title: Exploring Cosmic Origins with CORE: Cosmological Parameters

abstract:
  We forecast the main cosmological parameter constraints achievable with the
CORE space mission which is dedicated to mapping the polarisation of the Cosmic
Microwave Background (CMB). CORE was recently submitted in response to ESA's
fifth call for medium-sized mission proposals (M5). Here we report the results
from our pre-submission study of the impact of various instrumental options, in
particular the telescope size and sensitivity level, and review the great,
transformative potential of the mission as proposed. Specifically, we assess
the impact on a broad range of fundamental parameters of our Universe as a
function of the expected CMB characteristics, with other papers in the series
focusing on controlling astrophysical and instrumental residual systematics. In
this paper, we assume that only a few central CORE frequency channels are
usable for our purpose, all others being devoted to the cleaning of
astrophysical contaminants. On the theoretical side, we assume LCDM as our
general framework and quantify the improvement provided by CORE over the
current constraints from the Planck 2015 release. We also study the joint
sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale
Structure experiments like DESI and Euclid. Specific constraints on the physics
of inflation are presented in another paper of the series. In addition to the
six parameters of the base LCDM, which describe the matter content of a
spatially flat universe with adiabatic and scalar primordial fluctuations from
inflation, we derive the precision achievable on parameters like those
describing curvature, neutrino physics, extra light relics, primordial helium
abundance, dark matter annihilation, recombination physics, variation of
fundamental constants, dark energy, modified gravity, reionization and cosmic
birefringence. (ABRIDGED)


title: Radiation Hydrodynamic Simulations of Dust-Driven Winds

abstract:
  We study dusty winds driven by radiation pressure in the atmosphere of a
rapidly star-forming environment. We apply the variable Eddington tensor
algorithm to re-examine the two-dimensional radiation hydrodynamic problem of a
column of gas that is accelerated by a constant infrared radiation flux. In the
absence of gravity, the system is primarily characterized by the initial
optical depth of the gas. We perform several runs with different initial
optical depth and resolution. We find that the gas spreads out along the
vertical direction, as its mean velocity and velocity dispersion increase. In
contrast to previous work using flux-limited diffusion algorithm, we find
little evolution in the trapping factor. The momentum coupling between
radiation and gas in the absence of gravity is similar to that with gravity.
For Eddington ratio increasing with the height in the system, the momentum
transfer from the radiation to the gas is not merely $\sim L/c$, but amplified
by a factor of $1+\eta \tau_{\rm IR}$, where $\tau_{\rm IR}$ is the integrated
infrared optical depth through the system, and $\eta\sim0.5-0.9$, decreasing
with the optical depth. We apply our results to the atmosphere of galaxies and
conclude that radiation pressure may be an important mechanism for driving
winds in the most rapidly star-forming galaxies and starbursts.


title: Resolving-Power Quantization

abstract:
  Starting with a general discussion, a program is sketched for a quantization
based on dilations. This resolving-power quantization is simplest for scalar
field theories. The hope is to find a way to relax the requirement of locality
so that the necessity to fine tune mass parameters is eliminated while
universality is still preserved.


title:
Three loop form factors of a massive spin-2 particle with nonuniversal
  coupling

abstract:
  We investigate the interaction of spin-2 fields with those of Standard Model
in a model independent framework. We have considered interactions where the
spin-2 fields couple to two sets of gauge invariant tensorial operators that
are not conserved unlike the energy momentum tensor with different coupling
strengths. Such interactions not only change the ultraviolet behaviour of the
couplings but also expand the scope of the searches of spin-2 particles at the
colliders. We present all the relevant renormalisation constants up to three
loop level in QCD and also the form factors that contribute to potential
observables. This sets the ground to investigate the phenomenological
consequences of these interactions with spin-2 fields through more than one
tensorial operator.


title:
Extreme points of matrix convex sets, free spectrahedra and dilation
  theory

abstract:
  For matrix convex sets a unified geometric interpretation of notions of
extreme points and of Arveson boundary points is given. These notions include,
in increasing order of strength, the core notions of "Euclidean" extreme
points, "matrix" extreme points, and "absolute" extreme points. A seemingly
different notion, the "Arveson boundary", has by contrast a dilation theoretic
flavor. An Arveson boundary point is an analog of a (not necessarily
irreducible) boundary representation for an operator system. This article
provides and explores dilation theoretic formulations for the above notions of
extreme points.
  The scalar solution set of a linear matrix inequality (LMI) is known as a
spectrahedron. The matricial solution set of an LMI is a free spectrahedron.
Spectrahedra (resp. free spectrahedra) lie between general convex sets (resp.
matrix convex sets) and convex polyhedra (resp. free polyhedra). As
applications of our theorems on extreme points, it is shown the polar dual of a
matrix convex set K is generated, as a matrix convex set, by finitely many
Arveson boundary points if and only if K is a free spectrahedron; and if the
polar dual of a free spectrahedron K is again a free spectrahedron, then at the
scalar level K is a polyhedron.


title:
Don't be left in the dark: Improving LHC searches for dark photons using
  lepton-jet substructure

abstract:
  Collider signals of dark photons are an exciting probe for new gauge forces
and are characterized by events with boosted lepton jets. Existing techniques
are efficient in searching for muonic lepton jets but due to substantial
backgrounds have difficulty constraining lepton jets containing only electrons.
This is unfortunate since upcoming intensity frontier experiments are sensitive
to dark photon masses which only allow electron decays. Analyzing a recently
proposed model of kinetic mixing, with new scalar particles decaying into dark
photons, we find that existing techniques for electron jets can be
substantially improved. We show that using lepton-jet-substructure variables,
in association with a boosted decision tree, improves background rejection,
significantly increasing the LHC's reach for dark photons in this region of
parameter space.


title:
Irreducible tensor basis and general Fierz relations for Bhabha
  scattering like amplitudes

abstract:
  We construct an irreducible s- and t-channel tensor basis for Bhabha
scattering like amplitudes based on the properties of the underlying Lorentz
symmetry in four space-time dimensions. In the given basis the calculation of
amplitude contractions like the amplitude square reduces to the contraction of
their corresponding coefficient tensors. Further the basis retains the full
amplitude information and thus can be applied in off-shell cases. The general
Fierz transformations which relate the s- and t-channel basis with each other
are obtained. As an example for application we use the basis to calculate the
tree-level Bhabha scattering amplitude.


title:
Two-Dimensional Oscillatory Neural Network Based on Charge-Density-Wave
  Devices Operating at Room Temperature

abstract:
  We propose an oscillatory neural network implemented with two-dimensional
tantalum disulfide devices operating in the change density wave regime at room
temperature. An elementary cell of the network consists of two 1T-TaS2 devices
connected in series. Such a cell has constant output and oscillatory states.
All cells have the same bias voltage. There is constant current flowing through
the cell in the constant output mode. The oscillations occur at a certain bias
voltage due to the electrical-field driven metal-to-insulator transition owing
to the changes in the charge density wave phase in the 1T-TaS2 channel. Two
1T-TaS2 devices oscillate out-of-phase where one of the devices is in the
insulator phase while the other one is in the metallic state. The
nearest-neighbor cells are coupled via graphene transistors. The cells are
resistively coupled if the graphene transistor is in the On state while they
are capacitively coupled if the transistor is in the Off state. The operation
of the oscillatory neural network is simulated numerically for the 30x30 node
network. The results of our numerical modeling show the formation of artificial
vortexes and cellular-automata type data processing. The two-dimensional
1T-TaS2 devices, utilized in the network, offer a unique combination of
properties such as scalability, high operational frequency, fast
synchronization speed, and radiation hardness, which makes them promising for
both consumer electronic and defense applications.


title: Quantum thermodynamics with local control

abstract:
  We investigate the limitations that emerge in thermodynamic tasks as a result
of having local control only over the components of a thermal machine. These
limitations are particularly relevant for devices composed of interacting
many-body systems. Specifically, we study protocols of work extraction that
employ a many-body system as a working medium whose evolution can be driven by
tuning the on-site Hamiltonian terms. This provides a restricted set of
thermodynamic operations, giving rise to novel bounds for the performance of
engines. Our findings show that those limitations in control render it in
general impossible to reach Carnot efficiency; in its extreme ramification it
can even forbid to reach a finite efficiency of work per particle. We focus on
the 1D Ising model in the thermodynamic limit as a case study. We show that in
the limit of strong interactions the ferromagnetic case becomes useless for
work extraction, while the anti-ferromagnetic improves its performance with the
strength of the couplings, reaching Carnot in the limit of arbitrary strong
interactions. Our results provide a promising connection between the study of
quantum control and thermodynamics and introduce a more realistic set of
physical operations well suited to capture current experimental scenarios.


