. From this data set we identified 37 pulsation frequencies which show a
regular period spacing pattern that will be subject of a more detailed
asteroseismic analysis.


title: Topologically ordered magnesium-biopolymer hybrid composite structures

abstract:
  Magnesium and its alloys are intriguing as possible biodegradable
biomaterials due to their unique combination of biodegradability and high
specific mechanical properties. However, uncontrolled biodegradation of
magnesium during implantation remains a major challenge in spite of the use of
alloying and protective coatings. In this study, a hybrid composite structure
of magnesium metal and a biopolymer was fabricated as an alternative approach
to control the corrosion rate of magnesium. A multistep process that combines
metal foam production and injection molding was developed to create a hybrid
composite structure that is topologically ordered in all three dimensions.
Preliminary investigations of the mechanical properties and corrosion behavior
exhibited by the hybrid Mg-polymer composite structures suggest a new potential
approach to the development of Mg-based biomedical devices.


title:
Robust Semi-Supervised Graph Classifier Learning with Negative Edge
  Weights

abstract:
  In a semi-supervised learning scenario, (possibly noisy) partially observed
labels are used as input to train a classifier, in order to assign labels to
unclassified samples. In this paper, we study this classifier learning problem
from a graph signal processing (GSP) perspective. Specifically, by viewing a
binary classifier as a piecewise constant graph-signal in a high-dimensional
feature space, we cast classifier learning as a signal restoration problem via
a classical maximum a posteriori (MAP) formulation. Unlike previous
graph-signal restoration works, we consider in addition edges with negative
weights that signify anti-correlation between samples. One unfortunate
consequence is that the graph Laplacian matrix $\mathbf{L}$ can be indefinite,
and previously proposed graph-signal smoothness prior $\mathbf{x}^T \mathbf{L}
\mathbf{x}$ for candidate signal $\mathbf{x}$ can lead to pathological
solutions. In response, we derive an optimal perturbation matrix
$\boldsymbol{\Delta}$ - based on a fast lower-bound computation of the minimum
eigenvalue of $\mathbf{L}$ via a novel application of the Haynsworth inertia
additivity formula---so that $\mathbf{L} + \boldsymbol{\Delta}$ is positive
semi-definite, resulting in a stable signal prior. Further, instead of forcing
a hard binary decision for each sample, we define the notion of generalized
smoothness on graph that promotes ambiguity in the classifier signal. Finally,
we propose an algorithm based on iterative reweighted least squares (IRLS) that
solves the posed MAP problem efficiently. Extensive simulation results show
that our proposed algorithm outperforms both SVM variants and graph-based
classifiers using positive-edge graphs noticeably.


title: Phase Jump Method for Efficiency Enhancement in Free-Electron Lasers

abstract:
  The efficiency of a free-electron laser can be enhanced by sustaining the
growth of the radiation power beyond the initial saturation. One notable method
is undulator tapering, which involves the variation of the gap height and/or
the period along the undulator. Another method is the introduction of phase
jumps, using phase-shifting chicanes in the drift sections separating the
undulator segments. In this article, we develop a physics model of this phase
jump method, and verify it with numerical simulations. The model elucidates the
energy extraction process in the longitudinal phase space. The main ingredient
is the microbunch deceleration cycle, which enables the microbunched electron
beam to decelerate and radiate coherently beyond the initial saturation. The
ponderomotive bucket is stationary, and energy can even be extracted from
electrons outside the bucket. The model addresses the selection criteria for
the phase jump values, and the requirement on the undulator segment length. It
also describes the mechanism of the final saturation. In addition, we discuss
the similarities and differences between the phase jump method and undulator
tapering, by comparing our phase jump model to the classic
Kroll-Morton-Rosenbluth model.


