title: Secure Analog Network Coding in Layered Networks

abstract:
  We consider a class of Gaussian layered networks where a source communicates
with a destination through $L$ intermediate relay layers with $N$ nodes in each
layer in the presence of a single eavesdropper which can overhear the
transmissions of the nodes in any one layer. The problem of maximum secrecy
rate achievable with analog network coding for a unicast communication over
such layered wireless relay networks with directed links is considered. A relay
node performing analog network coding scales and forwards the signals received
at its input. The key contribution of this work is a lemma that provides the
globally optimal set of scaling factors for the nodes that maximizes the
end-to-end secrecy rate for a class of layered networks. We also show that in
the high-SNR regime, ANC achieves secrecy rates within a constant gap of the
cutset upper bound on the secrecy capacity. To the best of our knowledge, this
work offers the first characterization of the performance of secure ANC in
multi-layered networks in the presence of an eavesdropper.


title:
Linear Quadratic Stochastic Two-Person Nonzero-Sum Differential Games:
  Open-Loop and Closed-Loop Nash Equilibria

abstract:
  In this paper, we consider a linear quadratic stochastic two-person
nonzero-sum differential game. Open-loop and closed-loop Nash equilibria are
introduced. The existence of the former is characterized by the solvability of
a system of forward-backward stochastic differential equations, and that of the
latter is characterized by the solvability of a system of coupled symmetric
Riccati differential equations. Sometimes, open-loop Nash equilibria admit a
closed-loop representation, via the solution to a system of non-symmetric
Riccati equations, which is different from the outcome of the closed-loop Nash
equilibria in general. However, it is found that for the case of zero-sum
differential games, the Riccati equation system for the closed-loop
representation of open-loop saddle points coincides with that for the
closed-loop saddle points, which leads to the conclusion that the closed-loop
representation of open-loop saddle points is the outcome of the corresponding
closed-loop saddle point as long as both exist. In particular, for linear
quadratic optimal control problem, the closed-loop representation of open-loop
optimal controls coincides with the outcome of the corresponding closed-loop
optimal strategy, provided both exist.


title:
Maximizing a Monotone Submodular Function with a Bounded Curvature under
  a Knapsack Constraint

abstract:
  We consider the problem of maximizing a monotone submodular function under a
knapsack constraint. We show that, for any fixed $\epsilon > 0$, there exists a
polynomial-time algorithm with an approximation ratio $1-c/e-\epsilon$, where
$c \in [0,1]$ is the (total) curvature of the input function. This
approximation ratio is tight up to $\epsilon$ for any $c \in [0,1]$. To the
best of our knowledge, this is the first result for a knapsack constraint that
incorporates the curvature to obtain an approximation ratio better than
$1-1/e$, which is tight for general submodular functions. As an application of
our result, we present a polynomial-time algorithm for the budget allocation
problem with an improved approximation ratio.


title: Equiangular tight frames and unistochastic matrices

abstract:
  In this work, we show that a complex equiangular tight frame (ETF) composed
by $N$ vectors in dimension $d$ exists if and only if a certain bistochastic
matrix, univocally determined by $N$ and $d$, belongs to a special class of
unistochastic matrices. This connection allows us to find new complex ETF in
infinitely many dimensions and to derive a method to introduce non-trivial free
parameters in ETF. We derive a 6-parametric family of complex ETF(6,16), which
defines a family of symmetric POVM. Minimal and maximal possible average
entanglement of the vectors within this qubit-qutrit family are presented.
Furthermore, we propose an efficient numerical procedure to find the unitary
matrix underlying a unistochastic matrix, which we apply to find all existing
classes of complex ETF containing up to 19 vectors.


title:
Relative Cohen-Macaulay filtered modules with a view toward relative
  Cohen-Macaulay modules

abstract:
  Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite
R-module. It is shown that, if (R;m) is a complete local ring, then under
certain conditions a contains a regular element on DR(Hc a(M)), where c =
cd(a;M). A non-zerodivisor characterization of relative Cohen-Macaulay modules
w.r.t a is given. We introduce the concept of relative Cohen-Macaulay filtered
modules w.r.t a and study some basic properties of such modules. In paticular,
we provide a non-zerodivisor characterization of relative Cohen-Macaulay
filtered modules w.r.t a. Furthermore, a characterization of cohomological
dimension filtration of M by the associated prime ideals of its factors is
established. As a consequence, we present a cohomological dimension filtration
for those modules whose zero submodule has a primary decomposition. Finally, we
bring some new results about relative Cohen- Macaulay modules w.r.t a.


title: Prohorov-type local limit theorems on abstract Wiener spaces

abstract:
  We prove that the density of
$\frac{X_1+\cdot\cdot\cdot+X_n-nE[X_1]}{\sqrt{n}}$, where $\{X_n\}_{n\geq 1}$
is a sequence of independent and identically distributed random variables
taking values on an abstract Wiener space, converges in $\mathcal{L}^1$ to the
density of a certain Gaussian measure which is absolutely continuous with
respect to the reference Wiener measure. The crucial feature in our
investigation is that we do not require the covariance structure of
$\{X_n\}_{n\geq 1}$ to coincide with the one of the Wiener measure. This
produces a non trivial (different from the constant function one) limiting
object which reflects the different covariance structures involved. The present
paper generalizes the results proved in [18] and deepens the connection between
local limit theorems on (infinite dimensional) Gaussian spaces and some key
tools from the Analysis on the Wiener space, like the Wiener-It\^o chaos
decomposition, Ornstein-Uhlenbeck semigroup and Wick product. We also verify
and discuss our main assumptions on some examples arising from the
applications: dimension independent Berry-Esseen-type bounds and weak solutions
of stochastic differential equations.


title:
Nano strain-amplifier: making ultra-sensitive piezoresistance in
  nanowires possible without the need of quantum and surface charge effects

abstract:
  This paper presents an innovative nano strain-amplifier employed to
significantly enhance the sensitivity of piezoresistive strain sensors.
Inspired from the dogbone structure, the nano strain-amplifier consists of a
nano thin frame released from the substrate, where nanowires were formed at the
centre of the frame. Analytical and numerical results indicated that a nano
strain-amplifier significantly increases the strain induced into a free
standing nanowire, resulting in a large change in their electrical conductance.
The proposed structure was demonstrated in p-type cubic silicon carbide
nanowires fabricated using a top down process. The experimental data showed
that the nano strain-amplifier can enhance the sensitivity of SiC strain
sensors at least 5.4 times larger than that of the conventional structures.
This result indicates the potential of the proposed strain-amplifier for
ultra-sensitive mechanical sensing applications.


title:
Should I stay or should I go? A latent threshold approach to large-scale
  mixture innovation models

abstract:
  This paper proposes a straightforward algorithm to carry out inference in
large time-varying parameter vector autoregressions (TVP-VARs) with mixture
innovation components for each coefficient in the system. We significantly
decrease the computational burden by approximating the latent indicators that
drive the time-variation in the coefficients with a latent threshold process
that depends on the absolute size of the shocks. The merits of our approach are
illustrated with two applications. First, we forecast the US term structure of
interest rates and demonstrate forecast gains of the proposed mixture
innovation model relative to other benchmark models. Second, we apply our
approach to US macroeconomic data and find significant evidence for
time-varying effects of a monetary policy tightening.


title: Infrared Interferometry and AGNs: Parsec-scale Disks and Dusty Outflows

abstract:
  The "torus" is the central element of the most popular theory unifying
various classes of AGNs, but it is usually described as "putative" because it
has not been imaged yet. Since it is too small to be resolved with single-dish
telescopes, one can only make indirect assumptions about its structure using
models. Using infrared interferometry, however, we were able to resolve the
circum-nuclear dust distributions for several nearby AGNs and achieved
constraints on some further two dozen sources. We discovered circum-nuclear
dust on parsec scales in all sources and, in two nearby sources, were able to
dissect this dust into two distinct components. The compact component, a very
thin disk, appears to be connected to the maser disk and the extended one,
which is responsible for most of the mid-IR flux, is oriented perpendicularly
to the circum-nuclear gas disks. What may come as a surprise when having in
mind the standard unification cartoon actually connects well to observations on
larger scales. Optically thin dust in the polar region, perhaps driven by a
disk wind, could solve both the scale height problem of the torus and explain
the missing anisotropy in the mid-IR - X-ray relation.


title: Bulk Higgs and the 750 GeV diphoton signal

abstract:
  We consider scenarios of warped extra-dimensions with all matter fields in
the bulk and in which both the hierarchy and the flavor puzzles of the Standard
Model are addressed. The simplest extra dimensional extension of the Standard
Model Higgs sector, i.e a 5D bulk Higgs doublet, can be a natural and simple
explanation to the 750 GeV excess of diphotons hinted at the LHC, with the
resonance responsible for the signal being the lightest CP odd excitation
coming from the Higgs sector. No new matter content is invoked, the only new
ingredient being the presence of (positive) brane localized kinetic terms
associated to the 5D bulk Higgs, which allow to reduce the mass of the lightest
CP odd Higgs excitation to 750 GeV. Production and decay of this resonance can
naturally fit the observed signal when the mass scale of the rest of
extradimensional resonances is of order 1 TeV.


title:
Theory of spin-coherent transport through a defect spin state in a
  metal/ferromagnet tunnel junction during ferromagnetic resonance

abstract:
  We describe the coherent interaction between a defect spin at the interface
of a ferromagnet and a non-magnetic material, under bias and when the
magnetization of the ferromagnetic contact precesses during ferromagnetic
resonance. The magnet filters charge carriers by preferentially allowing in
parallel spins, which leads to a dynamic spin accumulation on the defect. Local
effective fields acting on the defect spin site modify the defect spin's
precession, which also modifies the charge current through the defect. This new
form of current-detected spin resonance reveals the local environment of the
defect, and thus can yield the defect identity.


title:
Hamiltonian effective field theory study of the $\mathbf{N^*(1440)}$
  resonance in lattice QCD

abstract:
  We examine the phase shifts and inelasticities associated with the
$N^*(1440)$ Roper resonance and connect these infinite-volume observables to
the finite-volume spectrum of lattice QCD using Hamiltonian effective field
theory. We explore three hypotheses for the structure of the Roper resonance.
All three hypotheses are able to describe the scattering data well. In the
third hypothesis the Roper resonance couples the low-lying bare basis-state
component associated with the ground state nucleon with the virtual
meson-baryon contributions. Here the non-trivial superpositions of the
meson-baryon scattering states are complemented by bare basis-state components
explaining their observation in contemporary lattice QCD calculations. The
merit of this scenario lies in its ability to not only describe the observed
nucleon energy levels in large-volume lattice QCD simulations but also explain
why other low-lying states have been missed in today's lattice QCD results for
the nucleon spectrum.