title:
Element Abundances and Source Plasma Temperatures of Solar Energetic
  Particles

abstract:
  Thirty years ago Breneman and Stone observed that the enhancement or
suppression of element abundances in large solar energetic-particle (SEP)
events varies as a power of the mass-to-charge ratio, A/Q, of the elements.
Since Q during acceleration or transport may depend upon the source plasma
temperature T, the pattern of element enhancements can provide a best-fit
measure of T. The small SEP events we call 3He-rich or "impulsive" show average
enhancements, relative to coronal abundances, rising as the 3.6 power of A/Q to
a factor of ~1000 for (76<=Z<=82)/O and temperature in the range 2-4 MK. This
acceleration is believed to occur in islands of magnetic reconnection on open
field lines in solar flares and jets. It has been recently found that the large
shock-accelerated "gradual" SEP events have a broad range of source plasma
temperatures; 69% have coronal temperatures of T < 1.6 MK, while 24% have T ~ 3
MK, the latter suggesting a seed population containing residual impulsive
suprathermal ions. Most of the large event-to-event abundance variations and
their time variation are largely explained by variations in T magnified by
A/Q-dependent fractionation during transport. However, the non-thermal variance
of impulsive SEP events (~30%) exceeds that of the ~3 MK gradual events (~10%)
so that several small impulsive events must be averaged together with the
ambient plasma to form the seed population for shock acceleration in these
events.


title: From Solitons to Rogue Waves in Nonlinear Left-Handed Metamaterials

abstract:
  In the present work, we explore soliton and rogue-like wave solutions in the
transmission line analogue of a nonlinear left-handed metamaterial. The
nonlinearity is expressed through a voltagedependent and symmetric capacitance
motivated by the recently developed ferroelectric barium strontium titanate
(BST) thin film capacitor designs. We develop both the corresponding nonlinear
dynamical lattice, as well as its reduction via a multiple scales expansion to
a nonlinear Schr\"odinger (NLS) model for the envelope of a given carrier wave.
The reduced model can feature either a focusing or a defocusing nonlinearity
depending on the frequency (wavenumber) of the carrier. We then consider the
robustness of different types of solitary waves of the reduced model within the
original nonlinear left-handed medium. We find that both bright and dark
solitons persist in a suitable parametric regime, where the reduction to the
NLS is valid. Additionally, for suitable initial conditions, we observe a rogue
wave type of behavior, that differs significantly from the classic Peregrine
rogue wave evolution, including most notably the breakup of a single
Peregrine-like pattern into solutions with multiple wave peaks. Finally, we
touch upon the behavior of generalized members of the family of the Peregrine
solitons, namely Akhmediev breathers and Kuznetsov-Ma solitons, and explore how
these evolve in the left-handed transmission line.


title: Energy Conservation and the Chiral Magnetic Effect

abstract:
  We analyze the chiral magnetic effect in a homogeneous neutral plasma from
the point of view of energy conservation, and construct an effective potential
for the growth of maximally helical perturbations of the electromagnetic field.
We show that a negative curvature at the origin of the potential, indicating
instability of the plasma, is induced by a chiral asymmetry in electron Fermi
energy, as opposed to number density, while the potential grows at large field
value. It follows that the ground state for a plasma has zero magnetic
helicity; a nonzero electron mass will allow an excited state of a plasma with
nonzero helicity to relax to that ground state quickly. We conclude that a
chiral plasma instability triggered by weak interactions is not a viable
mechanism for explaining magnetic fields in stars except possibly when dynamics
drives the system far from equilibrium.


title: How Gaussian can our Universe be?

abstract:
  Gravity is a non-linear theory, and hence, barring cancellations, the initial
super-horizon perturbations produced by inflation must contain some minimum
amount of mode coupling, or primordial non-Gaussianity. In single-field
slow-roll models, where this lower bound is saturated, non-Gaussianity is
controlled by two observables: the tensor-to-scalar ratio, which is uncertain
by more than fifty orders of magnitude; and the scalar spectral index, or tilt,
which is relatively well measured. It is well known that to leading and
next-to-leading order in derivatives, the contributions proportional to the
tilt disappear from any local observable, and suspicion has been raised that
this might happen to all orders, allowing for an arbitrarily low amount of
primordial non-Gaussianity. Employing Conformal Fermi Coordinates, we show
explicitly that this is not the case. Instead, a contribution of order the tilt
appears in local observables. In summary, the floor of physical primordial
non-Gaussianity in our Universe has a squeezed-limit scaling of
$k_\ell^2/k_s^2$, similar to equilateral and orthogonal shapes, and a
dimensionless amplitude of order $0.1\times(n_\mathrm{s}-1)$.


title: Efficient quantum tomography II

abstract:
  Following [OW16], we continue our analysis of: (1) "Quantum tomography",
i.e., learning a quantum state, i.e., the quantum generalization of learning a
discrete probability distribution; (2) The distribution of Young diagrams
output by the RSK algorithm on random words. Regarding (2), we introduce two
powerful new tools: (i) A precise upper bound on the expected length of the
longest union of $k$ disjoint increasing subsequences in a random length-$n$
word with letter distribution $\alpha_1 \geq \alpha_2 \geq \cdots \geq
\alpha_d$; (ii) A new majorization property of the RSK algorithm that allows
one to analyze the Young diagram formed by the lower rows $\lambda_k,
\lambda_{k+1}, \dots$ of its output.
  These tools allow us to prove several new theorems concerning the
distribution of random Young diagrams in the nonasymptotic regime, giving
concrete error bounds that are optimal, or nearly so, in all parameters. As one
example, we give a fundamentally new proof of the fact that the expected length
of the longest increasing sequence in a random length-$n$ permutation is
bounded by $2\sqrt{n}$. This is the $k = 1$, $\alpha_i \equiv \frac1d$, $d \to
\infty$ special case of a much more general result we prove: the expected
length of the $k$th Young diagram row produced by an $\alpha$-random word is
$\alpha_k n \pm 2\sqrt{\alpha_kd n}$.
  From our new analyses of random Young diagrams we derive several new results
in quantum tomography, including: (i) Learning the eigenvalues of an unknown
state to $\epsilon$-accuracy in Hellinger-squared, chi-squared, or KL distance,
using $n = O(d^2/\epsilon)$ copies; (ii) Learning the optimal rank-$k$
approximation of an unknown state to $\epsilon$-fidelity (Hellinger-squared
distance) using $n = \widetilde{O}(kd/\epsilon)$ copies.


title: Quantum quenches during inflation

abstract:
  We propose a new technique to study fast transitions during inflation, by
studying the dynamics of quantum quenches in an $O(N)$ scalar field theory in
de Sitter spacetime. We compute the time evolution of the system using a
non-perturbative large-$N$ limit approach. We derive the self-consistent mass
equation for several physically relevant transitions of the parameters of the
theory, in a slow motion approximation. Our computations reveal that the
effective mass after the quench evolves in the direction of recovering its
value before the quench, but stopping at a different asymptotic value, in which
the mass squared is strictly positive. Furthermore, we tentatively find
situations in which the effective mass squared can be temporarily negative,
thus breaking the $O(N)$ symmetry of the system for a certain time, only to
then come back to a positive value, restoring the symmetry. We argue the
relevance of our new method in a cosmological scenario.


title: A quantitative definition of organismality and its application to lichen

abstract:
  The organism is a fundamental concept in biology. However there is no
universally accepted, formal, and yet broadly applicable definition of what an
organism is. Here we introduce a candidate definition. We adopt the view that
the "organism" is a functional concept, used by scientists to address
particular questions concerning the future state of a biological system, rather
than something wholly defined by that system. In this approach organisms are a
coarse-graining of a fine-grained dynamical model of a biological system.
Crucially, the coarse-graining of the system into organisms is chosen so that
their dynamics can be used by scientists to make accurate predictions of those
features of the biological system that interests them, and do so with minimal
computational burden. To illustrate our framework we apply it to a dynamic
model of lichen symbiosis---a system where either the lichen or its constituent
fungi and algae could reasonably be considered "organisms." We find that the
best choice for what organisms are in this scenario are complex mixtures of
many entities that do not resemble standard notions of organisms. When we
restrict our allowed coarse-grainings to more traditional types of organisms,
we find that ecological conditions, such as niche competition and predation
pressure, play a significant role in determining the best choice for organisms.


title: Two-dimensional Phononic Crystals with Acoustic-Band Negative Refraction

abstract:
  A two-dimensional phononic crystal (PC) can exhibit longitudinal-mode
negative energy refraction on its lowest (acoustical) frequency pass band. The
effective elastodynamic properties of a typical PC are calculated and it is
observed that the components of the effective density tensor can achieve
negative values at certain low frequencies on the acoustical branches for the
longitudinal-mode pass-band, and that negative refraction may be accompanied by
either positive or negative effective density. Furthermore, such a PC has a
high anisotropy ratio at certain low frequencies, offering potential for
application to acoustic cloaking where effective material anisotropy is
essential.


title:
Constraining Black Holes with Light Boson Hair and Boson Stars using
  Epicyclic Frequencies and QPOs

abstract:
  Light bosonic fields are ubiquitous in extensions of the Standard Model. Even
when minimally coupled to gravity, these fields might evade the assumptions of
the black-hole no-hair theorems and give rise to spinning black holes which can
be drastically different from the Kerr metric. Furthermore, they allow for
self-gravitating compact solitons, known as (scalar or Proca) boson stars. The
quasi-periodic oscillations (QPOs) observed in the X-ray flux emitted by
accreting compact objects carry information about the strong-field region, thus
providing a powerful tool to constrain deviations from Kerr's geometry and to
search for exotic compact objects. By using the relativistic precession model
as a proxy to interpret the QPOs in terms of geodesic frequencies, we
investigate how the QPO frequencies could be used to test the no-hair theorem
and the existence of light bosonic fields near accreting compact objects. We
show that a detection of two QPO triplets with current sensitivity can already
constrain these models, and that the future eXTP mission or a LOFT-like mission
can set very stringent constraints on black holes with bosonic hair and on
(scalar or Proca) boson stars. The peculiar geodesic structure of compact
scalar/Proca boson stars implies that these objects can easily be ruled out as
alternative models for X-ray source GRO J1655-40.