title:
Locality and Efficient Evaluation of Lattice Composite Fields:
  Overlap-Based Gauge Operators

abstract:
  We propose a novel general approach to locality of lattice composite fields,
which in case of QCD involves locality in both quark and gauge degrees of
freedom. The method is applied to gauge operators based on the overlap Dirac
matrix elements, showing for the first time their local nature on realistic
path-integral backgrounds. The framework entails a method for efficient
evaluation of such non-ultralocal operators, whose computational cost is
volume-indepenent at fixed accuracy, and only grows logarithmically as this
accuracy approaches zero. This makes computation of useful operators, such as
overlap-based topological density, practical. The key notion underlying these
features is that of exponential insensitivity to distant fields, made rigorous
by introducing the procedure of statistical regularization. The scales
associated with insensitivity property are useful characteristics of non-local
continuum operators.


title: Probing the String Winding Sector

abstract:
  We probe a slice of the massive winding sector of bosonic string theory from
toroidal compactifications of Double Field Theory (DFT). This string subsector
corresponds to states containing one left and one right moving oscillators. We
perform a generalized Kaluza Klein compactification of DFT on generic
$2n$-dimensional toroidal constant backgrounds and show that, up to third order
in fluctuations, the theory coincides with the corresponding effective theory
of the bosonic string compactified on $n$-dimensional toroidal constant
backgrounds, obtained from three-point amplitudes. The comparison between both
theories is facilitated by noticing that generalized diffeomorphisms in DFT
allow to fix generalized harmonic gauge conditions that help in identifying the
physical degrees of freedom. These conditions manifest as conformal anomaly
cancellation requirements on the string theory side. The explicit expression
for the gauge invariant effective action containing the physical massless
sector (gravity+antisymmetric+gauge+ scalar fields) coupled to towers of
generalized Kaluza Klein massive states (corresponding to compact momentum and
winding modes) is found. The action acquires a very compact form when written
in terms of fields carrying $O(n,n)$ indices, and is explicitly T-duality
invariant. The global algebra associated to the generalized Kaluza Klein
compactification is discussed.


title: Neural Machine Translation with Pivot Languages

abstract:
  While recent neural machine translation approaches have delivered
state-of-the-art performance for resource-rich language pairs, they suffer from
the data scarcity problem for resource-scarce language pairs. Although this
problem can be alleviated by exploiting a pivot language to bridge the source
and target languages, the source-to-pivot and pivot-to-target translation
models are usually independently trained. In this work, we introduce a joint
training algorithm for pivot-based neural machine translation. We propose three
methods to connect the two models and enable them to interact with each other
during training. Experiments on Europarl and WMT corpora show that joint
training of source-to-pivot and pivot-to-target models leads to significant
improvements over independent training across various languages.


title:
Vertical slice modelling of nonlinear Eady waves using a compatible
  finite element method

abstract:
  A vertical slice model is developed for the Euler-Boussinesq equations with a
constant temperature gradient in the direction normal to the slice (the
Eady-Boussinesq model). The model is a solution of the full three-dimensional
equations with no variation normal to the slice, which is an idealized problem
used to study the formation and subsequent evolution of weather fronts. A
compatible finite element method is used to discretise the governing equations.
To extend the Charney-Phillips grid staggering in the compatible finite element
framework, we use the same node locations for buoyancy as the vertical part of
velocity and apply a transport scheme for a partially continuous finite element
space. For the time discretisation, we solve the semi-implicit equations
together with an explicit strong-stability-preserving Runge-Kutta scheme to all
of the advection terms. The model reproduces several quasi-periodic lifecycles
of fronts despite the presence of strong discontinuities. An asymptotic limit
analysis based on the semi-geostrophic theory shows that the model solutions
are converging to a solution in cross-front geostrophic balance. The results
are consistent with the previous results using finite difference methods,
indicating that the compatible finite element method is performing as well as
finite difference methods for this test problem. We observe dissipation of
kinetic energy of the cross-front velocity in the model due to the lack of
resolution at the fronts, even though the energy loss is not likely to account
for the large gap on the strength of the fronts between the model result and
the semi-geostrophic limit solution.