title:
Trajectory Optimization Through Contacts and Automatic Gait Discovery
  for Quadrupeds

abstract:
  In this work we present a trajectory Optimization framework for whole-body
motion planning through contacts. We demonstrate how the proposed approach can
be applied to automatically discover different gaits and dynamic motions on a
quadruped robot. In contrast to most previous methods, we do not pre-specify
contact switches, timings, points or gait patterns, but they are a direct
outcome of the optimization. Furthermore, we optimize over the entire dynamics
of the robot, which enables the optimizer to fully leverage the capabilities of
the robot. To illustrate the spectrum of achievable motions, here we show eight
different tasks, which would require very different control structures when
solved with state-of-the-art methods. Using our trajectory Optimization
approach, we are solving each task with a simple, high level cost function and
without any changes in the control structure. Furthermore, we fully integrated
our approach with the robot's control and estimation framework such that
optimization can be run online. By demonstrating a rough manipulation task with
multiple dynamic contact switches, we exemplarily show how optimized
trajectories and control inputs can be directly applied to hardware.


title:
An NLO+PS generator for $t\bar{t}$ and $Wt$ production and decay
  including non-resonant and interference effects

abstract:
  We present a Monte Carlo generator that implements significant theoretical
improvements in the simulation of top-quark pair production and decay at the
LHC. Spin correlations and off-shell effects in top-decay chains are described
in terms of exact matrix elements for $p p \to
\ell^+\nu_{\scriptscriptstyle\ell}\, l^-\bar{\nu}_{\scriptscriptstyle l} b
\bar{b}$ at NLO QCD, where the leptons $\ell$ and $l$ belong to different
families, and $b$ quarks are massive. Thus, the contributions from $t\bar{t}$
and $Wt$ single-top production as well as their quantum interference are fully
included. Matrix elements are matched to the Pythia8 parton shower using a
recently proposed method that allows for a consistent treatment of resonances
in the POWHEG framework. These theoretical improvements are especially
important for the interpretation of precision measurements of the top-quark
mass, for single-top analyses in the $Wt$ channel, and for $t\bar{t}$ and $Wt$
backgrounds in the presence of jet vetoes or cuts that enhance off-shell
effects. The new generator is based on a process-independent interface of the
OpenLoops amplitude generator with the POWHEGBOX framework.


title: Spectroscopic investigations of divertor detachment in TCV

abstract:
  The aim of this work is to provide an understanding of detachment at TCV with
emphasis on analysis of the Balmer line emission. A new Divertor Spectroscopy
System has been developed for this purpose. Further development of Balmer line
analysis techniques has allowed detailed information to be extracted from the
three-body recombination contribution to the n=7 Balmer line intensity.
  During density ramps, the plasma at the target detaches as inferred from a
drop in ion current to the target. At the same time the Balmer $6\rightarrow2$
and $7\rightarrow2$ line emission near the target is dominated by
recombination. As the core density increases further, the density and
recombination rate are rising all along the outer leg to the x-point while
remaining highest at the target. Even at the highest core densities accessed
(Greenwald fraction 0.7) the peaks in recombination and density may have moved
not more than a few cm poloidally away from the target which is different to
other, higher density tokamaks, where both the peak in recombination and
density continue to move towards the x-point as the core density is increased.
  The inferred magnitude of recombination is small compared to the target ion
current at the time detachment (particle flux drop) starts at the target.
However, recombination may be having more localized effects (to a flux tube)
which we cannot discern at this time. Later, at the highest densities achieved,
the total recombination does reach levels similar to the particle flux.


title: Kazdan-Warner equation on graph

abstract:
  Let $G=(V,E)$ be a finite graph and $\Delta$ be the usual graph Laplacian.
Using the calculus of variations and a method of upper and lower solutions, we
give various conditions such that the Kazdan-Warner equation $\Delta u=c-he^u$
has a solution on $V$, where $c$ is a constant, and $h:V\rightarrow\mathbb{R}$
is a function. We also consider similar equations involving higher order
derivatives on graph. Our results can be compared with the original manifold
case of Kazdan-Warner (Ann. Math., 1974).


title: Electrical conductivity tensor of dense plasma in magnetic fields

abstract:
  Electrical conductivity of finite-temperature plasma in neutron star crusts
is studied for applications in magneto-hydrodynamical description of compact
stars. We solve the Boltzmann kinetic equation in relaxation time approximation
taking into account the anisotropy of transport due to the magnetic field, the
effects of dynamical screening in the scattering matrix element and corre-
lations among the nuclei. We show that conductivity has a minimum at a non-zero
temperature, a low-temperature decrease and a power-law increase with
increasing temperature. Selected numerical results are shown for matter
composed of carbon, iron, and heavier nuclei present in the outer crusts of
neutron star.


title:
Diffusions under a local strong H\"ormander condition. Part I: density
  estimates

abstract:
  We study lower and upper bounds for the density of a diffusion process in
${\mathbb{R}}^n$ in a small (but not asymptotic) time, say $\delta$. We assume
that the diffusion coefficients $\sigma_1,\ldots,\sigma_d$ may degenerate at
the starting time $0$ and point $x_0$ but they satisfy a strong H\"ormander
condition involving the first order Lie brackets. The density estimates are
written in terms of a norm which accounts for the non-isotropic structure of
the problem: in a small time $\delta$, the diffusion process propagates with
speed $\sqrt{\delta}$ in the direction of the diffusion vector fields
$\sigma_{j}$ and with speed $\delta=\sqrt{\delta}\times \sqrt{\delta}$ in the
direction of $[\sigma_{i},\sigma_{j}]$. In the second part of this paper, such
estimates will be used in order to study lower and upper bounds for the
probability that the diffusion process remains in a tube around a skeleton path
up to a fixed time.


title:
The gmwm R package: a comprehensive tool for time series analysis from
  state-space models to robustness

abstract:
  The gmwm R package for inference on time series models is mainly based on the
quantity called wavelet variance which is derived from a wavelet decomposition
of a time series. This quantity provides a means to summarize and graphically
represent the features of time series in order to identify possible models.
Moreover, it is used as a moment condition for model estimation through the
generalized method of wavelet moments. Based on the latter method, this package
not only provides an alternative method to estimate classical ARMA models but
also delivers a general framework for the robust estimation of many time series
models as well as a quick and efficient estimation of many linear state-space
models.


title:
Diffusions under a local strong H\"ormander condition. Part II: tube
  estimates

abstract:
  We study lower and upper bounds for the probability that a diffusion process
in $\mathbb{R}^n$ remains in a tube around a skeleton path up to a fixed time.
We assume that the diffusion coefficients $\sigma_1,\ldots,\sigma_d$ may
degenerate but they satisfy a strong H\"ormander condition involving the first
order Lie brackets around the skeleton of interest. The tube is written in
terms of a norm which accounts for the non-isotropic structure of the problem:
in a small time $\delta$, the diffusion process propagates with speed
$\sqrt{\delta}$ in the direction of the diffusion vector fields $\sigma_{j}$
and with speed $\delta=\sqrt{\delta}\times \sqrt{\delta}$ in the direction of
$[\sigma_{i},\sigma_{j}]$. The proof consists in a concatenation technique
which strongly uses the lower and upper bounds for the density proved in the
part I.


title:
On Distance-$d$ Independent Set and other problems in graphs with few
  minimal separators

abstract:
  Fomin and Villanger (STACS 2010) proved that Maximum Independent Set,
Feedback Vertex Set, and more generally the problem of finding a maximum
induced subgraph of treewith at most a constant $t$, can be solved in
polynomial time on graph classes with polynomially many minimal separators. We
extend these results in two directions. Let $\Gpoly$ be the class of graphs
with at most $\poly(n)$ minimal separators, for some polynomial $\poly$.
  We show that the odd powers of a graph $G$ have at most as many minimal
separators as $G$. Consequently, \textsc{Distance-$d$ Independent Set}, which
consists in finding maximum set of vertices at pairwise distance at least $d$,
is polynomial on $\Gpoly$, for any even $d$. The problem is NP-hard on chordal
graphs for any odd $d \geq 3$.
  We also provide polynomial algorithms for Connected Vertex Cover and
Connected Feedback Vertex Set on subclasses of $\Gpoly$ including chordal and
circular-arc graphs, and we discuss variants of independent domination
problems.


title:
Maximal Orthoplectic Fusion Frames from Mutually Unbiased Bases and
  Block Designs

abstract:
  The construction of optimal line packings in real or complex Euclidean spaces
has shown to be a tantalizingly difficult task, because it includes the problem
of finding maximal sets of equiangular lines. In the regime where equiangular
lines are not possible, some optimal packings are known, for example, those
achieving the orthoplex bound related to maximal sets of mutually unbiased
bases. In this paper, we investigate the packing of subspaces instead of lines
and determine the implications of maximality in this context. We leverage the
existence of real or complex maximal mutually unbiased bases with a
combinatorial design strategy in order to find optimal subspace packings that
achieve the orthoplex bound. We also show that maximal sets of mutually
unbiased bases convert between coordinate projections associated with certain
balanced incomplete block designs and Grassmannian 2-designs. Examples of
maximal orthoplectic fusion frames already appeared in the works by Shor,
Sloane and by Zauner. They are realized in dimensions that are a power of four
in the real case or a power of two in the complex case.


title:
A continuous/discontinuous Galerkin solution of the shallow water
  equations with dynamic viscosity, high-order wetting and drying, and implicit
  time integration

abstract:
  The high-order numerical solution of the non-linear shallow water equations
(and of hyperbolic systems in general) is susceptible to unphysical Gibbs
oscillations that form in the proximity of strong gradients. The solution to
this problem is still an active field of research as no general cure has been
found yet. In this paper, we tackle this issue by presenting a dynamically
adaptive viscosity based on a residual-based sub-grid scale model that has the
following properties: $(i)$ it removes the spurious oscillations in the
proximity of strong wave fronts while preserving the overall accuracy and
sharpness of the solution. This is possible because of the residual-based
definition of the dynamic diffusion coefficient. $(ii)$ For coarse grids, it
prevents energy from building up at small wave-numbers. $(iii)$ The model has
no tunable parameter. Our interest in the shallow water equations is tied to
the simulation of coastal inundation, where a careful handling of the
transition between dry and wet surfaces is particularly challenging for
high-order Galerkin approximations. In this paper, we extend to a unified
continuous/discontinuous Galerkin (CG/DG) framework a very simple, yet
effective wetting and drying algorithm originally designed for DG [Xing, Zhang,
Shu (2010)]. We show its effectiveness for problems in one and two dimensions
on domains of increasing characteristic lengths varying from centimeters to
kilometers. Finally, to overcome the time-step restriction incurred by the
high-order Galerkin approximation, we advance the equations forward in time via
a three stage, second order explicit-first-stage, singly diagonally implicit
Runge-Kutta (ESDIRK) time integration scheme. Via ESDIRK, we are able to
preserve numerical stability for an advective CFL number 10 times larger than
its explicit counterpart.