title: Use of Feedback to Maximize Photon Count Rate in XRF Spectroscopy

abstract:
  The effective bandwidth of an energy dispersive x-ray fluorescence
spectroscopy system is limited by the timing of incident photons. When multiple
photons strike the detector within the processing time of the detector photon
pile-up occurs and the signal received by the detector during this interval
must be ignored. In conventional ED-XRF systems the probability of a photon
being incident upon the detector is uniform over time, and thus pile-up follows
Poisson statistics. In this paper we present a mathematical treatment of the
relationship between photon timing statistics and the count rate of an XRF
system. We show that it is possible to increase the maximum count rates by
applying feedback from the detector to the x-ray source to alter the timing
statistics of photon emission. Monte-Carlo simulations, show that this
technique can increase the maximum count rate of an XRF spectroscopy system by
a factor of 2.94 under certain circumstances.


title:
Principal component analysis of periodically correlated functional time
  series

abstract:
  Within the framework of functional data analysis, we develop principal
component analysis for periodically correlated time series of functions. We
define the components of the above analysis including periodic, operator-valued
filters, score processes and the inversion formulas. We show that these objects
are defined via convergent series under a simple condition requiring
summability of the Hilbert-Schmidt norms of the filter coefficients, and that
they poses optimality properties.
  We explain how the Hilbert space theory reduces to an approximate
finite-dimensional setting which is implemented in a custom build R package. A
data example and a simulation study show that the new methodology is superior
to existing tools if the functional time series exhibit periodic
characteristics.


title: Constraints for proton structure fluctuations from exclusive scattering

abstract:
  We constrain the average density profile of the proton and the amount of
event-by-event fluctuations by simultaneously calculating the coherent and
incoherent exclusive diffractive vector meson production cross section in deep
inelastic scattering. Working within the Color Glass Condensate picture, we
find that the gluonic density of the proton must have large geometric
fluctuations in order to describe the experimentally measured large incoherent
cross section.


title:
Comment on "AdS nonlinear instability: moving beyond spherical symmetry"
  [Class. Quantum Grav. 33 23LT01 (2016)]

abstract:
  We argue that if the degeneracy of the spectrum of linear perturbations of
AdS is properly taken into account, there are globally regular, time-periodic,
asymptotically AdS solutions (geons) bifurcating from each linear
eigenfrequency of AdS.


title: On the moduli space of flat symplectic surface bundles

abstract:
  In this paper, we prove homological stability of symplectomorphisms and
extended hamiltonians of surfaces made discrete. We construct an isomorphism
from the stable homology group of symplectomorphisms and extended Hamiltonians
of surfaces to the homology of certain infinite loop spaces. We use these
infinite loop spaces to study characteristic classes of surface bundles whose
holonomy groups are area preserving, in particular we give a homotopy theoretic
proof of the Kotschick-Morita theorem.


title:
Time-multiplexed structured illumination using a DMD for optical
  diffraction tomography

abstract:
  We present a novel illumination control technique for optical diffraction
tomography (ODT). Various spatial frequencies of beam illumination were
controlled by displaying time-averaged sinusoidal patterns using a digital
micromirror device (DMD). Compared to the previous method using binary Lee
holograms, the present method eliminates unwanted diffracted beams which may
deteriorate the image quality of the ODT. We demonstrated the capability of the
present method by reconstructing three-dimensional refractive index (RI)
distributions of various samples, with high RI sensitivity (\sigma_\Delta n =
3.15 +/- 10-4), and reconstructing 3-D RI tomograms of biological samples,
which provided quantitative biochemical and morphological information about the
samples.


title:
An Upper Limit on the Mass of a Central Black Hole in the Large
  Magellanic Cloud from the Stellar Rotation Field

abstract:
  We constrain the possible presence of a central black hole (BH) in the center
of the Large Magellanic Cloud (LMC). This requires spectroscopic measurements
over an area of order a square degree, due to the poorly known position of the
kinematic center. Such measurements are now possible with the impressive field
of view of the Multi Unit Spectroscopic Explorer (MUSE) on the ESO Very Large
Telescope. We used the Calcium Triplet (~850nm) spectral lines in many
short-exposure MUSE pointings to create a two-dimensional integrated-light
line-of-sight velocity map from the ~$10^8$ individual spectra, taking care to
identify and remove Galactic foreground populations. The data reveal a clear
velocity gradient at an unprecedented spatial resolution of 1 arcmin$^{2}$. We
fit kinematic models to arrive at a $3\sigma$ upper-mass-limit of $10^{7.1}$
M$_{Sun}$ for any central BH - consistent with the known scaling relations for
supermassive black holes and their host systems. This adds to the growing body
of knowledge on the presence of BHs in low-mass and dwarf galaxies, and their
scaling relations with host-galaxy properties, which can shed light on theories
of BH growth and host system interaction.


title:
Scintillation and irregularities from the nightside part of a
  Sun-aligned polar cap arc

abstract:
  In this paper we study the presence of irregularities and scintillation in
relation to the nightside part of a long-lived, Sun-aligned transpolar arc on
15 January 2015. The arc was observed in DMSP UV and particle data and lasted
at least 3 h between 1700 and 2000 UT. The arc was more intense than the main
oval during this time. From all-sky imagers on Svalbard we were able to study
the evolution of the arc, which drifted slowly westward toward the dusk cell.
The intensity of the arc as observed from ground was 10-17 kR in 557.7 nm and
2-3.5 kR in 630.0 nm, i.e., significant emissions in both green and red
emission lines. We have used high-resolution raw data from global navigation
satellite systems (GNSS) receivers and backscatter from Super Dual Auroral
Radar Network (SuperDARN) radars to study irregularities and scintillation in
relation to the polar cap arc. Even though the literature has suggested that
polar cap arcs are potential sources for irregularities, our results indicate
only very weak irregularities. This may be due to the background density in the
northward IMF polar cap being too low for significant irregularities to be
created.


title: LHC Signals from Cascade Decays of Warped Vector Resonances

abstract:
  Recently (arXiv:1608.00526), a new framework for warped higher-dimensional
compactifications with "bulk" standard model (SM) was proposed: in addition to
the UV (Planck scale) and IR (a couple of TeV) branes, there is an intermediate
brane, taken to be around 10 TeV. The SM matter and Higgs fields propagate from
the UV brane down to this intermediate brane only, while gauge and gravity
fields propagate in the entire bulk. Such a configuration renders the lightest
gauge Kaluza-Klein (KK) states within LHC reach, simultaneously satisfying
flavor and CP constraints. In addition, the usual leading decay modes of the
lightest KK gauge bosons into top and Higgs bosons are suppressed. This effect
permits erstwhile subdominant channels to become significant. These include
flavor-universal decays to SM fermions and Higgs bosons, and a novel channel -
decay to a radion and a SM gauge boson, followed by radion decay to a pair of
SM gauge bosons. In this work, we first delineate the parameter space where the
above mentioned cascade decay of gauge KK particles dominates, and thereby can
be the discovery mode at the LHC. We then perform a detailed analysis of the
LHC signals from this model, finding that 300/fb suffices for evidence of
KK-gluon in tri-jet, jet + di-photon and jet + di-boson channels. However, KK
photon in photon + di-jet, and KK-W in leptonic W + di-jet require 3000/fb. The
crucial feature of this decay chain is a "double" resonance, i.e. 3-particle
and 2-particle invariant mass peaks, corresponding to the KK gauge boson and
the radion respectively.


title: Astroinformatics Challenges from Next-generation Radio Continuum Surveys

abstract:
  The tens of millions of radio sources to be detected with next-generation
surveys pose new challenges, quite apart from the obvious ones of processing
speed and data volumes. For example, existing algorithms are inadequate for
source extraction or cross-matching radio and optical/IR sources, and a new
generation of algorithms are needed using machine learning and other
techniques. The large numbers of sources enable new ways of testing
astrophysical models, using a variety of "large-n astronomy" techniques such as
statistical redshifts. Furthermore, while unexpected discoveries account for
some of the most significant discoveries in astronomy, it will be difficult to
discover the unexpected in large volumes of data, unless specific software is
developed to mine the data for the unexpected.


title: Nanocrystalline Al-Mg with extreme strength due to grain boundary doping

abstract:
  Nanocrystalline Al-Mg alloys are used to isolate the effect of grain boundary
doping on the strength of nanostructured metals. Mg is added during mechanical
milling, followed by low homologous temperature annealing treatments to induce
segregation without grain growth. Nanocrystalline Al -7 at.% Mg that is
annealed for 1 h at 200 {\deg}C is the strongest alloy fabricated, with a
hardness of 4.56 GPa or approximately three times that of pure nanocrystalline
Al. Micropillar compression experiments indicate a yield strength of 865 MPa
and a specific strength of 329 kN m/kg, making this one of the strongest
lightweight metals reported to date.