title: B-decay Anomalies in a Composite Leptoquark Model

abstract:
  The collection of a few anomalies in semileptonic $B$-decays, especially in
$b\rightarrow c \tau \bar{\nu}$, invites to speculate about the emergence of
some striking new phenomena, perhaps interpretable in terms of a weakly broken
$U(2)^n$ flavor symmetry and of leptoquark mediators. Here we aim at a partial
UV completion of this interpretation by generalizing the minimal composite
Higgs model to include a composite vector leptoquark as well.


title:
A Novel Approach for Learning How to Automatically Match Job Offers and
  Candidate Profiles

abstract:
  Automatic matching of job offers and job candidates is a major problem for a
number of organizations and job applicants that if it were successfully
addressed could have a positive impact in many countries around the world. In
this context, it is widely accepted that semi-automatic matching algorithms
between job and candidate profiles would provide a vital technology for making
the recruitment processes faster, more accurate and transparent. In this work,
we present our research towards achieving a realistic matching approach for
satisfactorily addressing this challenge. This novel approach relies on a
matching learning solution aiming to learn from past solved cases in order to
accurately predict the results in new situations. An empirical study shows us
that our approach is able to beat solutions with no learning capabilities by a
wide margin.


title: Inflation and pseudo-Goldstone Higgs boson

abstract:
  We consider inflation within a model framework where the Higgs boson arises
as a pseudo-Goldstone boson associated with the breaking of a global symmetry
at a scale significantly larger than the electroweak one. We show that in such
a model the scalar self-couplings can be parametrically suppressed and,
consequently, the non-minimal couplings to gravity can be of order one or less,
while the inflationary predictions of the model remain compatible with the
precision cosmological observations. Furthermore, in the model we study, the
existence of the electroweak scale is entirely due to the inflaton field. Our
model therefore suggests that inflation and low energy particle phenomenology
may be more entwined than assumed so far.


title:
Effects of model approximations for electron, hole, and photon transport
  in swift heavy ion tracks

abstract:
  The event-by-event Monte Carlo code, TREKIS, was recently developed to
describe excitation of the electron subsystems of solids in the nanometric
vicinity of a trajectory of a nonrelativistic swift heavy ion (SHI) decelerated
in the electronic stopping regime. The complex dielectric function (CDF)
formalism was applied in the used cross sections to account for collective
response of a matter to excitation. Using this model we investigate effects of
the basic assumptions on the modeled kinetics of the electronic subsystem which
ultimately determine parameters of an excited material in an SHI track. In
particular, (a) effects of different momentum dependencies of the CDF on
scattering of projectiles on the electron subsystem are investigated. The
'effective one-band' approximation for target electrons produces good
coincidence of the calculated electron mean free paths with those obtained in
experiments in metals. (b) Effects of collective response of a lattice appeared
to dominate in randomization of electron motion. We study how sensitive these
effects are to the target temperature. We also compare results of applications
of different model forms of (quasi-) elastic cross sections in simulations of
the ion track kinetics, e.g. those calculated taking into account optical
phonons in the CDF form vs. Mott's atomic cross sections. (c) It is
demonstrated that the kinetics of valence holes significantly affects
redistribution of the excess electronic energy in the vicinity of an SHI
trajectory as well as its conversion into lattice excitation in dielectrics and
semiconductors. (d) It is also shown that induced transport of photons
originated from radiative decay of core holes brings the excess energy faster
and farther away from the track core, however, the amount of this energy is
relatively small.