title:
Existence of positive solutions to some nonlinear equations on locally
  finite graphs

abstract:
  Let $G=(V,E)$ be a locally finite graph, whose measure $\mu(x)$ have positive
lower bound, and $\Delta$ be the usual graph Laplacian. Applying the
mountain-pass theorem due to Ambrosetti-Rabinowitz, we establish existence
results for some nonlinear equations, namely $\Delta u+hu=f(x,u)$, $x\in V$. In
particular, we prove that if $h$ and $f$ satisfy certain assumptions, then the
above mentioned equation has strictly positive solutions. Also, we consider
existence of positive solutions of the perturbed equation $\Delta
u+hu=f(x,u)+\epsilon g$. Similar problems have been extensively studied on the
Euclidean space as well as on Riemannian manifolds.


title: DiaSys: Improving SoC Insight Through On-Chip Diagnosis

abstract:
  To find the cause of a functional or non-functional defect (bug) in software
running on a multi-processor System-on-Chip (MPSoC), developers need insight
into the chip. Tracing systems provide this insight non-intrusively, at the
cost of high off-chip bandwidth requirements. This I/O bottleneck limits the
observability, a problem becoming more severe as more functionality is
integrated on-chip. In this paper, we present DiaSys, an MPSoC diagnosis system
with the potential to replace today's tracing systems. Its main idea is to
partially execute the analysis of observation data on the chip; in consequence,
more information and less data is sent to the attached host PC. With DiaSys,
the data analysis is performed by the diagnosis application. Its input are
events, which are generated by observation hardware at interesting points in
the program execution (like a function call). Its outputs are events with
higher information density. The event transformation is modeled as dataflow
application. For execution, it is mapped in part to dedicated and distributed
on-chip components, and in part to the host PC; the off-chip boundary is
transparent to the developer of the diagnosis application. We implement DiaSys
as extension to an existing SoC with four tiles and a mesh network running on
an FPGA platform. Two usage examples confirm that DiaSys is flexible enough to
replace a tracing system, while significantly lowering the off-chip bandwidth
requirements. In our examples, the debugging of a race-condition bug, and the
creation of a lock contention profile, we see a reduction of trace bandwidth of
more than three orders of magnitude, compared to a full trace created by a
common tracing system.


title:
Geometry of the Fisher-Rao metric on the space of smooth densities on a
  compact manifold

abstract:
  It is known that on a closed manifold of dimension greater than one, every
smooth weak Riemannian metric on the space of smooth positive densities that is
invariant under the action of the diffeomorphism group, is of the form $$
G_\mu(\alpha,\beta)=C_1(\mu(M)) \int_M \frac{\alpha}{\mu}\frac{\beta}{\mu}\,\mu
+ C_2(\mu(M)) \int_M\alpha \cdot \int_M\beta $$ for some smooth functions
$C_1,C_2$ of the total volume $\mu(M)$. Here we determine the geodesics and the
curvature of this metric and study geodesic and metric completeness.


title:
Approach to a Proof of the Riemann Hypothesis by the Second Mean-Value
  Theorem of Calculus

abstract:
  By the second mean-value theorem of calculus (Gauss-Bonnet theorem) we prove
that the class of functions ${\mit \Xi}(z)$ with an integral representation of
the form $\int_{0}^{+\infty}du\,{\mit \Omega}(u)\,{\rm ch}(uz)$ with a
real-valued function ${\mit \Omega}(u) \ge 0$ which is non-increasing and
decreases in infinity more rapidly than any exponential functions
$\exp\left(-\lambda u\right),\,\lambda >0$ possesses zeros only on the
imaginary axis. The Riemann zeta function $\zeta(s)$ as it is known can be
related to an entire function $\xi(s)$ with the same non-trivial zeros as
$\zeta(s)$. Then after a trivial argument displacement $s\leftrightarrow
z=s-\frac{1}{2}$ we relate it to a function ${\mit \Xi}(z)$ with a
representation of the form ${\mit \Xi}(z)=\int_{0}^{+\infty}du\,{\mit
\Omega}(u)\,{\rm ch}(uz)$ where ${\mit \Omega}(u)$ is rapidly decreasing in
infinity and satisfies all requirements necessary for the given proof of the
position of its zeros on the imaginary axis $z={\rm i} y$ by the second
mean-value theorem. Besides this theorem we apply the Cauchy-Riemann
differential equation in an integrated operator form derived in the Appendix B.
All this means that we prove a theorem for zeros of ${\mit \Xi}(z)$ on the
imaginary axis $z={\rm i} y$ for a whole class of function ${\mit \Omega}(u)$
which includes in this way the proof of the Riemann hypothesis. This whole
class includes, in particular, the modified Bessel functions ${\rm I}_{\nu}(z)$
for which it is known that their zeros lie on the imaginary axis and which
affirms our conclusions. A class of almost-periodic functions to piece-wise
constant nonincreasing functions ${\rm \Omega}(u)$ belongs also to this case.
At the end we give shortly an equivalent way of a more formal description of
the obtained results using the Mellin transform of functions with its variable
substituted by an operator.


title: Optimal Orderings of k-subsets for Star Identification

abstract:
  Finding the optimal ordering of k-subsets with respect to an objective
function is known to be an extremely challenging problem. In this paper we
introduce a new objective for this task, rooted in the problem of star
identification on spacecrafts: subsets of detected spikes are to be generated
in an ordering that minimizes time to detection of a valid star constellation.
We carry out an extensive analysis of the combinatorial optimization problem,
and propose multiple algorithmic solutions, offering different
quality-complexity trade-offs. Three main approaches are investigated:
exhaustive search (branch and prune), goal-driven (greedy scene elimination,
minimally intersecting subsets), and stateless algorithms which implicitly seek
to satisfy the problem's goals (pattern shifting, base unrank). In practical
terms, these last algorithms are found to provide satisfactory approximations
to the ideal performance levels, at small computational costs.


title: Generalized Optimal Liquidation Problems Across Multiple Trading Venues

abstract:
  In this paper, we generalize the Almgren-Chriss's market impact model to a
more realistic and flexible framework and employ it to derive and analyze some
aspects of optimal liquidation problem in a security market. We illustrate how
a trader's liquidation strategy alters when multiple venues and extra
information are brought into the security market and detected by the trader.
This study gives some new insights into the relationship between liquidation
strategy and market liquidity, and provides a multi-scale approach to the
optimal liquidation problem with randomly varying volatility.


title:
Measurement of open heavy-flavour production as a function of
  charged-particle multiplicity with ALICE at the LHC

abstract:
  Heavy quarks are produced in the early stages of ultra-relativistic hadron
collisions via hard scatterings and are an important tool for studying
different aspects of Quantum Chromodynamics (QCD) in hadronic collisions.
Charged-particle multiplicity gives information on the global characteristics
of the event and could be used to characterize particle production mechanisms.
In hadronic collisions at Large Hadron Collider (LHC) energies, there is a
significant contribution of multi-parton interactions. The measurement of
heavy-flavour yields as a function of charged-particle multiplicity gives
insight into the mechanisms influencing their production in hadronic collisions
at these energies and it is a tool to test the possible influence of
multi-parton interactions. Furthermore, the charged-particle multiplicity
dependence of open heavy flavours is used to test the ability of QCD
theoretical models to describe the data. In ALICE, heavy-flavour production is
measured via the hadronic and semi-leptonic decay channels (electrons at
central rapidity and muons at forward rapidity). Charged-particle multiplicity
is measured at central and forward rapidity. We will present the results on
open heavy-flavour production as a function of the charged-particle
multiplicity in pp and pPb collisions. Results will be compared to quarkonia
measurements as well as theoretical model calculations.


title: Simultaneous models for commuting holomorphic self-maps of the ball

abstract:
  We prove that a finite family of commuting holomorphic self-maps of the unit
ball $\mathbb{B}^q\subset \mathbb{C}^q$ admits a simultaneous holomorphic
conjugacy to a family of commuting automorphisms of a possibly lower
dimensional ball, and that such conjugacy satisfies a universal property. As an
application we describe when a hyperbolic and a parabolic holomorphic self-map
of $\mathbb{B}^q$ can commute.


title: Effect of thin film on the generation of vorticity by surface waves

abstract:
  Recently a theoretical scheme explaining the vorticity generation by surface
waves in liquids was developed [S. Filatov et al., Phys. Rev. Lett. 116, 054501
(2016)]. Here we study how a thin (monomolecular) film presented at the surface
of liquid affects the generated vorticity. We demonstrate that the vorticity
becomes parametrically larger than for the case with a clean surface and now it
depends on viscosity of the liquid. We also discuss the motion of particles
passively advected by the generated surface flow. The results can be used in
different applications: from the analysis of pollutants' diffusion on the ocean
surface till the reconstruction of vorticity based on the particle image
velocimetry (PIV) measurements.


title: Local Search for Max-Sum Diversification

abstract:
  We provide simple and fast polynomial time approximation schemes (PTASs) for
several variants of the max-sum diversification problem which, in its most
basic form, is as follows: Given n points p_1,...,p_n in R^d and an integer k,
select k points such that the average Euclidean distance between these points
is maximized. This problem commonly appears in information retrieval and
web-search in order to select a diverse set of points from the input. In this
context, it has recently received a lot of attention.
  We present new techniques to analyze natural local search algorithms. This
leads to a (1-O(1/k))-approximation for distances of negative type, even
subject to any matroid constraint of rank k, in time O(n k^2 log k), when
assuming that distance evaluations and calls to the independence oracle are
constant time. Negative type distances include as special cases Euclidean
distances and many further natural distances. Our result easily transforms into
a PTAS and improves on the only previously known PTAS for this setting, which
relies on convex optimization techniques in an n-dimensional space and is
impractical for large data sets. In contrast, our procedure has an (optimal)
linear dependence on n.
  Using generalized exchange properties of matroid intersection, we show that a
PTAS can be obtained for matroid intersection constraints as well. Moreover,
our techniques, being based on local search, are conceptually simple and allow
for various extensions. In particular, we get asymptotically optimal
O(1)-approximations when combining the classic dispersion function with a
monotone submodular objective, which is a very common class of functions to
measure diversity and relevance. This result leverages recent advances on local
search techniques based on proxy functions to obtain optimal approximations for
monotone submodular function maximization subject to a matroid constraint.