title: Higher decay inequalities for multilinear oscillatory integrals

abstract:
  In this paper we establish sharp estimates (up to logarithmic losses) for the
multilinear oscillatory integral operator studied by Phong, Stein, and Sturm
and Carbery and Wright on any product $\prod_{j=1}^d L^{p_j}(\mathbb R)$ with
each $p_j \geq 2$, expanding the known results for this operator well outside
the previous range $\sum_{j=1}^d p_j^{-1} = d-1$. Our theorem assumes
second-order nondegeneracy condition of Varchenko type, and as a corollary
reproduces Varchenko's theorem and implies Fourier decay estimates for measures
of smooth density on degenerate hypersurfaces in $\mathbb R^d$.


title: Images of Maass-Poincar\'e series in the lower half-plane

abstract:
  In this note we extend integral weight harmonic Maass forms to functions
defined on the upper and lower half-planes using the method of Poincar\'e
series. This relates to Rademacher's "expansion of zero" principle, which was
recently employed by Rhoades to link mock theta functions and partial theta
functions.


title:
On a common carrier hypothesis for the 6613.6 and 6196.0 {\AA} diffuse
  interstellar bands

abstract:
  We explore via spectroscopic modeling whether the highly correlated diffuse
interstellar bands at 6613.6 and 6196.0 {\AA} might originate from a single
molecule. Efforts were made to simulate the band contours of the DIBs along the
three lines-of-sight, which have been observed by others at high resolution:
HD179406, HD174165, and Her 36. Reasonable simultaneous fits were obtained
using a prolate symmetric top molecule that exhibits transitions of two
different band types, type-a parallel and type-b perpendicular bands. Two
different excited states of a long- or heavy-chain, forked molecule are
proposed. A minimum number of adjustable parameters were used including ground
and excited state A and B rotational constants, an excited state centrifugal
distortion constant, and three different rotational excitation temperatures.
Points in favor and against the hypothesis are discussed.


title: A Novel Propulsion Method of Flexible Underwater Robots

abstract:
  This paper presents aims at mobility improvement of flexible underwater
robots. For this purpose, a novel propulsion method using planar structural
vibration pattern is proposed, and tested on two kinds of prototypes. The
result of experiments showed the possibility of the movements for multiple
directions: forward, backward, turn, rotation, drift, and their combination.
These movements are achieved by only one structure with two actuators. The
results also indicated the possibility of driving using eigenmodes since
movements were concentrated on low driving frequency area. To investigate the
relation between movement and structural vibration pattern, we established a
simulation model.


title: Trace Finite Element Methods for PDEs on Surfaces

abstract:
  In this paper we consider a class of unfitted finite element methods for
discretization of partial differential equations on surfaces. In this class of
methods known as the Trace Finite Element Method (TraceFEM), restrictions or
traces of background surface-independent finite element functions are used to
approximate the solution of a PDE on a surface. We treat equations on steady
and time-dependent (evolving) surfaces. Higher order TraceFEM is explained in
detail. We review the error analysis and algebraic properties of the method.
The paper navigates through the known variants of the TraceFEM and the
literature on the subject.


title: Accurate frequency referencing for fieldable dual-comb spectroscopy

abstract:
  A fieldable dual-comb spectrometer is described based on a "bootstrapped"
frequency referencing scheme in which short-term optical phase coherence
between combs is attained by referencing each to a free-running diode laser,
whilst high frequency resolution and long-term accuracy is derived from a
stable quartz oscillator. This fieldable dual-comb spectrometer was used to
measure spectra with full comb-tooth resolution spanning from 140 THz (2.14 um,
4670 cm^-1) to 184 THz (1.63 um, 6140 cm^-1) in the near infrared with a
frequency sampling of 200 MHz (0.0067 cm^-1), ~ 120 kHz frequency resolution,
and ~ 1 MHz frequency accuracy. High resolution spectra of water and carbon
dioxide transitions at 1.77 um, 1.96 um and 2.06 um show that the molecular
transmission acquired with this fieldable system did not deviate from those
measured with a laboratory-based system (referenced to a maser and
cavity-stabilized laser) to within 5.6x10^-4. Additionally, the fieldable
system optimized for carbon dioxide quantification at 1.60 um, demonstrated a
sensitivity of 2.8 ppm-km at 1 s integration time, improving to 0.10 ppm-km at
13 minutes of integration time.


title:
Generalized Fourier-Bessel operator and almost-periodic interpolation
  and approximation

abstract:
  We consider functions $f$ of two real variables, given as trigonometric
functions over a finite set $F$ of frequencies. This set is assumed to be
closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for
some integer $M$. Firstly, we address the problem of evaluating these functions
over a similar finite set $E$ in the space plane and, secondly, we address the
problems of interpolating or approximating a function $g$ of two variables by
such an $f$ over the grid $E.$ In particular, for this aim, we establish an
abstract factorization theorem for the evaluation function, which is a key
point for an efficient numerical solution to these problems. This result is
based on the very special structure of the group $SE(2,N)$, subgroup of the
group $SE(2)$ of motions of the plane corresponding to discrete rotations,
which is a maximally almost periodic group.
  Although the motivation of this paper comes from our previous works on
biomimetic image reconstruction and pattern recognition, where these questions
appear naturally, this topic is related with several classical problems: the
FFT in polar coordinates, the Non Uniform FFT, the evaluation of general
trigonometric polynomials, and so on.


title:
Temperature-dependent magnetic anisotropy from directional-dependent
  interactions

abstract:
  Magnetic anisotropy of spin models with directional-dependent interactions in
the high-temperature paramagnetic phase is theoretically studied. Using a high
temperature expansion, we show that the Ising type directional-dependent
interaction gives rise to magnetic anisotropy which depends on the temperature
as $\propto T^{-5}$. This phenomenon arises from the anisotropic exchange
interaction, and is distinct from the orbital effect, such as van Vleck
susceptibility. It is shown that while the quadratic term in the magnetization
favors to point the spins along the bond, the fourth order term in
magnetization prefers to point spins to the perpendicular direction. The theory
is applied to the Heisenberg-Kitaev model on the honeycomb lattice and a cubic
lattice model that is potentially relevant to perovskite iridates. We show
that, in these models, the anisotropic terms in quadratic order cancels out,
and the leading order for the magnetic anisotropy arises from the fourth order
contribution. The result shows that the anisotropy from the
directional-dependent interaction gives rise to $\langle100\rangle$ magnetic
anisotropy. These results are potentially relevant to heavy transition metal
oxides such as iridates. Experimental observation of the magnitude of
anisotropic interactions using magnetic torque measurement is also discussed.


title: On the local-global divisibility over abelian varieties

abstract:
  Let $p \geq 2$ be a prime number and let $k$ be a number field. Let
$\mathcal{A}$ be an abelian variety defined over $k$. We prove that if ${\rm
Gal} ( k ( {\mathcal{A}}[p] ) / k )$ contains an element $g$ of order dividing
$p-1$ not fixing any non-trivial element of ${\mathcal{A}}[p]$ and $H^1 ( {\rm
Gal} ( k ( {\mathcal{A}}[p] ) / k ), {\mathcal{A}}[p] )$ is trivial, then the
local-global divisibility by $p^n$ holds for ${\mathcal{A}} ( k )$ for every $n
\in \mathbb{N}$. Moreover, we prove a similar result without the hypothesis on
the triviality of $H^1 ( {\rm Gal} ( k ( {\mathcal{A}}[p] ) / k ) ,
{\mathcal{A}}[p] )$, in the particular case where ${\mathcal{A}}$ is a
principally polarized abelian variety. Then, we get a more precise result in
the case when ${\mathcal{A}}$ has dimension $2$. Finally we show with a
counterexample that the hypothesis over the order of $g$ is necessary. In the
Appendix, we explain how our results are related to a question of Cassels on
the divisibility of the Tate-Shafarevich group, studied by Ciperani and Stix.


title: Synchronization over Cartan motion groups via contraction

abstract:
  Group contraction is an algebraic map that relates two classes of Lie groups
by a limiting process. We utilize this notion for the compactification of the
class of Cartan motion groups. The compactification process is then applied to
reduce a non-compact synchronization problem to a problem where the solution
can be obtained by means of a unitary, faithful representation. We describe
this method of synchronization via contraction in detail and analyze several
important aspects of this application. One important special case of Cartan
motion groups is the group of rigid motions, also called the special Euclidean
group. We thoroughly discuss the synchronization over this group and show
numerically the advantages of our approach compared to some current
state-of-the-art synchronization methods on both synthetic and real data.


title: Plaquette Ising models, degeneracy and scaling

abstract:
  We review some recent investigations of the 3d plaquette Ising model. This
displays a strong first-order phase transition with unusual scaling properties
due to the size-dependent degeneracy of the low-temperature phase. In
particular, the leading scaling correction is modified from the usual inverse
volume behaviour 1/L^3 to 1/L^2. The degeneracy also has implications for the
magnetic order in the model which has an intermediate nature between local and
global order and gives rise to novel fracton topological defects in a related
quantum Hamiltonian.