title: HPAT: High Performance Analytics with Scripting Ease-of-Use

abstract:
  Big data analytics requires high programmer productivity and high performance
simultaneously on large-scale clusters. However, current big data analytics
frameworks (e.g. Apache Spark) have prohibitive runtime overheads since they
are library-based. We introduce a novel auto-parallelizing compiler approach
that exploits the characteristics of the data analytics domain such as the
map/reduce parallel pattern and is robust, unlike previous auto-parallelization
methods. Using this approach, we build High Performance Analytics Toolkit
(HPAT), which parallelizes high-level scripting (Julia) programs automatically,
generates efficient MPI/C++ code, and provides resiliency. Furthermore, it
provides automatic optimizations for scripting programs, such as fusion of
array operations. Thus, HPAT is 369x to 2033x faster than Spark on the Cori
supercomputer and 20x to 256x times on Amazon AWS.


title: The Fate of the Higgs Vacuum

abstract:
  This talk reviews our recent work showing how tiny black holes can act as
nucleation sites for the decay of the metastable Higgs vacuum. We start by
discussing the formation of thin wall bubbles of true vacuum inside a false
vacuum, and show how adding a black hole lowers the action of the Euclidean
tunneling solution, thus strongly enhancing the probability of vacuum decay. We
then review numerical results for the Higgs vacuum showing that the decay rate
is even higher for these "thick wall" bubbles. The results imply either tiny
black holes are not a component of our universe, or BSM corrections to the
Higgs potential must stabilise our vacuum.


title: Luminous Red Nova 2015 in the Galaxy M101

abstract:
  We present the results of the study of the red nova PSN J14021678+5426205
based on the observations carried out with the Russian 6-m telescope (BTA)
along with other telescopes of SAO RAS and SAI MSU. To investigate the nova
progenitor, we used the data from the Digital Sky Survey and amateur photos
available on the internet. In the period between April 1993 and July 2014, the
brightness of the progenitor gradually increased by 2.2 mag in the V band. At
the peak of the first outburst in mid-November of 2014, the star reached an
absolute visual magnitude of -12.75 mag but was discovered later, in February
2015, in a repeated outburst at the absolute magnitude of -11.65 mag. The
amplitude of the outburst was minimum among the red novae, only 5.6 mag in the
V band. The H alpha emission line and the continuum of a cool supergiant with a
gradually decreasing surface temperature were observed in the spectra. Such
process is typical for red novae, although the object under study showed
extreme parameters: maximum luminosity, maximum outburst duration, minimum
outburst amplitude, unusual shape of the light curve. This event is interpreted
as a massive OB star system components merging accompanied by the formation of
a common envelope and then the expansion of this envelope with minimal energy
losses.


title: W-algebras and Whittaker categories

abstract:
  Affine W-algebras are a somewhat complicated family of (topological)
associative algebras associated with a semisimple Lie algebra, quantizing
functions on the algebraic loop space of Kostant's slice. They have attracted a
great deal of attention in geometric representation theory because of
Feigin-Frenkel's duality theorem for them, which identifies W-algebras for a
Lie algebra and its Langlands dual through a subtle construction.
  The main result of this paper is an affine version of Skryabin's theorem,
describing the category of modules over the W-algebra in simpler categorical
terms. But unlike the classical story, it is essential to work with derived
categories in the affine setting.
  One novel feature is the use of geometric techniques to study W-algebras: the
theory of D-modules on the loop group and the geometry of the affine
Grassmannian are indispensable tools. These are used to give an infinite family
of affine analogues of the Bezrukavnikov-Braverman-Mirkovic theorem, providing
a geometric version of Rodier's compact approximation to the Whittaker model
from the arithmetic setting. We also use these methods to generalize Beraldo's
theorem identifying Whittaker invariants and Whittaker coinvariants, extending
his result from GL_n to a general reductive group. At integral level, these
methods seem to have deep intrinsic meaning in the local geometric Langlands
program.
  The theory developed here provides systematic proofs of many classical
results in the subject. In particular, we clarify the exactness properties of
the quantum Drinfeld-Sokolov functor.