title: Equations and Rational Points of the Modular Curves $X^+_0(p)$

abstract:
  Let $p$ be an odd prime number and let $X_0^+(p)$ be the quotient of the
classical modular curve $X_0(p)$ by the action of the Atkin-Lehner operator
$w_p$. In this paper we show how to compute explicit equations for the
canonical model of $X_0^+(p)$. Then we show how to compute the modular
parametrization, when it exists, from $X_0^+(p)$ to an isogeny factor $E$ of
dimension 1 of its jacobian $J_0^+(p)$. Finally we show how use this map to
determine the rational points on $X_0^+(p)$ up to a large fixed height.


title:
Low RF-Complexity Technologies to Enable Millimeter-Wave MIMO with Large
  Antenna Array for 5G Wireless Communications

abstract:
  Millimeter-wave (mmWave) MIMO with large antenna array has attracted
considerable interests from academic and industry communities, as it can
provide larger bandwidth and higher spectrum efficiency. However, with hundreds
of antennas, the number of radio frequency (RF) chains required by mmWave MIMO
is also huge, leading to unaffordable hardware cost and power consumption in
practice. In this paper, we investigate low RF-complexity technologies to solve
this bottleneck. We first review the evolution of low RF-complexity
technologies from microwave frequencies to mmWave frequencies. Then, we discuss
two promising low RF-complexity technologies for mmWave MIMO systems in detail,
i.e., phased array based hybrid precoding (PAHP) and lens array based hybrid
precoding (LAHP), including their principles, advantages, challenges, and
recent results. We compare the performance of these two technologies to draw
some insights about how they can be deployed in practice. Finally, we conclude
this paper and point out some future research directions in this area.


title:
Measurement of the cosmogenic activation of germanium detectors in
  EDELWEISS-III

abstract:
  We present a measurement of the cosmogenic activation in the germanium
cryogenic detectors of the EDELWEISS III direct dark matter search experiment.
The decay rates measured in detectors with different exposures to cosmic rays
above ground are converted into production rates of different isotopes. The
measured production rates in units of nuclei/kg/day are 82 $\pm$ 21 for $^3$H,
2.8 $\pm$ 0.6 for $^{49}$V, 4.6 $\pm$ 0.7 for $^{55}$Fe, and 106 $\pm$ 13 for
$^{65}$Zn. These results are the most accurate for these isotopes. A lower
limit on the production rate of $^{68}$Ge of 74 nuclei/kg/day is also
presented. They are compared to model predictions present in literature and to
estimates calculated with the ACTIVIA code.

categories: astro-ph.CO hep-ex nucl-ex physics.ins-det


title:
FOXTAIL: Modeling the nonlinear interaction between Alfv\'en eigenmodes
  and energetic particles in tokamaks

abstract:
  FOXTAIL is a new hybrid magnetohydrodynamic-kinetic code used to describe
interactions between energetic particles and Alfv\'en eigenmodes in tokamaks
with realistic geometries. The code simulates the nonlinear dynamics of the
amplitudes of individual eigenmodes and of a set of discrete markers in
five-dimensional phase space representing the energetic particle distribution.
Action-angle coordinates of the equilibrium system are used for efficient
tracing of energetic particles, and the particle acceleration by the wave
fields of the eigenmodes is Fourier decomposed in the same angles. The
eigenmodes are described using temporally constant eigenfunctions with dynamic
complex amplitudes. Possible applications of the code are presented, e.g.,
making a quantitative validity evaluation of the one-dimensional bump-on-tail
approximation of the system. Expected effects of the fulfillment of the
Chirikov criterion in two-mode scenarios have also been verified.


title: Learning from the New Higgs-like Scalar before It Vanishes

abstract:
  Motivated by a di-photon anomaly observed by ATLAS and CMS we develop an
SFitter analysis for a combined electroweak-Higgs sector, and a scalar portal
at the LHC. The theoretical description is based on the linear effective
Lagrangian for the Higgs and gauge fields, combined with an additional singlet
scalar. The key feature is the extraction of reliable information on the portal
structure of the combined scalar potential. For the specific di-photon anomaly
we find that the new state might well form such a Higgs portal. To obtain more
conclusive results we define and test the connection of the Wilson coefficients
in the Higgs and heavy scalar sectors, as suggested by a portal setup.


title:
A Priori Assessment of Prediction Confidence for Data-Driven Turbulence
  Modeling

abstract:
  Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the
dominant tool for engineering design and analysis applications involving
turbulent flows, standard RANS models are known to be unreliable in many flows
of engineering relevance, including flows with separation, strong pressure
gradients or mean flow curvature. With increasing amounts of 3-dimensional
experimental data and high fidelity simulation data from Large Eddy Simulation
(LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling
has become a promising approach to increase the predictive capability of RANS
simulations. Recently, a data-driven turbulence modeling approach via machine
learning has been proposed to predict the Reynolds stress anisotropy of a given
flow based on high fidelity data from closely related flows. In this work, the
closeness of different flows is investigated to assess the prediction
confidence a priori. Specifically, the Mahalanobis distance and the kernel
density estimation (KDE) technique are used as metrics to quantify the distance
between flow data sets in feature space. The flow over periodic hills at
Re=10595 is used as the test set and seven flows with different configurations
are individually used as training set. The results show that the prediction
error of the Reynolds stress anisotropy is positively correlated with
Mahalanobis distance and KDE distance, demonstrating that both extrapolation
metrics can be used to estimate the prediction confidence a priori. A
quantitative comparison using correlation coefficients shows that the
Mahalanobis distance is less accurate in estimating the prediction confidence
than KDE distance. The extrapolation metrics introduced in this work and the
corresponding analysis provide an approach to aid in the choice of the data
source and to assess the prediction confidence for data-driven turbulence
modeling.


title: DAVE: A Unified Framework for Fast Vehicle Detection and Annotation

abstract:
  Vehicle detection and annotation for streaming video data with complex scenes
is an interesting but challenging task for urban traffic surveillance. In this
paper, we present a fast framework of Detection and Annotation for Vehicles
(DAVE), which effectively combines vehicle detection and attributes annotation.
DAVE consists of two convolutional neural networks (CNNs): a fast vehicle
proposal network (FVPN) for vehicle-like objects extraction and an attributes
learning network (ALN) aiming to verify each proposal and infer each vehicle's
pose, color and type simultaneously. These two nets are jointly optimized so
that abundant latent knowledge learned from the ALN can be exploited to guide
FVPN training. Once the system is trained, it can achieve efficient vehicle
detection and annotation for real-world traffic surveillance data. We evaluate
DAVE on a new self-collected UTS dataset and the public PASCAL VOC2007 car and
LISA 2010 datasets, with consistent improvements over existing algorithms.


title:
Extension and boundedness of operators on Morrey spaces from
  extrapolation techniques and embeddings

abstract:
  We prove that operators satisfying the hypotheses of the extrapolation
theorem for Muckenhoupt weights are bounded on weighted Morrey spaces. As a
consequence, we obtain at once a number of results that have been proved
individually for many operators. On the other hand, our theorems provide a
variety of new results even for the unweighted case because we do not use any
representation formula or pointwise bound of the operator as was assumed by
previous authors. To extend the operators to Morrey spaces we show different
(continuous) embeddings of (weighted) Morrey spaces into appropriate
Muckenhoupt $A_1$ weighted $L_p$ spaces, which enable us to define the
operators on the considered Morrey spaces by restriction. In this way, we can
avoid the delicate problem of the definition of the operator, often ignored by
the authors. In dealing with the extension problem through the embeddings
(instead of using duality) one is neither restricted in the parameter range of
the $p$'s (in particular $p=1$ is admissible and applies to weak-type
inequalities) nor the operator has to be linear. Another remarkable consequence
of our results is that vector-valued inequalities in Morrey spaces are
automatically deduced. On the other hand, we also obtain $A_\infty$-weighted
inequalities with Morrey quasinorms.


title: Spectral Echolocation via the Wave Embedding

abstract:
  Spectral embedding uses eigenfunctions of the discrete Laplacian on a
weighted graph to obtain coordinates for an embedding of an abstract data set
into Euclidean space. We propose a new pre-processing step of first using the
eigenfunctions to simulate a low-frequency wave moving over the data and using
both position as well as change in time of the wave to obtain a refined metric
to which classical methods of dimensionality reduction can then applied. This
is motivated by the behavior of waves, symmetries of the wave equation and the
hunting technique of bats. It is shown to be effective in practice and also
works for other partial differential equations -- the method yields improved
results even for the classical heat equation.


title: Optical Characterization of the BICEP3 CMB Polarimeter at the South Pole

abstract:
  BICEP3 is a small-aperture refracting cosmic microwave background (CMB)
telescope designed to make sensitive polarization maps in pursuit of a
potential B-mode signal from inflationary gravitational waves. It is the latest
in the BICEP/Keck Array series of CMB experiments at the South Pole, which has
provided the most stringent constraints on inflation to date. For the 2016
observing season, BICEP3 was outfitted with a full suite of 2400 optically
coupled detectors operating at 95 GHz. In these proceedings we report on the
far field beam performance using calibration data taken during the 2015-2016
summer deployment season in situ with a thermal chopped source. We generate
high-fidelity per-detector beam maps, show the array-averaged beam profile, and
characterize the differential beam response between co-located, orthogonally
polarized detectors which contributes to the leading instrumental systematic in
pair differencing experiments. We find that the levels of differential
pointing, beamwidth, and ellipticity are similar to or lower than those
measured for BICEP2 and Keck Array. The magnitude and distribution of BICEP3's
differential beam mismatch - and the level to which temperature-to-polarization
leakage may be marginalized over or subtracted in analysis - will inform the
design of next-generation CMB experiments with many thousands of detectors.