title: Brauer graph algebras

abstract:
  These lecture notes on Brauer graph algebras are the result of a series of
four lectures given at the CIMPA research school in Mar del Plata, Argentina,
in March 2016. After motivating the study of Brauer graph algebras by relating
them to special biserial algebras, the definition of Brauer graph algebras is
given in great detail with many examples to illustrate the concepts. This is
followed by a short section on the interpretation of Brauer graphs as decorated
ribbon graphs. A section on gentle algebras and their graphs, trivial
extensions of gentle algebras, admissible cuts of Brauer graph algebras and a
first connection of Brauer graph algebras with Jacobian algebras associated to
triangulations of marked oriented surfaces follows. The interpretation of flips
of diagonals in triangulations of marked oriented surfaces as derived
equivalences of Brauer graph algebras and the comparison of derived
equivalences of Brauer graph algebras with derived equivalences of frozen
Jacobian algebras is the topic of the next section. In the last section, after
defining Green's walk around the Brauer graph, a complete description of the
Auslander Reiten quiver of a Brauer graph algebra is given.


title:
Dynamic origin-to-destination routing of wirelessly connected,
  autonomous vehicles on a congested network

abstract:
  Up-to-date information wirelessly communicated among vehicles can be used to
select the optimal route between a given origin and destination. To elucidate
how to make use of such information, simulations are performed for autonomous
vehicles traveling on a square lattice of roads. All the possible routes
between the origin and the destination (without backtracking) are of the same
length. Congestion is the only determinant of delay. At each intersection,
right-of-way is given to the closest vehicle. There are no traffic lights. Trip
times of a subject vehicle are recorded for various initial conditions using
different routing algorithms. Surprisingly, the simplest algorithm, which is
based on the total number of vehicles on a route, is as good as one based on
computing travel times from the average velocity of vehicles on each road
segment.


title:
A lower bound on adiabatic heating of compressed turbulence for
  simulation and model validation

abstract:
  The energy in turbulent flow can be amplified by compression, when the
compression occurs on a timescale shorter than the turbulent dissipation time.
This mechanism may play a part in sustaining turbulence in various
astrophysical systems, including molecular clouds. The amount of turbulent
amplification depends on the net effect of the compressive forcing and
turbulent dissipation. By giving an argument for a bound on this dissipation,
we give a lower bound for the scaling of the turbulent velocity with
compression ratio in compressed turbulence. That is, turbulence undergoing
compression will be enhanced at least as much as the bound given here, subject
to a set of caveats that will be outlined. Used as a validation check, this
lower bound suggests that some simulations and models of compressing
astrophysical turbulence are too dissipative. The technique used highlights the
relationship between compressed turbulence and decaying turbulence.


title: Objective Priors in the Empirical Bayes Framework

abstract:
  When dealing with Bayesian inference the choice of the prior often remains a
debatable question. Empirical Bayes methods offer a data-driven solution to
this problem by estimating the prior itself from an ensemble of data. In the
nonparametric case, the maximum likelihood estimate is known to overfit the
data, an issue that is commonly tackled by regularization. However, the
majority of regularizations are ad hoc choices which lack invariance under
reparametrization of the model and result in inconsistent estimates for
equivalent models. We introduce a non-parametric, transformation invariant
estimator for the prior distribution. Being defined in terms of the missing
information similar to the reference prior, it can be seen as an extension of
the latter to the data-driven setting. This implies a natural interpretation as
a trade-off between choosing the least informative prior and incorporating the
information provided by the data, a symbiosis between the objective and
empirical Bayes methodologies.


title:
The Initial Mass Function in the Nearest Strong Lenses from SNELLS:
  Assessing the Consistency of Lensing, Dynamical, and Spectroscopic
  Constraints

abstract:
  We present new observations of the three nearest early-type galaxy (ETG)
strong lenses discovered in the SINFONI Nearby Elliptical Lens Locator Survey
(SNELLS). Based on their lensing masses, these ETGs were inferred to have a
stellar initial mass function (IMF) consistent with that of the Milky Way, not
the bottom-heavy IMF that has been reported as typical for high-$\sigma$ ETGs
based on lensing, dynamical, and stellar population synthesis techniques. We
use these unique systems to test the consistency of IMF estimates derived from
different methods. We first estimate the stellar $M_*/L$ using lensing and
stellar dynamics. We then fit high-quality optical spectra of the lenses using
an updated version of the stellar population synthesis models developed by
Conroy & van Dokkum. When examined individually, we find good agreement among
these methods for one galaxy. The other two galaxies show 2-3$\sigma$ tension
with lensing estimates, depending on the dark matter contribution, when
considering IMFs that extend to 0.08 Msol. Allowing a variable low-mass cutoff
or a nonparametric form of the IMF reduces the tension among the IMF estimates
to $<2\sigma$. There is moderate evidence for a reduced number of low-mass
stars in the SNELLS spectra, but no such evidence in a composite spectrum of
matched-$\sigma$ ETGs drawn from the SDSS. Such variation in the form of the
IMF at low stellar masses (m <~ 0.03 Msol), if present, could reconcile
lensing/dynamical and spectroscopic IMF estimates for the SNELLS lenses and
account for their lighter $M_*/L$ relative to the mean matched-$\sigma$ ETG. We
provide the spectra used in this study to facilitate future comparisons.


title:
Numerical studies of serendipity and tensor product elements for
  eigenvalue problems

abstract:
  While the use of finite element methods for the numerical approximation of
eigenvalues is a well-studied problem, the use of serendipity elements for this
purpose has received little attention in the literature. We show by numerical
experiments that serendipity elements, which are defined on a square reference
geometry, can attain the same order of accuracy as their tensor product
counterparts while using dramatically fewer degrees of freedom. In some cases,
the serendipity method uses only half as many basis functions as the tensor
product method while still producing the same numerical approximation of an
eigenvalue. To encourage the further use and study of serendipity elements, we
provide a table of serendipity basis functions for low order cases and a
Mathematica file that can be used to generate the basis functions for higher
order cases.


title:
Measuring alignments between galaxies and the cosmic web at $z \sim 2-3$
  using IGM tomography

abstract:
  Many galaxy formation models predict alignments between galaxy spin and the
cosmic web (i.e. the directions of filaments and sheets), leading to intrinsic
alignment between galaxies that creates a systematic error in weak lensing
measurements. These effects are often predicted to be stronger at
high-redshifts ($z\gtrsim1$) that are inaccessible to massive galaxy surveys on
foreseeable instrumentation, but IGM tomography of the Ly$\alpha$ forest from
closely-spaced quasars and galaxies is starting to measure the $z\sim2-3$
cosmic web with the requisite fidelity. Using mock surveys from hydrodynamical
simulations, we examine the utility of this technique, in conjunction with
coeval galaxy samples, to measure alignment between galaxies and the cosmic web
at $z\sim2.5$. We show that IGM tomography surveys with $\lesssim5$ $h^{-1}$
Mpc sightline spacing can accurately recover the eigenvectors of the tidal
tensor, which we use to define the directions of the cosmic web. For galaxy
spins and shapes, we use a model parametrized by the alignment strength,
$\Delta\langle\cos\theta\rangle$, with respect to the tidal tensor eigenvectors
from the underlying density field, and also consider observational effects such
as errors in the galaxy position angle, inclination, and redshift. Measurements
using the upcoming $\sim1\,\mathrm{deg}^2$ CLAMATO tomographic survey and 600
coeval zCOSMOS-Deep galaxies should place $3\sigma$ limits on extreme alignment
models with $\Delta\langle\cos\theta\rangle\sim0.1$, but much larger surveys
encompassing $>10,000$ galaxies, such as Subaru PFS, will be required to
constrain models with $\Delta\langle\cos\theta\rangle\sim0.03$. These
measurements will constrain models of galaxy-cosmic web alignment and test
tidal torque theory at $z\sim2$, improving our understanding of the redshift
dependence of galaxy-cosmic web alignment and the physics of intrinsic
alignments.


title: Efficient Estimation in Single Index Models through Smoothing splines

abstract:
  We consider estimation and inference in a single index regression model with
an unknown but smooth link function. In contrast to the standard approach of
using kernels or regression splines, we use smoothing splines to estimate the
smooth link function. We develop a method to compute the penalized least
squares estimators (PLSEs) of the parametric and the nonparametric components
given independent and identically distributed (i.i.d.)~data. We prove the
consistency and find the rates of convergence of the estimators. We establish
asymptotic normality under under mild assumption and prove asymptotic
efficiency of the parametric component under homoscedastic errors. A finite
sample simulation corroborates our asymptotic theory. We also analyze a car
mileage data set and a Ozone concentration data set. The identifiability and
existence of the PLSEs are also investigated.