title: Nonlocal symmetries of Lax integrable equations: a comparative study

abstract:
  We continue here the study of Lax integrable equations. We consider four
three-dimensional equations: (1) the rdDym equation $u_{ty} = u_x u_{xy} - u_y
u_{xx}$, (2) the 3D Pavlov equation $u_{yy} = u_{tx} + u_y u_{xx} - u_x
u_{xy}$; (3) the universal hierarchy equation $u_{yy} = u_t u_{xy} - u_y
u_{tx}$, and (4) the modified Veronese web equation $u_{ty} = u_t u_{xy} - u_y
u_{tx}$. For each equation, using the know Lax pairs and expanding the latter
in formal series in spectral parameter, we construct two infinite-dimensional
differential coverings and give a full description of nonlocal symmetry
algebras associated to these coverings. For all the for pairs of coverings, the
obtained Lie algebras of symmetries manifest similar (but not the same)
structures: the are (semi) direct sums of the Witt algebra, the algebra of
vector fields on the line, and loop algebras; all of them contain a component
of finite grading. We also discuss actions of recursion operators on shadows
(in the sense of [I.S.Krasil'shchik, A.M. Vinogradov, Acta Appl. Math., 15
(1989) 1-2, 161--209.]) of nonlocal symmetries.


title:
High-order filtered schemes for time-dependent second order HJB
  equations

abstract:
  In this paper, we present and analyse a class of "filtered" numerical schemes
for second order Hamilton-Jacobi-Bellman equations. Our approach follows the
ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes
for the Monge-Amp\`ere partial differential equation, SIAM J. Numer. Anal.,
51(1):423--444, 2013, and more recently applied by other authors to stationary
or time-dependent first order Hamilton-Jacobi equations. For high order
approximation schemes (where "high" stands for greater than one), the
inevitable loss of monotonicity prevents the use of the classical theoretical
results for convergence to viscosity solutions. The work introduces a suitable
local modification of these schemes by "filtering" them with a monotone scheme,
such that they can be proven convergent and still show an overall high order
behaviour for smooth enough solutions. We give theoretical proofs of these
claims and illustrate the behaviour with numerical tests from mathematical
finance, focussing also on the use of backward difference formulae (BDF) for
constructing the high order schemes.


title: A generalization of the b-function lemma

abstract:
  We establish some cohomological bounds in D-module theory that are known in
the holonomic case and folklore in general. The method rests on a
generalization of the b-function lemma for non-holonomic D-modules.


title:
Empirical analysis of daily cash flow time series and its implications
  for forecasting

abstract:
  Cash managers make daily decisions based on predicted monetary inflows from
debtors and outflows to creditors. Usual assumptions on the statistical
properties of daily net cash flow include normality, absence of correlation and
stationarity. We provide a comprehensive study based on a real-world cash flow
data set from small and medium companies, which is the most common type of
companies in Europe. We also propose a new cross-validated test for time-series
non-linearity showing that: (i) the usual assumption of normality, absence of
correlation and stationarity hardly appear; (ii) non-linearity is often
relevant for forecasting; and (iii) typical data transformations have little
impact on linearity and normality. Our results provide a forecasting strategy
for cash flow management which performs better than classical methods. This
evidence may lead to consider a more data-driven approach such as time-series
forecasting in an attempt to provide cash managers with expert systems in cash
management.


title: Fast and Accurate Mining of Correlated Heavy Hitters

abstract:
  The problem of mining Correlated Heavy Hitters (CHH) from a two-dimensional
data stream has been introduced recently, and a deterministic algorithm based
on the use of the Misra--Gries algorithm has been proposed by Lahiri et al. to
solve it. In this paper we present a new counter-based algorithm for tracking
CHHs, formally prove its error bounds and correctness and show, through
extensive experimental results, that our algorithm outperforms the Misra--Gries
based algorithm with regard to accuracy and speed whilst requiring
asymptotically much less space.