title:
Polarized near-infrared light of the Dusty S-cluster Object (DSO/G2) at
  the Galactic Center

abstract:
  We investigate an infrared-excess source called G2 or Dusty S-cluster Object
(DSO) moving on a highly eccentric orbit around the Galaxy's central black
hole, Sgr A*. We use, for the first time, near-infrared polarimetric imaging
data to determine the nature and the properties of the DSO, and obtain an
improved K_s-band identification of this source in median polarimetry images of
different observing years. The source starts to deviate from the stellar
confusion in 2008, and it does not show any flux density variability over the
years we analyzed it. We measure the polarization degree and angle of the DSO
between 2008 and 2012 and conclude, based on the significance analysis on
polarization parameters, that it is an intrinsically polarized source (>20%)
with a varying polarization angle as it approaches Sgr A* position. DSO shows a
near-infrared excess of K_s-L' > 3 that remains compact close to the pericenter
of its orbit. Its observed parameters and the significant polarization obtained
in this work show that the DSO might be a dust-enshrouded young star, forming a
bow shock as it approaches the super massive black hole. The significantly high
measured polarization degree indicates that it has a non-spherical geometry and
it can be modelled as a combination of a bow shock with a bipolar wind of the
star. We use a 3D radiative transfer model that can reproduce the observed
properties of the source such as the total flux density and the polarization
degree. We obtain that the change of the polarization angle can be due to an
intrinsic change in the source structure. Accretion disc precession of the
young star in the gravitational field of the black hole can lead to the change
of the bipolar outflow and therefore the polarization angle variation. It might
also be the result of the source interaction with the ambient medium.


title:
The redshift evolution of massive galaxy clusters in the MACSIS
  simulations

abstract:
  We present the MAssive ClusterS and Intercluster Structures (MACSIS) project,
a suite of 390 clusters simulated with baryonic physics that yields realistic
massive galaxy clusters capable of matching a wide range of observed
properties. MACSIS extends the recent BAHAMAS simulation to higher masses,
enabling robust predictions for the redshift evolution of cluster properties
and an assessment of the effect of selecting only the hottest systems. We study
the observable-mass scaling relations and the X-ray luminosity-temperature
relation over the complete observed cluster mass range. As expected, we find
the slope of these scaling relations and the evolution of their normalization
with redshift departs significantly from the self-similar predictions. However,
for a sample of hot clusters with core-excised temperatures
$k_{\rm{B}}T\geq5\,\rm{keV}$ the normalization and slope of the observable-mass
relations and their evolution are significantly closer to self-similar. The
exception is the temperature-mass relation, for which the increased importance
of non-thermal pressure support and biased X-ray temperatures leads to a
greater departure from self-similarity in the hottest systems. As a
consequence, these also affect the slope and evolution of the normalization in
the luminosity-temperature relation. The median hot gas profiles show good
agreement with observational data at $z=0$ and $z=1$, with their evolution
again departing significantly from the self-similar prediction. However,
selecting a hot sample of clusters yields profiles that evolve significantly
closer to the self-similar prediction. In conclusion, our results show that
understanding the selection function is vital for robust calibration of cluster
properties with mass and redshift.


title: Deterministic strong-field quantum control

abstract:
  Strong-field quantum-state control is investigated, taking advantage of the
full---amplitude and phase---characterization of the interaction between matter
and intense ultrashort pulses via transient-absorption spectroscopy. A sequence
of intense delayed pulses is used, whose parameters are tailored to steer the
system into a desired quantum state. We show how to experimentally enable this
optimization by retrieving all quantum features of the light-matter interaction
from observable spectra. This provides a full characterization of the action of
strong fields on the atomic system, including the dependence upon possibly
unknown pulse properties and atomic structures. Precision and robustness of the
scheme are tested, in the presence of surrounding atomic levels influencing the
system's dynamics.


title: Translating solitons from semi-Riemannian foliations

abstract:
  We recall the notion of (vertical) translating solitons in a product of a
semi-Riemannian manifold $(M,g)$ and the real line. Mainly, we restrict our
attention to those which are the graph of a smooth function. When dealing with
submersions, we show a criteria to lift (or project) translating solitons from
the base manifold to the total space (or viceversa). In particular, manifolds
foliated by codimension 1 orbits of a Lie group action give rise to such
solitons, up to solving a first-order ordinary differential equation. This
gives us explicit criteria under which the graph of a function is a soliton,
and we employ them to construct many examples of solitons, both new and old, in
a unified way.


title: Moving Charged Particles in Lattice Boltzmann-Based Electrokinetics

abstract:
  The motion of ionic solutes and charged particles under the influence of an
electric field and the ensuing hydrodynamic flow of the underlying solvent is
ubiquitous in aqueous colloidal suspensions. The physics of such systems is
described by a coupled set of differential equations, along with boundary
conditions, collectively referred to as the electrokinetic equations. Capuani
et al. [J. Chem. Phys. 121, 973 (2004)] introduced a lattice-based method for
solving this system of equations, which builds upon the lattice Boltzmann
algorithm for the simulation of hydrodynamic flow and exploits computational
locality. However, thus far, a description of how to incorporate moving
boundary conditions into the Capuani scheme has been lacking. Moving boundary
conditions are needed to simulate multiple arbitrarily-moving colloids. In this
paper, we detail how to introduce such a particle coupling scheme, based on an
analogue to the moving boundary method for the pure LB solver. The key
ingredients in our method are mass and charge conservation for the solute
species and a partial-volume smoothing of the solute fluxes to minimize
discretization artifacts. We demonstrate our algorithm's effectiveness by
simulating the electrophoresis of charged spheres in an external field; for a
single sphere we compare to the equivalent electro-osmotic (co-moving) problem.
Our method's efficiency and ease of implementation should prove beneficial to
future simulations of the dynamics in a wide range of complex nanoscopic and
colloidal systems that was previously inaccessible to lattice-based continuum
algorithms.


title:
Analyzing features learned for Offline Signature Verification using Deep
  CNNs

abstract:
  Research on Offline Handwritten Signature Verification explored a large
variety of handcrafted feature extractors, ranging from graphology, texture
descriptors to interest points. In spite of advancements in the last decades,
performance of such systems is still far from optimal when we test the systems
against skilled forgeries - signature forgeries that target a particular
individual. In previous research, we proposed a formulation of the problem to
learn features from data (signature images) in a Writer-Independent format,
using Deep Convolutional Neural Networks (CNNs), seeking to improve performance
on the task. In this research, we push further the performance of such method,
exploring a range of architectures, and obtaining a large improvement in
state-of-the-art performance on the GPDS dataset, the largest publicly
available dataset on the task. In the GPDS-160 dataset, we obtained an Equal
Error Rate of 2.74%, compared to 6.97% in the best result published in
literature (that used a combination of multiple classifiers). We also present a
visual analysis of the feature space learned by the model, and an analysis of
the errors made by the classifier. Our analysis shows that the model is very
effective in separating signatures that have a different global appearance,
while being particularly vulnerable to forgeries that very closely resemble
genuine signatures, even if their line quality is bad, which is the case of
slowly-traced forgeries.


title:
Spin-Dipole Oscillation and Polarizability of a Binary Bose-Einstein
  Condensate near the Miscible-Immiscible Phase Transition

abstract:
  We report on the measurement of the spin-dipole (SD) polarizability and of
the frequency of the SD oscillation of a two-component Bose-Einstein condensate
of sodium atoms occupying the $|3^2S_{1/2}, F=1, m_F=\pm1\rangle$ hyperfine
states. This binary spin-mixture presents the important properties of being, at
the same time, fully miscible and rid of the limit set by buoyancy. It is also
characterized by a huge enhancement of the SD polarizability and by the
consequent softening of the frequency of the SD oscillation, due to the
vicinity to the transition to the immiscible phase. The experimental data are
successfully compared with the predictions of theory.


title: Electro-optic dual-comb interferometry over 40-nm bandwidth

abstract:
  Dual-comb interferometry is a measurement technique that uses two laser
frequency combs to retrieve complex spectra in a line-by-line basis. This
technique can be implemented with electro-optic frequency combs, offering
intrinsic mutual coherence, high acquisition speed and flexible repetition-rate
operation. A challenge with the operation of this kind of frequency comb in
dual-comb interferometry is its limited optical bandwidth. Here, we use
coherent spectral broadening and demonstrate electro-optic dual-comb
interferometry over the entire telecommunications C band (200 lines covering ~
40 nm, measured within 10 microseconds at 100 signal-to-noise ratio per
spectral line). These results offer new prospects for electro-optic dual-comb
interferometry as a suitable technology for high-speed broadband metrology, for
example in optical coherence tomography or coherent Raman microscopy.


title: Neural Discourse Modeling of Conversations

abstract:
  Deep neural networks have shown recent promise in many language-related tasks
such as the modeling of conversations. We extend RNN-based sequence to sequence
models to capture the long range discourse across many turns of conversation.
We perform a sensitivity analysis on how much additional context affects
performance, and provide quantitative and qualitative evidence that these
models are able to capture discourse relationships across multiple utterances.
Our results quantifies how adding an additional RNN layer for modeling
discourse improves the quality of output utterances and providing more of the
previous conversation as input also improves performance. By searching the
generated outputs for specific discourse markers we show how neural discourse
models can exhibit increased coherence and cohesion in conversations.


title:
Optical dispersion of composite particles consisting of millicharged
  constituents

abstract:
  Composite dark matter (DM) comprised of electrically charged constituents can
interact with the electromagnetic field via the particle's dipole moment. This
interaction results in a dispersive optical index of refraction for the DM
medium. We compute this refractive index for atomic dark matter and more
strongly bound systems, modeled via a harmonic oscillator potential. The
dispersive nature of the index will result in a time lag between high and low
energy photons simultaneously emitted from a distant astrophysical observable.
This time lag, due to matter dispersion, could confound potential claims of
Lorentz invariance violation (LIV) which can also result in such time lags. We
compare the relative size of the two effects and determine that the dispersion
due to DM is dwarfed by potential LIV effects for energies below the Planck
scale.


title: Bell inequalities tailored to maximally entangled states

abstract:
  Bell inequalities have traditionally been used to demonstrate that quantum
theory is nonlocal, in the sense that there exist correlations generated from
composite quantum states that cannot be explained by means of local hidden
variables. With the advent of device-independent quantum information protocols,
Bell inequalities have gained an additional role as certificates of relevant
quantum properties. In this work we consider the problem of designing Bell
inequalities that are tailored to detect maximally entangled states. We
introduce a class of Bell inequalities valid for an arbitrary number of
measurements and results, derive analytically their tight classical,
non-signalling and quantum bounds and prove that the latter is attained by
maximally entangled states. Our inequalities can therefore find an application
in device-independent protocols requiring maximally entangled states.