title: D-groups and the Dixmier-Moeglin equivalence

abstract:
  A differential-algebraic geometric analogue of the Dixmier-Moeglin
equivalence is articulated, and proven to hold for $D$-groups over the
constants. The model theory of differentially closed fields of characteristic
zero, in particular the notion of analysability in the constants, plays a
central role. As an application it is shown that if $R$ is a commutative affine
Hopf algebra over a field of characteristic zero, and $A$ is an Ore extension
to which the Hopf algebra structure extends, then $A$ satisfies the classical
Dixmier-Moeglin equivalence. Along the way it is shown that all such $A$ are
Hopf Ore extensions


title: Rotation Periods of Wide Binaries in the Kepler Field

abstract:
  In a search of proper motion catalogs for common proper motion stars in the
field of the Kepler spacecraft I identified 93 likely binary systems. A
comparison of their rotation periods is a test of the gyrochronology concept.
To find their periods I calculated the autocorrelation function of the Kepler
mission photometry for each star. In most systems for which good periods can be
found, the cooler star has a longer period than the hotter component in general
agreement with models. However, there is a wide range in the gradients of lines
connecting binary pairs in a period-color diagram. Furthermore, near the solar
color, only a few stars have longer periods than the Sun, suggesting that they,
and their cooler companions are not much older than the Sun. In addition, there
is an apparent gap at intermediate periods in the period distribution of the
late K and early M stars. Either star formation in this direction has been
variable, or stars evolve in period at a non-uniform rate, or some stars evolve
more rapidly than others at the same mass. Finally, using the autocorrelation
function as a measure of the activity level, I found that while the F, G and
early K stars become less active as their periods increase, there is no
correlation between period and activity for the mid K to early M stars.


title: Phenomenological theory of collective decision-making

abstract:
  An essential task of groups is to provide efficient solutions for the complex
problems they face. Indeed, considerable efforts have been devoted to the
question of collective decision-making related to problems involving a single
dominant feature. Here we introduce a quantitative formalism for finding the
optimal distribution of the group members' competences in the more typical case
when the underlying problem is complex, i.e., multidimensional. Thus, we
consider teams that are aiming at obtaining the best possible answer to a
problem having a number of independent sub-problems. Our approach is based on a
generic scheme for the process of evaluating the proposed solutions (i.e.,
negotiation). We demonstrate that the best performing groups have at least one
specialist for each sub-problem -- but a far less intuitive result is that
finding the optimal solution by the interacting group members requires that the
specialists also have some insight into the sub-problems beyond their unique
field(s). We present empirical results obtained by using a large-scale database
of citations being in good agreement with the above theory. The framework we
have developed can easily be adapted to a variety of realistic situations since
taking into account the weights of the sub-problems, the opinions or the
relations of the group is straightforward. Consequently, our method can be used
in several contexts, especially when the optimal composition of a group of
decision-makers is designed.


title:
Unified treatment of fractional integral inequalities via linear
  functionals

abstract:
  In the paper we prove several inequalities involving two isotonic linear
functionals. We consider inequalities for functions with variable bounds, for
Lipschitz and H\" older type functions etc. These results give us an elegant
method for obtaining a number of inequalities for various kinds of fractional
integral operators such as for the Riemann-Liouville fractional integral
operator, the Hadamard fractional integral operator, fractional hyperqeometric
integral and corresponding q-integrals.


title: Sparse generalised polynomials

abstract:
  We investigate generalised polynomials (i.e. polynomial-like expressions
involving the use of the floor function) which take the value $0$ on all
integers except for a set of density $0$.
  Our main result is that the set of integers where a sparse generalised
polynomial takes non-zero value cannot contain a translate of an IP set. We
also study some explicit constructions, and show that the characteristic
functions of the Fibonacci and Tribonacci numbers are given by generalised
polynomails. Finally, we show that any sufficiently sparse $\{0,1\}$-valued
sequence is given by a generalised polynomial.
  (This paper is essentially the first half of our earlier submission
arXiv:1610.03900 [math.NT]. Because the material in arXiv:1610.03900 [math.NT]
touches upon many different subjects, we believe it is preferable to split it
into two independent papers.)


title:
Long-range interactions in the effective low energy Hamiltonian of
  Sr2IrO4: a core level resonant inelastic x-ray scattering study

abstract:
  We have investigated the electronic structure of Sr2IrO4 using core level
resonant inelastic x-ray scattering. The experimental spectra can be well
reproduced using ab initio density functional theory based multiplet ligand
field theory calculations, thereby validating these calculations. We found that
the low-energy, effective Ir t2g orbitals are practically degenerate in energy.
We uncovered that covalency in Sr2IrO4, and generally in iridates, is very
large with substantial oxygen ligand hole character in the Ir t2g Wannier
orbitals. This has far reaching consequences, as not only the onsite
crystal-field energies are determined by the long range crystal-structure, but,
more significantly, magnetic exchange interactions will have long range
distance dependent anisotropies in the spin direction. These findings set
constraints and show pathways for the design of d^5 materials that can host
compass-like magnetic interactions.


title: Schauder estimates for equations with cone metrics, I

abstract:
  This is the first paper in a series to develop a linear and nonlinear theory
for elliptic and parabolic equations on K\"ahler varieties with mild
singularities. Donaldson has established a Schauder estimate for linear and
complex Monge-Amp\`ere equations when the background K\"ahler metrics on
$\mathbb{C}^n$ have cone singularities along a smooth complex hypersurface. We
prove a sharp pointwise Schauder estimate for linear elliptic and parabolic
equations on $\mathbb{C}^n$ with background metric $g_\beta= \sqrt{-1} ( dz_1
\wedge d\bar{z_1} + \ldots + \beta^2|z_n|^{-2(1-\beta)} dz_n \wedge d\bar{z_n})
$ for $\beta\in (0,1)$. Our results give an effective elliptic Schauder
estimate of Donaldson and a direct proof for the short time existence of the
conical K\"ahler-Ricci flow.


title:
Ground State Properties of Antiferromagnetic Chains with Unrestricted
  Spin: Integer Spin Chains as Realisations of the O(3) Non-Linear Sigma Model

abstract:
  A continuum limit treatment of planar spin chains with arbitrary S is
presented. The difference between integer and half-integer spins is emphasised.
While isotropic half-integer spin chains are gapless,and have power-law decay
of correlations at T = 0 with exponent eta = 1, integer spin systems have a
singlet ground state with a gap for S=1 excitations and exponential decay of
correlations. The easy-plane to easy-axis transition is described.
  Note: this is a verbatim transcription of ILL preprint SP-81/95, which is
cited in a number of places, but was rejected for publication in 1981, and
remained unpublished in this original form, which gives somewhat different
arguments for the central result as compared to the later paper finally
published in Phys. Lett. 93A, 464 (1983); many thanks to Jeno Solyom for
preserving this historical document.


title: Adapted time steps explicit scheme for monotone BSDEs

abstract:
  We study the numerical strong stability of explicit schemes for the numerical
approximation of the solution to a BSDE where the driver has polynomial growth
in the primary variable and satisfies a monotone decreasing condition, and we
introduce an explicit scheme with adapted time-steps that guarantee numerical
strong stability. We then prove the convergence of this scheme and illustrate
it with numerical simulations.


title:
Full-Projection explicit FBSDE scheme for parabolic PDEs with
  superlinear nonlinearities

abstract:
  Developing efficient and stable approximations for high dimensional PDEs is
of key importance for numerous applications. The language of Forward-Backward
Stochastic Differential Equations (FBSDE), with its nonlinear Feynman-Kac
formula, allows for purely probabilistic representations of the solution and
its gradient for parabolic nonlinear PDEs.
  In this work we build on the recent results of [Lionnet, dos Reis and Szpruch
2015] by introducing and studying a Full-Projection explicit
time-discretization scheme for the approximation of FBSDEs with non-globally
Lipschitz drivers of polynomial growth. We establish convergence rates and we
show that, unlike classical explicit schemes, it preserves stability properties
present in the continuous-time dynamics, in particular, the scheme is able to
preserve the possible coercivity/contraction property of the PDE's
coefficients.
  The scheme is then coupled with a quantization-type approximation of the
conditional expectations on a space-time grid in order to provide a complete
approximation scheme for these FBSDEs/nonlinear PDEs and a full analysis is
also carried out. We illustrate our findings with numerical examples.


title: My Century of Physics

abstract: A short autobiography written for a centennial party.


title:
Mutual Photoluminescence Quenching and Photovoltaic Effect in Large-Area
  Single-Layer MoS2-Polymer Heterojunctions

abstract:
  Two-dimensional transition metal dichalcogenides (TMDCs) have recently
attracted attention due to their superlative optical and electronic properties.
In particular, their extraordinary optical absorption and semiconducting band
gap have enabled demonstrations of photovoltaic response from heterostructures
composed of TMDCs and other organic or inorganic materials. However, these
early studies were limited to devices at the micrometer scale and/or failed to
exploit the unique optical absorption properties of single-layer TMDCs. Here we
present an experimental realization of a large-area type-II photovoltaic
heterojunction using single-layer molybdenum disulfide (MoS2) as the primary
absorber, by coupling it to the organic {\pi}-donor polymer PTB7. This
TMDC-polymer heterojunction exhibits photoluminescence intensity that is
tunable as a function of the thickness of the polymer layer, ultimately
enabling complete quenching of the TMDC photoluminescence. The strong optical
absorption in the TMDC-polymer heterojunction produces an internal quantum
efficiency exceeding 40% for an overall cell thickness of less than 20 nm,
resulting in exceptional current density per absorbing thickness in comparison
to other organic and inorganic solar cells. Furthermore, this work provides new
insight into the recombination processes in type-II TMDC-polymer
heterojunctions and thus provides quantitative guidance to ongoing efforts to
realize efficient TMDC-based solar cells.