title:
Tunneling of Hybridized Pairs of Electrons through a One-Dimensional
  Channel

abstract:
  Recently, the electron transport through a quasi-one dimensional (quasi-1D)
electron gas was investigated experimentally as a function of the confining
potential. We present a physical model for quantum ballistic transport of
electrons through a short conduction channel, and investigate the role played
by the Coulomb interaction in modifying the energy levels of two-electron
states at low temperatures as the width of the channel is increased. In this
regime, the effect of the Coulomb interaction on the two-electron states has
been shown to lead to four split energy levels, including two anti-crossings
and two crossing-level states. Due to the interplay between the anti-crossing
and crossing of the energy levels, the ground state for the two-electron model
switches from one anti-crossing state for strong confinement to a crossing
state for intermediate confinement as the channel width is first increased, and
then returned to its original anti-crossing state. This switching behavior is
related to the triplet spin degeneracy as well as the Coulomb repulsion and
reflected in the ballistic conductance. Here, many-body effects can still
affect electron occupations in the calculation of quantum ballistic conductance
although it cannot vary the center-of-mass velocity.


title: Volumes of Random Alternating Link Diagrams

abstract:
  We describe a model of random links based on random 4-valent maps, which can
be sampled due to the work of Schaeffer. We will look at the relationship
between the combinatorial information in the diagram and the hyperbolic volume.
Specifically, we show that for random alternating diagrams, the expected
hyperbolic volume is asymptotically linear in the number of crossings. For
nonalternating diagrams, we compute the probability of finding a given,
arbitrary tangle around a given crossing, and show that a random link diagram
will be highly composite. Additionally, we present some results of computer
experiments obtained from implementing the model in the program SnapPy.


title: Extending the coherence of a quantum dot hybrid qubit

abstract:
  Identifying and ameliorating dominant sources of decoherence are important
steps in understanding and improving quantum systems. Here we show that the
free induction decay time ($T_{2}^{*}$) and the Rabi decay rate
($\Gamma_{\mathrm{Rabi}}$) of the quantum dot hybrid qubit can be increased by
more than an order of magnitude by appropriate tuning of the qubit parameters
and operating points. By operating in the spin-like regime of this qubit, and
choosing parameters that increase the qubit's resilience to charge noise (which
we show is presently the limiting noise source for this qubit), we achieve a
Ramsey decay time $T_{2}^{*}$ of $177~\mathrm{ns}$ and a Rabi decay time,
$1/\Gamma_{\mathrm{Rabi}}$, exceeding $1~\mathrm{\mu s}$. We find that the
slowest $\Gamma_{\mathrm{Rabi}}$ is limited by fluctuations in the Rabi
frequency induced by charge noise and not by fluctuations in the qubit energy
itself.


title: Safety Model Checking with Complementary Approximations

abstract:
  Formal verification techniques such as model checking, are becoming popular
in hardware design. SAT-based model checking techniques such as IC3/PDR, have
gained a significant success in hardware industry. In this paper, we present a
new framework for SAT-based safety model checking, named Complementary
Approximate Reachability (CAR). CAR is based on standard reachability analysis,
but instead of maintaining a single sequence of reachable- state sets, CAR
maintains two sequences of over- and under- approximate reachable-state sets,
checking safety and unsafety at the same time. To construct the two sequences,
CAR uses standard Boolean-reasoning algorithms, based on satisfiability
solving, one to find a satisfying cube of a satisfiable Boolean formula, and
one to provide a minimal unsatisfiable core of an unsatisfiable Boolean
formula. We applied CAR to 548 hardware model-checking instances, and compared
its performance with IC3/PDR. Our results show that CAR is able to solve 42
instances that cannot be solved by IC3/PDR. When evaluated against a portfolio
that includes IC3/PDR and other approaches, CAR is able to solve 21 instances
that the other approaches cannot solve. We conclude that CAR should be
considered as a valuable member of any algorithmic portfolio for safety model
checking.