title: Learning from Conditional Distributions via Dual Embeddings

abstract:
  Many machine learning tasks, such as learning with invariance and policy
evaluation in reinforcement learning, can be characterized as problems of
learning from conditional distributions. In such problems, each sample $x$
itself is associated with a conditional distribution $p(z|x)$ represented by
samples $\{z_i\}_{i=1}^M$, and the goal is to learn a function $f$ that links
these conditional distributions to target values $y$. These learning problems
become very challenging when we only have limited samples or in the extreme
case only one sample from each conditional distribution. Commonly used
approaches either assume that $z$ is independent of $x$, or require an
overwhelmingly large samples from each conditional distribution.
  To address these challenges, we propose a novel approach which employs a new
min-max reformulation of the learning from conditional distribution problem.
With such new reformulation, we only need to deal with the joint distribution
$p(z,x)$. We also design an efficient learning algorithm, Embedding-SGD, and
establish theoretical sample complexity for such problems. Finally, our
numerical experiments on both synthetic and real-world datasets show that the
proposed approach can significantly improve over the existing algorithms.


title: Extra dimensions and violations of Lorentz symmetry

abstract:
  We use experimental limits on Lorentz violation to obtain new constraints on
Kaluza-Klein-type theories in which the extra dimensions may be large but do
not necessarily have units of length. The associated variation in fundamental
quantities such as rest mass must occur slowly, on cosmological scales.


title:
On the local monodromy of A-hypergeometric functions and some monodromy
  invariant subspaces

abstract:
  We obtain an explicit formula for the characteristic polynomial of the local
monodromy of $A$-hypergeometric functions with respect to small loops around a
coordinate hyperplane $x_i =0$. This formula is similar to the one obtained by
Ando, Esterov and Takeuchi for the local monodromy at infinity. Our proof is
combinatorial and can be adapted to provide an alternative proof for the latter
formula as well. On the other hand, we also prove that the solution space at a
nonsingular point of certain irregular and irreducible $A$--hypergeometric
$D$--modules has a nontrivial global monodromy invariant subspace.


title:
Global mild solutions for the nonautonomous 2D Navier-Stokes equations
  with impulse effects

abstract:
  The present paper deals with existence and uniqueness of global mild
solutions for the 2D Navier-Stokes equations with impulses. Using the framework
of nonautonomous dynamical systems, we extend previous results considering the
2D Navier-Stokes equations with impulse effects and allowing that the nonlinear
terms are explicitly time-dependent. Additionally, we present sufficient
conditions to obtain dissipativity (boundedness) for solutions starting in
bounded sets.


title:
A Counterexample to the Forward Recursion in Fuzzy Critical Path
  Analysis Under Discrete Fuzzy Sets

abstract:
  Fuzzy logic is an alternate approach for quantifying uncertainty relating to
activity duration. The fuzzy version of the backward recursion has been shown
to produce results that incorrectly amplify the level of uncertainty. However,
the fuzzy version of the forward recursion has been widely proposed as an
approach for determining the fuzzy set of critical path lengths. In this paper,
the direct application of the extension principle leads to a proposition that
must be satisfied in fuzzy critical path analysis. Using a counterexample it is
demonstrated that the fuzzy forward recursion when discrete fuzzy sets are used
to represent activity durations produces results that are not consistent with
the theory presented. The problem is shown to be the application of the fuzzy
maximum. Several methods presented in the literature are described and shown to
provide results that are consistent with the extension principle.


title:
Temperature coefficients of crystalline-quartz elastic constants over
  the cryogenic range [4 K, 15 K]

abstract:
  This paper brings out results of a measurement campaign aiming to determine
the temperature coefficients of synthetic quartz elastic constants at liquid
helium temperature. The method is based on the relationship between the
resonance frequencies of a quartz acoustic cavity and the elastic constants of
the material. The temperature coefficients of the elastic constants are
extracted from experimental frequency-temperature data collected from a set of
resonators of various cut angles, because of the anisotropy of quartz, measured
on the very useful cryogenic range [4 K - 15 K]. The knowledge of these
temperature coefficients would allow to further design either quartz
temperature sensors or conversely frequency-temperature compensated quartz
cuts. With extremely low losses, lower than $10^{-9}$ for the best ones, key
applications of such devices are ultra-low loss mechanical systems used in many
research areas including frequency control and fundamental measurements. The
Eulerian formalism is used in this study to identify the temperature
coefficients.


title:
Chiral Phonons and Electrical Resistivity of Ferromagnetic Metals at Low
  Temperatures

abstract:
  Ferromagnetism is an exciting phase of matter exhibiting strongly correlated
electron behavior and a standard example of spontaneously broken rotational
symmetry: below the Curie temperature, atomic magnets in an isotropic
single-domain ferromagnetic metal align along a spontaneously chosen direction.
The scattering of conduction electrons from thermal perturbations to this spin
order, together with electron-electron collisions, mark the material electrical
behavior at low temperatures, where the resistivity varies mostly quadratically
with the temperature. Around liquid-helium temperatures however, an interesting
phenomenon occurs, giving rise to an extra \emph{linear} contribution to the
variation of the electrical resistivity with temperature, whose theoretical
explanation has encountered problems for a long time. Here I introduce a
spin-flip scattering mechanism of conduction electrons in ferromagnetic metals
arising from their interaction with the internal magnetic induction and
mediated by chiral modes of the crystal lattice vibrations carrying spin 1.
This mechanism is able to explain the above anomaly and give a good account of
the spin-lattice relaxation times of iron, cobalt and nickel at room
temperatures.


title: p-adic functionals on torsion-free abelian groups

abstract:
  Let p be a prime. A p-adic functional on a torsion-free abelian group G is a
group homomorphism from G to the p-adic integers. The group of all such p-adic
functionals is viewed as a p-adic dual group of G, and is studied from the
point of view of functional analysis. An analogue of the Hahn--Banach Theorem
is proved; this result shows that there are sufficiently many p-adic
functionals to be interesting.
  There is a natural homomorphism from G to its p-adic double dual, and one
main result that is proved is that the image of G in this double dual is dense
in an appropriate topology. This is used to prove the second main result, which
says that the p-adic double dual of G is the same as the pro-p completion of G.
  The theory of p-adic functionals can then be used to produce a matrix
description of G if G has finite rank. This matrix description is related to
another matrix description due to Malcev.


title: Spin glass behavior in a random Coulomb antiferromagnet

abstract:
  We study spin glass behavior in a random Ising Coulomb antiferromagnet in two
and three dimensions using Monte Carlo simulations. In two dimensions, we find
a transition at zero temperature with critical exponents consistent with those
of the Edwards Anderson model, though with large uncertainties. In three
dimensions, evidence for a finite-temperature transition, as occurs in the
Edwards-Anderson model, is rather weak. This may indicate that the sizes are
too small to probe the asymptotic critical behavior, or possibly that the
universality class is different from that of the Edwards-Anderson model and has
a lower critical dimension equal to three.


title:
Active learning in pre-class assignments: Exploring the use of
  interactive simulations to enhance reading assignments

abstract:
  Pre-class reading assignments help prepare students for active classes by
providing a first exposure to the terms and concepts to be used during class.
We investigate if the use of inquiry-oriented PhET-based activities in
conjunction with pre-class reading assignments can improve both the preparation
of students for in-class learning and student attitudes towards and engagement
with pre-class assignments. Over three course modules covering different
topics, students were assigned randomly to complete either a textbook-only
pre-class assignment or both a textbook pre-class assignment and a PhET-based
activity. The assignments helped prepare students for class, as measured by
performance on the pre-class quiz relative to a beginning-of-semester pre-test,
but no evidence for increased learning due the PhET activity was observed.
Students rated the assignments which included PhET as more enjoyable and, for
the topic latest in the semester, reported engaging more with the assignments
when PhET was included.


title:
Automatic Environmental Sound Recognition: Performance versus
  Computational Cost

abstract:
  In the context of the Internet of Things (IoT), sound sensing applications
are required to run on embedded platforms where notions of product pricing and
form factor impose hard constraints on the available computing power. Whereas
Automatic Environmental Sound Recognition (AESR) algorithms are most often
developed with limited consideration for computational cost, this article seeks
which AESR algorithm can make the most of a limited amount of computing power
by comparing the sound classification performance em as a function of its
computational cost. Results suggest that Deep Neural Networks yield the best
ratio of sound classification accuracy across a range of computational costs,
while Gaussian Mixture Models offer a reasonable accuracy at a consistently
small cost, and Support Vector Machines stand between both in terms of
compromise between accuracy and computational cost.


title: A Comparison of Popular Point Configurations on $\mathbb{S}^2$

abstract:
  There are many ways to generate a set of nodes on the sphere for use in a
variety of problems in numerical analysis. We present a survey of quickly
generated point sets on $\mathbb{S}^2$, examine their equidistribution
properties, separation, covering, and mesh ratio constants and present a new
point set, equal area icosahedral points, with low mesh ratio. We analyze
numerically the leading order asymptotics for the Riesz and logarithmic
potential energy for these configurations with total points $N<50,000$ and
present some new conjectures.


title: Autonomous quantum machines and the finite sized Quasi-Ideal clock

abstract:
  Processes such as quantum computation, or the evolution of quantum cellular
automata are typically described by a unitary operation implemented by an
external observer. In particular, an interaction is generally turned on for a
precise amount of time, using a classical clock. A fully quantum mechanical
description of such a device would include a quantum description of the clock
whose state is generally disturbed because of the back-reaction on it. Such a
description is needed if we wish to consider finite sized autonomous quantum
machines requiring no external control. The extent of the back-reaction has
implications on how small the device can be, on the length of time the device
can run, and is required if we want to understand what a fully quantum
mechanical treatment of an observer would look like. Here, we consider the
implementation of a unitary by a finite sized device which we call the
"Quasi-Ideal clock", and show that the back-reaction on it can be made
exponentially small in the device's dimension with only a linear increase in
energy. As a result, an autonomous quantum machine need only be of modest size
and or energy. We are also able to solve a long-standing open problem by using
a finite sized quantum clock to approximate the continuous evolution of an
Idealised clock. The result has implications on the equivalence of different
paradigms of quantum thermodynamics, some which allow external control and some
which only allow autonomous thermal machines.


title:
Interplay of magnetic responses in all-dielectric oligomers to realize
  magnetic Fano resonances

abstract:
  We study the interplay between collective and individual optically-induced
magnetic responses in quadrumers made of identical dielectric nanoparticles.
Unlike their plasmonic counterparts, all-dielectric nanoparticle clusters are
shown to exhibit multiple dimensions of resonant magnetic responses that can be
employed for the realization of anomalous scattering signatures. We focus our
analysis on symmetric quadrumers made from silicon nanoparticles and verify our
theoretical results in proof-of-concept radio frequency experiments
demonstrating the existence of a novel type of magnetic Fano resonance in
nanophotonics.