title: Two Methods For Wild Variational Inference

abstract:
  Variational inference provides a powerful tool for approximate probabilistic
in- ference on complex, structured models. Typical variational inference
methods, however, require to use inference networks with computationally
tractable proba- bility density functions. This largely limits the design and
implementation of vari- ational inference methods. We consider wild variational
inference methods that do not require tractable density functions on the
inference networks, and hence can be applied in more challenging cases. As an
example of application, we treat stochastic gradient Langevin dynamics (SGLD)
as an inference network, and use our methods to automatically adjust the step
sizes of SGLD, yielding significant improvement over the hand-designed step
size schemes


title: On entanglement spreading from holography

abstract:
  A global quench is an interesting setting where we can study thermalization
of subsystems in a pure state. We investigate entanglement entropy (EE) growth
in global quenches in holographic field theories and relate some of its aspects
to quantities characterizing chaos. More specifically we obtain four key
results:
  1. We prove holographic bounds on the entanglement velocity $v_E$ and the
butterfly effect speed $v_B$ that arises in the study of chaos.
  2. We obtain the EE as a function of time for large spherical entangling
surfaces analytically. We show that the EE is insensitive to the details of the
initial state or quench protocol.
  3. In a thermofield double state we determine analytically the two-sided
mutual information between two large concentric spheres separated in time.
  4. We derive a bound on the rate of growth of EE for arbitrary shapes, and
develop an expansion for EE at early times.
  In a companion paper arXiv:1608.05101, we put these results in the broader
context of EE growth in chaotic systems: we relate EE growth to the chaotic
spreading of operators, derive bounds on EE at a given time, and compare the
holographic results to spin chain numerics and toy models. In this paper, we
perform holographic calculations that provide the basis of arguments presented
in that paper.


title: Model based approach for household clustering with mixed scale variables

abstract:
  The Ministry of Social Development in Mexico is in charge of creating and
assigning social programmes targeting specific needs in the population for the
improvement of quality of life. To better target the social programmes, the
Ministry is aimed to find clusters of households with the same needs based on
demographic characteristics as well as poverty conditions of the household.
Available data consists of continuous, ordinal, and nominal variables and the
observations are not iid but come from a survey sample based on a complex
design. We propose a Bayesian nonparametric mixture model that jointly models
this mixed scale data and accommodates for the different sampling
probabilities. The performance of the model is assessed via simulated data. A
full analysis of socio-economic conditions in households in the State of Mexico
is presented.


title: Directional mechanical response in the bulk of topological metamaterials

abstract:
  Mechanical metamaterials are those structures designed to convey force and
motion in novel and desirable ways. Recently, Kane and Lubensky showed that
lattices at the point of marginal mechanical stability (Maxwell lattices)
possess a topological invariant that describes the distribution of floppy,
zero-energy edge modes. Here, we show that applying force at a point in the
bulk of these lattices generates a directional mechanical response, in which
stress or strain is induced only on one side of the force. This provides both a
bulk metric for mechanical polarization and a design principle to convey
stresses and strains towards or away from parts of the structure. We also
characterize the effects of removing bonds on the material's structure and
floppy modes, establishing a relationship between edge modes and bulk response.


title:
Texture Enhancement via High-Resolution Style Transfer for Single-Image
  Super-Resolution

abstract:
  Recently, various deep-neural-network (DNN)-based approaches have been
proposed for single-image super-resolution (SISR). Despite their promising
results on major structure regions such as edges and lines, they still suffer
from limited performance on texture regions that consist of very complex and
fine patterns. This is because, during the acquisition of a low-resolution (LR)
image via down-sampling, these regions lose most of the high frequency
information necessary to represent the texture details. In this paper, we
present a novel texture enhancement framework for SISR to effectively improve
the spatial resolution in the texture regions as well as edges and lines. We
call our method, high-resolution (HR) style transfer algorithm. Our framework
consists of three steps: (i) generate an initial HR image from an interpolated
LR image via an SISR algorithm, (ii) generate an HR style image from the
initial HR image via down-scaling and tiling, and (iii) combine the HR style
image with the initial HR image via a customized style transfer algorithm.
Here, the HR style image is obtained by down-scaling the initial HR image and
then repetitively tiling it into an image of the same size as the HR image.
This down-scaling and tiling process comes from the idea that texture regions
are often composed of small regions that similar in appearance albeit sometimes
different in scale. This process creates an HR style image that is rich in
details, which can be used to restore high-frequency texture details back into
the initial HR image via the style transfer algorithm. Experimental results on
a number of texture datasets show that our proposed HR style transfer algorithm
provides more visually pleasing results compared with competitive methods.


title: Semi-supervised Kernel Metric Learning Using Relative Comparisons

abstract:
  We consider the problem of metric learning subject to a set of constraints on
relative-distance comparisons between the data items. Such constraints are
meant to reflect side-information that is not expressed directly in the feature
vectors of the data items. The relative-distance constraints used in this work
are particularly effective in expressing structures at finer level of detail
than must-link (ML) and cannot-link (CL) constraints, which are most commonly
used for semi-supervised clustering. Relative-distance constraints are thus
useful in settings where providing an ML or a CL constraint is difficult
because the granularity of the true clustering is unknown.
  Our main contribution is an efficient algorithm for learning a kernel matrix
using the log determinant divergence --- a variant of the Bregman divergence
--- subject to a set of relative-distance constraints. The learned kernel
matrix can then be employed by many different kernel methods in a wide range of
applications. In our experimental evaluations, we consider a semi-supervised
clustering setting and show empirically that kernels found by our algorithm
yield clusterings of higher quality than existing approaches that either use
ML/CL constraints or a different means to implement the supervision using
relative comparisons.


title: Visible lattice points and the Extended Lindel\"of Hypothesis

abstract:
  We consider the number of visible lattice points under the assumption of the
Extended Lindel\"{o}f Hypothesis. We get a relation between visible lattice
points and the Extended Lindel\"{o}f Hypothesis. And we also get a relation
between visible lattice points over $\mathbf{Q}(\sqrt{-1})$ and the Gauss
Circle Problem.


title:
Magnetic field sensitivity and decoherence spectroscopy of an ensemble
  of narrow-linewidth nitrogen-vacancy centers close to a diamond surface

abstract:
  We perform pulsed optically detected electron spin resonance to measure the
DC magnetic field sensitivity and electronic spin coherence time T_2 of an
ensemble of near-surface, high-density nitrogen-vacancy (NV) centers engineered
to have a narrow magnetic resonance linewidth. Combining pulsed spectroscopy
with dynamic nuclear polarization, we obtain the photon-shot-noise-limited DC
magnetic sensitivity of 35 nT Hz^{-0.5}. We find that T_2 is controlled by
instantaneous diffusion, enabling decoherence spectroscopy on residual nitrogen
impurity spins in the diamond lattice and a quantitative determination of their
density. The demonstrated high DC magnetic sensitivity and decoherence
spectroscopy are expected to broaden the application range for two-dimensional
magnetic imaging.


title:
Beyond standard benchmarks: Parameterizing performance evaluation in
  visual object tracking

abstract:
  Object-to-camera motion produces a variety of apparent motion patterns that
significantly affect performance of short-term visual trackers. Despite being
crucial for designing robust trackers, their influence is poorly explored in
standard benchmarks due to weakly defined, biased and overlapping attribute
annotations. In this paper we propose to go beyond pre-recorded benchmarks with
post-hoc annotations by presenting an approach that utilizes omnidirectional
videos to generate realistic, consistently annotated, short-term tracking
scenarios with exactly parameterized motion patterns. We have created an
evaluation system, constructed a fully annotated dataset of omnidirectional
videos and the generators for typical motion patterns. We provide an in-depth
analysis of major tracking paradigms which is complementary to the standard
benchmarks and confirms the expressiveness of our evaluation approach.


title: Free-Endpoint Optimal Control of Inhomogeneous Bilinear Ensemble Systems

abstract:
  Optimal control of bilinear systems has been a well-studied subject in the
areas of mathematical and computational optimal control. However, effective
methods for solving emerging optimal control problems involving an ensemble of
deterministic or stochastic bilinear systems are underdeveloped. These
burgeoning problems arise in diverse applications from quantum control and
molecular imaging to neuroscience. In this work, we develop an iterative method
to find optimal controls for an inhomogeneous bilinear ensemble system with
free-endpoint conditions. The central idea is to represent the bilinear
ensemble system at each iteration as a time-varying linear ensemble system, and
then solve it in an iterative manner. We analyze convergence of the iterative
procedure and discuss optimality of the convergent solutions. The method is
directly applicable to solve the same class of optimal control problems
involving a stochastic bilinear ensemble system driven by independent additive
noise processes. We demonstrate the robustness and applicability of the
developed iterative method through practical control designs in neuroscience
and quantum control.


title: A homogeneous distance catalogue for Galactic RV Tauri objects

abstract:
  A subset of Post-AGB (PAGB) objects are the highly luminous RV Tauri
variables that show similarities to Type-II Cepheids. By using a sample of
known RV Tauri stars from the Magellanic Clouds we are able to determine period
luminosity relationships (PLRs) in various bands that have been used to
determine the luminosities of their Galactic counterparts. We have gathered all
available photometry in order to generate an SED for each object and determine
the total integrated flux. This total flux combined with a calculated or
inferred intrinsic luminosity leads to a distance (Vickers et al. 2015). This
distance catalogue has allowed us to begin to constrain the physical parameters
of this poorly understood evolutionary phase and to determine links between
these physical characteristics as a function of their stellar population.