title:
Spatial Context based Angular Information Preserving Projection for
  Hyperspectral Image Classification

abstract:
  Dimensionality reduction is a crucial preprocessing for hyperspectral data
analysis - finding an appropriate subspace is often required for subsequent
image classification. In recent work, we proposed supervised angular
information based dimensionality reduction methods to find effective subspaces.
Since unlabeled data are often more readily available compared to labeled data,
we propose an unsupervised projection that finds a lower dimensional subspace
where local angular information is preserved. To exploit spatial information
from the hyperspectral images, we further extend our unsupervised projection to
incorporate spatial contextual information around each pixel in the image.
Additionally, we also propose a sparse representation based classifier which is
optimized to exploit spatial information during classification - we hence
assert that our proposed projection is particularly suitable for classifiers
where local similarity and spatial context are both important. Experimental
results with two real-world hyperspectral datasets demonstrate that our
proposed methods provide a robust classification performance.


title:
Accurate, robust and reliable calculations of Poisson-Boltzmann
  solvation energies

abstract:
  Developing accurate solvers for the Poisson Boltzmann (PB) model is the first
step to make the PB model suitable for implicit solvent simulation. Reducing
the grid size influence on the performance of the solver benefits to increasing
the speed of solver and providing accurate electrostatics analysis for solvated
molecules. In this work, we explore the accurate coarse grid PB solver based on
the Green's function treatment of the singular charges, matched interface and
boundary (MIB) method for treating the geometric singularities, and posterior
electrostatic potential field extension for calculating the reaction field
energy. We made our previous PB software, MIBPB, robust and provides almost
grid size independent reaction field energy calculation. Large amount of the
numerical tests verify the grid size independence merit of the MIBPB software.
The advantage of MIBPB software directly make the acceleration of the PB solver
from the numerical algorithm instead of utilization of advanced computer
architectures. Furthermore, the presented MIBPB software is provided as a free
online sever.


title:
Singly-Thermostated Ergodicity in Gibbs' Canonical Ensemble and the 2016
  Ian Snook Prize

abstract:
  For a harmonic oscillator, Nos\'e's single-thermostat approach to simulating
Gibbs' canonical ensemble with dynamics samples only a small fraction of the
phase space. Nos\'e's approach has been improved in a series of three steps: [
1 ] several two-thermostat sets of motion equations have been found which cover
the complete phase space in an ergodic fashion, [ 2 ] sets of single-thermostat
motion equations, exerting "weak control" over both forces and momenta, have
been shown to be ergodic, and [ 3 ] sets of single-thermostat motion equations
exerting weak control over two velocity moments provide ergodic phase-space
sampling for the oscillator and for the rigid pendulum, but not for the quartic
oscillator or for the Mexican Hat potential. The missing fourth step, motion
equations providing ergodic sampling for anharmonic potentials requires a
further advance. The 2016 Ian Snook Prize will be awarded to the author(s) of
the most interesting original submission addressing the problem of finding
ergodic algorithms for Gibbs' canonical ensemble using a single thermostat.


title:
Solving the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation for
  monodomain nanomagnets : A survey and analysis of numerical techniques

abstract:
  The stochastic Landau-Lifshitz-Gilbert-Slonczewski (s-LLGS) equation is
widely used to study the temporal evolution of the macrospin subject to spin
torque and thermal noise. The numerical simulation of the s-LLGS equation
requires an appropriate choice of stochastic calculus and numerical integration
scheme. In this paper, we comprehensively evaluate the accuracy and complexity
of various numerical techniques to solve the s-LLGS equation. We focus on
implicit midpoint, Heun, and Euler-Heun methods that converge to the
Stratonovich solution of the s-LLGS equation. By performing numerical tests for
both strong (path-wise) and weak (statistical) convergence, we quantify the
accuracy of various numerical schemes used to solve the s-LLGS equation. We
demonstrate a new method intended to solve Stochastic Differential Equations
(SDEs) with small noise (RK4-Heun), and test its capability to handle the
s-LLGS equation. We also discuss the circuit implementation of nanomagnets for
large-scale SPICE-based simulations. We evaluate the efficacy of SPICE in
handling the stochastic dynamics of the multiplicative noise in the s-LLGS
equation. Numerical schemes such as Euler and Gear, typically used by
SPICE-based circuit simulators do not yield the expected outcome when solving
the Stratonovich s-LLGS equation. While the trapezoidal method in SPICE does
solve for the Stratonovich solution, its accuracy is limited by the minimum
time step of integration in SPICE. We implement the s-LLGS equation in both its
cartesian and spherical coordinates form in SPICE and compare the stability and
accuracy of the two implementations. The results in this paper will serve as
guidelines for researchers to understand the tradeoffs between accuracy and
complexity of various numerical methods and the choice of appropriate calculus
to solve the s-LLGS equation.


title: Query Complexity of Mastermind Variants

abstract:
  We study variants of Mastermind, a popular board game in which the objective
is sequence reconstruction. In this two-player game, the so-called
\textit{codemaker} constructs a hidden sequence $H = (h_1, h_2, \ldots, h_n)$
of colors selected from an alphabet $\mathcal{A} = \{1,2,\ldots, k\}$
(\textit{i.e.,} $h_i\in\mathcal{A}$ for all $i\in\{1,2,\ldots, n\}$). The game
then proceeds in turns, each of which consists of two parts: in turn $t$, the
second player (the \textit{codebreaker}) first submits a query sequence $Q_t =
(q_1, q_2, \ldots, q_n)$ with $q_i\in \mathcal{A}$ for all $i$, and second
receives feedback $\Delta(Q_t, H)$, where $\Delta$ is some agreed-upon function
of distance between two sequences with $n$ components. The game terminates when
$Q_t = H$, and the codebreaker seeks to end the game in as few turns as
possible. Throughout we let $f(n,k)$ denote the smallest integer such that the
codebreaker can determine any $H$ in $f(n,k)$ turns. We prove three main
results: First, when $H$ is known to be a permutation of $\{1,2,\ldots, n\}$,
we prove that $f(n, n)\ge n - \log\log n$ for all sufficiently large $n$.
Second, we show that Knuth's Minimax algorithm identifies any $H$ in at most
$nk$ queries. Third, when feedback is not received until all queries have been
submitted, we show that $f(n,k)=\Omega(n\log k)$.


title:
Existence, Stability and Dynamics of Harmonically Trapped
  One-Dimensional Multi-Component Solitary Waves: The Near-Linear Limit

abstract:
  In the present work, we consider a variety of two-component, one-dimensional
states in nonlinear Schrodinger equations in the presence of a parabolic trap,
inspired by the atomic physics context of Bose-Einstein condensates. The use of
Lyapunov-Schmidt reduction methods allows us to identify persistence criteria
for the different families of solutions which we classify as (m,n), in
accordance with the number of nodes in each component. Upon developing the
existence theory, we turn to a stability analysis of the different
configurations, using the Krein signature and the Hamiltonian-Krein index as
topological tools identifying the number of potentially unstable
eigendirections for each branch. A systematic expansion of suitably reduced
eigenvalue problems when perturbing off of the linear limit permits us to
obtain explicit expressions for the eigenvalues of each of the states
considered. Finally, when the states are found to be unstable, typically by
virtue of Hamiltonian Hopf bifurcations, their dynamics is studied in order to
identify the nature of the respective instability. The dynamics is generally
found to lead to a vibrational evolution over long time scales.


title: On the violation of Bell's inequality for all non-product quantum states

abstract:
  We present an explicit reexamination of Gisin's 1991 original proof
concerning the violation of Bell's inequality for any pure entangled state of
two-particle systems. Given the relevance of Gisin's work, our analysis is
motivated by pedagogical reasons and allows the straightening of a few
mathematical points in the original proof that in no way change the physical
conclusions reached by Gisin.


title: Global Dynamics, Blow-Up, and Bianchi Cosmology

abstract:
  Many central problems in geometry, topology, and mathematical physics lead to
questions concerning the long-time dynamics of solutions to ordinary and
partial differential equations. Examples range from the Einstein field
equations of general relativity to quasilinear reaction-advection-diffusion
equations of parabolic type. Specific questions concern the convergence to
equilibria, the existence of periodic, homoclinic, and heteroclinic solutions,
and the existence and geometric structure of global attractors. On the other
hand, many solutions develop singularities in finite time. The singularities
have to be analyzed in detail before attempting to extend solutions beyond
their singularities, or to understand their geometry in conjunction with
globally bounded solutions. In this context we have also aimed at global
qualitative descriptions of blow-up and grow-up phenomena.


title: The many faces of LINER-like galaxies: a WISE view

abstract:
  We use the SDSS and WISE surveys to investigate the real nature of galaxies
defined as LINERs in the BPT diagram. After establishing a mid-infrared colour
W2-W3 = 2.5 as the optimal separator between galaxies with and without star
formation, we investigate the loci of different galaxy classes in the W_{Ha}
versus W2-W3 space. We find that: (1) A large fraction of LINER-like galaxies
are emission-line retired galaxies, i.e galaxies which have stopped forming
stars and are powered by hot low-mass evolved stars (HOLMES). Their W2-W3
colours show no sign of star formation and their Ha equivalent widths, W_{Ha},
are consistent with ionization by their old stellar populations. (2) Another
important fraction have W2-W3 indicative of star formation. This includes
objects located in the supposedly `pure AGN' zone of the BPT diagram. (3) A
smaller fraction of LINER-like galaxies have no trace of star formation from
W2-W3 and a high W_{Ha}, pointing to the presence of an AGN. (4) Finally, a few
LINERs tagged as retired by their W_{Ha} but with W2-W3 values indicative of
star formation are late-type galaxies whose SDSS spectra cover only the old
`retired' bulge. This reinforces the view that LINER-like galaxies are a mixed
bag of objects involving different physical phenomena and observational effects
thrusted into the same locus of the BPT diagram.


title:
Critical behavior of entropy production and learning rate: Ising model
  with an oscillating field

abstract:
  We study the critical behavior of the entropy production of the Ising model
subject to a magnetic field that oscillates in time. The mean-field model
displays a phase transition that can be either first or second-order, depending
on the amplitude of the field and on the frequency of oscillation. Within this
approximation the entropy production rate is shown to have a discontinuity when
the transition is first-order and to be continuous, with a jump in its first
derivative, if the transition is second-order. In two dimensions, we find with
numerical simulations that the critical behavior of the entropy production rate
is the same, independent of the frequency and amplitude of the field. Its first
derivative has a logarithmic divergence at the critical point. This result is
in agreement with the lack of a first-order phase transition in two dimensions.
We analyze a model with a field that changes at stochastic time-intervals
between two values. This model allows for an informational theoretic
interpretation, with the system as a sensor that follows the external field. We
calculate numerically a lower bound on the learning rate, which quantifies how
much information the system obtains about the field. Its first derivative with
respect to temperature is found to have a jump at the critical point.


title: The Burnside problem for $\text{Diff}_{\text{Vol}}(\mathbb{S}^2)$

abstract:
  Let $S$ be a closed surface and $\text{Diff}_{\text{Vol}}(S)$ be the group of
volume preserving diffeomorphisms of $S$. A finitely generated group $G$ is
periodic of bounded exponent if there exists $k \in \mathbb{N}$ such that every
element of $G$ has order at most $k$. We show that every periodic group of
bounded exponent $G \subset \text{Diff}_{\text{Vol}}(S)$ is a finite group.


title:
Best-case Analysis of MergeSort with an Application to the Sum of Digits
  Problem, A manuscript (MS) v2

abstract:
  An exact formula \[ B(n) = \frac{n}{2}(\lfloor \lg n \rfloor + 1) - \sum
_{k=0} ^{\lfloor \lg n \rfloor} 2^k Zigzag(\frac{n}{2^{k+1}}), \] where \[
Zigzag (x) = \min (x - \lfloor x \rfloor, \lceil x \rceil - x), \] for the
minimal number $ B(n) $ of comparisons of keys performed by $ {\tt MergeSort} $
on an $ n $-element array is derived and analyzed. The said formula is less
complex than any other known formula for the same and can be evaluated in $
O(\log ^{c}) $ time, where $ c $ is a constant. It is shown that there is no
closed-form formula for the above.
  Since the recurrence relation for the minimal number of comparisons of keys
for $ {\tt MergeSort} $ is identical with a recurrence relation for the number
of 1s in binary expansions of all integers between $ 0 $ and $ n $
(exclusively), the above results extend to the sum of binary digits problem.


title: Planar Zeros in Gauge Theories and Gravity

abstract:
  Planar zeros are studied in the context of the five-point scattering
amplitude for gauge bosons and gravitons. In the case of gauge theories, it is
found that planar zeros are determined by an algebraic curve in the projective
plane spanned by the three stereographic coordinates labelling the direction of
the outgoing momenta. This curve depends on the values of six independent color
structures. Considering the gauge group SU(N) with N=2,3,5 and fixed color
indices, the class of curves obtained gets broader by increasing the rank of
the group. For the five-graviton scattering, on the other hand, we show that
the amplitude vanishes whenever the process is planar, without imposing further
kinematic conditions. A rationale for this result is provided using
color-kinematics duality.


title: Enriching Word Vectors with Subword Information

abstract:
  Continuous word representations, trained on large unlabeled corpora are
useful for many natural language processing tasks. Popular models that learn
such representations ignore the morphology of words, by assigning a distinct
vector to each word. This is a limitation, especially for languages with large
vocabularies and many rare words. In this paper, we propose a new approach
based on the skipgram model, where each word is represented as a bag of
character $n$-grams. A vector representation is associated to each character
$n$-gram; words being represented as the sum of these representations. Our
method is fast, allowing to train models on large corpora quickly and allows us
to compute word representations for words that did not appear in the training
data. We evaluate our word representations on nine different languages, both on
word similarity and analogy tasks. By comparing to recently proposed
morphological word representations, we show that our vectors achieve
state-of-the-art performance on these tasks.


title: Characterizing meromorphic pseudo-lemniscates

abstract:
  Let $f$ be a meromorphic function with simply connected domain
$G\subset\mathbb{C}$, and let $\Gamma\subset\mathbb{C}$ be a smooth Jordan
curve. We call a component of $f^{-1}(\Gamma)$ in $G$ a
$\Gamma$-$pseudo$-$lemniscate$ of $f$. In this note we give criteria for a
smooth Jordan curve $\mathcal{S}$ in $G$ (with bounded face $D$) to be a
psuedo-lemniscate of $f$ in terms of the number of preimages (counted with
multiplicity) which a given $w$ has under $f$ in $D$, as $w$ ranges over the
Riemann sphere. We also develop a test, in the same terms, by which one may
show that the image of a Jordan curve under $f$ is not a Jordan curve.


title: The $d \: ^3 \Pi$ state of LiRb

abstract:
  We report our spectroscopic studies of the $d \ ^3\Pi$ state of ultra-cold
$^7$Li$^{85}$Rb using resonantly-enhanced multi-photon ionization and depletion
spectroscopy with bound-to-bound transitions originating from the metastable $a
\ ^3\Sigma^+$ state. We evaluate the potential of this state for use as the
intermediate state in a STIRAP transfer scheme from triplet Feshbach LiRb
molecules to the $X \ ^1\Sigma^+$ ground state, and find that the lowest
several vibrational levels possess the requisite overlap with initial and final
states, as well as convenient energies. Using depletion measurements, we
measured the well depth and spin-orbit splitting. We suggest possible pathways
for short-range photoassociation using deeply-bound vibrational levels of this
electronic state.


title:
Person Re-identification with Hyperspectral Multi-Camera Systems --- A
  Pilot Study

abstract:
  Person re-identification in a multi-camera environment is an important part
of modern surveillance systems. Person re-identification from color images has
been the focus of much active research, due to the numerous challenges posed
with such analysis tasks, such as variations in illumination, pose and
viewpoints. In this paper, we suggest that hyperspectral imagery has the
potential to provide unique information that is expected to be beneficial for
the re-identification task. Specifically, we assert that by accurately
characterizing the unique spectral signature for each person's skin,
hyperspectral imagery can provide very useful descriptors (e.g. spectral
signatures from skin pixels) for re-identification. Towards this end, we
acquired proof-of-concept hyperspectral re-identification data under
challenging (practical) conditions from 15 people. Our results indicate that
hyperspectral data result in a substantially enhanced re-identification
performance compared to color (RGB) images, when using spectral signatures over
skin as the feature descriptor.


title: Two-loop corrections to the $\rho$ parameter in Two-Higgs-Doublet Models

abstract:
  Models with two scalar doublets are among the simplest extensions of the
Standard Model which fulfill the relation $\rho = 1$ at lowest order for the
$\rho$ parameter as favored by experimental data for electroweak observables
allowing only small deviations from unity. Such small deviations $\Delta\rho$
originate exclusively from quantum effects with special sensitivity to mass
splittings between different isospin components of fermions and scalars. In
this paper the dominant two-loop electroweak corrections to $\Delta\rho$ are
calculated in the $CP$-conserving THDM, resulting from the top-Yukawa coupling
and the self-couplings of the Higgs bosons in the gauge-less limit. The
on-shell renormalization scheme is applied. With the assumption that one of the
$CP$-even neutral scalars represents the scalar boson observed by the LHC
experiments, with standard properties, the two-loop non-standard contributions
in $\Delta\rho$ can be separated from the standard ones. These contributions
are of particular interest since they increase with mass splittings between
non-standard Higgs bosons and can be additionally enhanced by $\tan\beta$ and
$\lambda_5$, an additional free coefficient of the Higgs potential, and can
thus modify the one-loop result substantially. Numerical results are given for
the dependence on the various non-standard parameters, and the influence on the
calculation of electroweak precision observables is discussed.


title: The recursion hierarchy for PCF is strict

abstract:
  We consider the sublanguages of Plotkin's PCF obtained by imposing some bound
k on the levels of types for which fixed point operators are admitted. We show
that these languages form a strict hierarchy, in the sense that a fixed point
operator for a type of level k can never be defined (up to observational
equivalence) using fixed point operators for lower types. This answers a
question posed by Berger. Our proof makes substantial use of the theory of
nested sequential procedures (also called PCF B\"ohm trees) as expounded in the
recent book of Longley and Normann.


title:
Direct measurements reveal non-Markovian fluctuations of DNA threading
  through a solid-state nanopore

abstract:
  The threading of a polymer chain through a small pore is a classic problem in
polymer dynamics and underlies nanopore sensing technology. However important
experimental aspects of the polymer motion in a solid-state nanopore, such as
an accurate measurement of the velocity variation during translocation, have
remained elusive. In this work we analysed the translocation through conical
quartz nanopores of a 7 kbp DNA double-strand labelled with six markers equally
spaced along its contour. These markers, constructed from DNA hairpins, give
direct experimental access to the translocation dynamics. On average we measure
a 5% reduction in velocity during the translocation. We also find a striking
correlation in velocity fluctuations with a decay constant of 100s of {\mu}s.
These results shed light on hitherto unresolved problems in the dynamics of DNA
translocation and provide guidance for experiments seeking to determine
positional information along a DNA strand.


title:
A search for very high-energy flares from the microquasars GRS 1915+105,
  Circinus X-1, and V4641 Sgr using contemporaneous H.E.S.S. and RXTE
  observations

abstract:
  Microquasars are potential $\gamma$-ray emitters. Indications of transient
episodes of $\gamma$-ray emission were recently reported in at least two
systems: Cyg X-1 and Cyg X-3. The identification of additional
$\gamma$-ray-emitting microquasars is required to better understand how
$\gamma$-ray emission can be produced in these systems. Theoretical models have
predicted very high-energy (VHE) $\gamma$-ray emission from microquasars during
periods of transient outburst. Observations reported herein were undertaken
with the objective of observing a broadband flaring event in the $\gamma$-ray
and X-ray bands. Contemporaneous observations of three microquasars, GRS
1915+105, Circinus X-1, and V4641 Sgr, were obtained using the High Energy
Spectroscopic System (H.E.S.S.) telescope array and the Rossi X-ray Timing
Explorer (RXTE) satellite. X-ray analyses for each microquasar were performed
and VHE $\gamma$-ray upper limits from contemporaneous H.E.S.S. observations
were derived. No significant $\gamma$-ray signal has been detected in any of
the three systems. The integral $\gamma$-ray photon flux at the observational
epochs is constrained to be $I(> 560 {\rm\ GeV}) < 7.3\times10^{-13}$ cm$^{-2}$
s$^{-1}$, $I(> 560 {\rm\ GeV}) < 1.2\times10^{-12}$ cm$^{-2}$ s$^{-1}$, and
$I(> 240 {\rm\ GeV}) < 4.5\times10^{-12}$ cm$^{-2}$ s$^{-1}$ for GRS 1915+105,
Circinus X-1, and V4641 Sgr, respectively. The $\gamma$-ray upper limits
obtained using H.E.S.S. are examined in the context of previous Cherenkov
telescope observations of microquasars. The effect of intrinsic absorption is
modelled for each target and found to have negligible impact on the flux of
escaping $\gamma$-rays. When combined with the X-ray behaviour observed using
RXTE, the derived results indicate that if detectable VHE $\gamma$-ray emission
from microquasars is commonplace, then it is likely to be highly transient.