title: Computer Assisted Composition with Recurrent Neural Networks

abstract:
  Sequence modeling with neural networks has lead to powerful models of
symbolic music data. We address the problem of exploiting these models to reach
creative musical goals, by combining with human input. To this end we
generalise previous work, which sampled Markovian sequence models under the
constraint that the sequence belong to the language of a given finite state
machine provided by the human. We consider more expressive non-Markov models,
thereby requiring approximate sampling which we provide in the form of an
efficient sequential Monte Carlo method. In addition we provide and compare
with a beam search strategy for conditional probability maximisation.
  Our algorithms are capable of convincingly re-harmonising famous musical
works. To demonstrate this we provide visualisations, quantitative experiments,
a human listening test and audio examples. We find both the sampling and
optimisation procedures to be effective, yet complementary in character. For
the case of highly permissive constraint sets, we find that sampling is to be
preferred due to the overly regular nature of the optimisation based results.
The generality of our algorithms permits countless other creative applications.


title: Topological Attractors of Contracting Lorenz Maps

abstract:
  We study the non-wandering set of contracting Lorenz maps. We show that if
such a map $f$ doesn't have any attracting periodic orbit, then there is a
unique topological attractor. Precisely, there is a compact set $\Lambda$ such
that $\omega_f(x)=\Lambda$ for a residual set of points $x \in [0,1]$.
Furthermore, we classify the possible kinds of attractors that may occur.


title: Optimizing Quantiles in Preference-based Markov Decision Processes

abstract:
  In the Markov decision process model, policies are usually evaluated by
expected cumulative rewards. As this decision criterion is not always suitable,
we propose in this paper an algorithm for computing a policy optimal for the
quantile criterion. Both finite and infinite horizons are considered. Finally
we experimentally evaluate our approach on random MDPs and on a data center
control problem.


title:
Cross-talk between topological defects in different fields revealed by
  nematic microfluidics

abstract:
  Topological defects are singularities in material fields that play a vital
role across a range of systems: from cosmic microwave background polarization
to superconductors, and biological materials. Although topological defects and
their mutual interactions have been extensively studied, little is known about
the interplay between defects in different fields -- especially when they
co-evolve -- within the same physical system. Here, using nematic
microfluidics, we study the cross-talk of topological defects in two different
material fields -- the velocity field and the molecular orientational field.
Specifically, we generate hydrodynamic stagnation points of different
topological charges at the center of star-shaped microfluidic junctions, which
then interact with emergent topological defects in the orientational field of
the nematic director. We combine experiments, and analytical and numerical
calculations to demonstrate that a hydrodynamic singularity of given
topological charge can nucleate a nematic defect of equal topological charge,
and corroborate this by creating $-1$, $-2$ and $-3$ topological defects in
$4-$, $6-$, and $8-$arm junctions. Our work is an attempt toward understanding
materials that are governed by distinctly multi-field topology, where disparate
topology-carrying fields are coupled, and concertedly determine the material
properties and response.


title: Six-dimensional regularization of chiral gauge theories on a lattice

abstract:
  We propose a six-dimensional regularization of four dimensional chiral gauge
theories. We consider a massive Dirac fermion in six dimensions with two
different operators having domain-wall profiles in the fifth and the sixth
directions, respectively. A Weyl fermion appears as a localized mode at the
junction of the two domain-walls. In our formulation, the Stora-Zumino chain of
the anomaly descent equations, starting from the axial $U(1)$ anomaly in
six-dimensions to the gauge anomaly in four-dimensions, is naturally embedded.
Moreover, a similar inflow of the global anomalies is found. The anomaly free
condition is equivalent to requiring that the axial $U(1)$ anomaly and the
parity anomaly are canceled among the six-dimensional Dirac fermions. Putting
the gauge field at the four- dimensional junction and extending it to the bulk
using the Yang-Mills gradient flow, as recently proposed by Grabowska and
Kaplan, we define the four-dimensional path integral of the target chiral gauge
theory.


title: A representation-theoretic interpretation of positroid classes

abstract:
  A positroid is the matroid of a real matrix with nonnegative maximal minors,
a positroid variety is the closure of the locus of points in a complex
Grassmannian whose matroid is a fixed positroid, and a positroid class is the
cohomology class Poincar\'e dual to a positroid variety. We define a family of
representations of general linear groups whose characters are symmetric
polynomials representing positroid classes. These representations are certain
diagram Schur modules in the sense of James and Peel. This gives a new
algebraic interpretation of the Schubert structure constants for the product of
a Schubert polynomial and Schur polynomial, and of the 3-point Gromov-Witten
invariants for Grassmannians, proving a conjecture of Postnikov. As a
byproduct, we obtain an effective algorithm for decomposing positroid classes
into Schubert classes.


title:
Interspecific allometric scaling of multicellular organisms as an
  evolutionary process of food chain creation, influenced by mechanical
  constraints

abstract:
  Metabolism is a foundation of life. Metabolic rate of organisms (amount of
energy produced per unit time) increases slower than organisms' mass, which has
important consequences for life organization. This phenomenon, when considered
across different taxa, is called interspecific allometric scaling. Here, on the
basis of introduced biomechanical models, physiological and evolutionary
principles, we discover and validate its fundamental mechanisms. Calculated
theoretical values of allometric exponents for the maximal and basal metabolic
rates, for mammals, reptiles, fish and birds, correspond to experimental data.
This proves that the cooperative action of discovered mechanisms, indeed, is
the cause of this phenomenon, and that allometric scaling is rather a
statistical effect of individual evolutionary and physiological adaptations of
organisms within the food chain, both in terms of metabolism and biomechanical
constraints. The increase in size is coupled with the increase of the overall
metabolic rate due to the change of biomechanical characteristics and the need
to meet certain functional requirements for a successful reproduction (like the
speed advantage over the prey). On one hand, organisms have to reliably acquire
sufficient food for that. On the other hand, neither biomechanical nor
metabolic advantage can be too strong - otherwise, the food chain could be
destroyed. The counteraction of these two needs establishes a dynamic balance
in the food chain, which, together with biomechanical constraints, explains the
phenomenon of allometric scaling. Once acknowledged, this discovery will have
numerous important implications in ecological, evolutionary, physiological and
other studies, as well as in practical applications.


title:
PAG2ADMG: An Algorithm for the Complete Causal Enumeration of a Markov
  Equivalence Class

abstract:
  Causal graphs, such as directed acyclic graphs (DAGs) and partial ancestral
graphs (PAGs), represent causal relationships among variables in a model.
Methods exist for learning DAGs and PAGs from data and for converting DAGs to
PAGs. However, these methods are significantly limited in that they only output
a single causal graph consistent with the independencies and dependencies (the
Markov equivalence class $M$) estimated from the data. This is problematic and
insufficient because many distinct graphs may be consistent with $M$. A data
modeler may wish to select among these numerous consistent graphs using domain
knowledge or other model selection algorithms. Enumeration of the set of
consistent graphs is the bottleneck. In this paper, we present a method that
makes this desired enumeration possible. We introduce PAG2ADMG, the first
algorithm for enumerating all causal graphs consistent with $M$. PAG2ADMG
converts a given PAG into the complete set of acyclic directed mixed graphs
(ADMGs) consistent with $M$. We prove the correctness of the approach and
demonstrate its efficiency relative to brute-force enumeration.


title: Noise-Tolerant Life-Long Matrix Completion via Adaptive Sampling

abstract:
  We study the problem of recovering an incomplete $m\times n$ matrix of rank
$r$ with columns arriving online over time. This is known as the problem of
life-long matrix completion, and is widely applied to recommendation system,
computer vision, system identification, etc. The challenge is to design
provable algorithms tolerant to a large amount of noises, with small sample
complexity. In this work, we give algorithms achieving strong guarantee under
two realistic noise models. In bounded deterministic noise, an adversary can
add any bounded yet unstructured noise to each column. For this problem, we
present an algorithm that returns a matrix of a small error, with sample
complexity almost as small as the best prior results in the noiseless case. For
sparse random noise, where the corrupted columns are sparse and drawn randomly,
we give an algorithm that exactly recovers an $\mu_0$-incoherent matrix by
probability at least $1-\delta$ with sample complexity as small as
$O\left(\mu_0rn\log (r/\delta)\right)$. This result advances the
state-of-the-art work and matches the lower bound in a worst case. We also
study the scenario where the hidden matrix lies on a mixture of subspaces and
show that the sample complexity can be even smaller. Our proposed algorithms
perform well experimentally in both synthetic and real-world datasets.


title: Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis

abstract:
  We introduce a data-driven approach to complete partial 3D shapes through a
combination of volumetric deep neural networks and 3D shape synthesis. From a
partially-scanned input shape, our method first infers a low-resolution -- but
complete -- output. To this end, we introduce a 3D-Encoder-Predictor Network
(3D-EPN) which is composed of 3D convolutional layers. The network is trained
to predict and fill in missing data, and operates on an implicit surface
representation that encodes both known and unknown space. This allows us to
predict global structure in unknown areas at high accuracy. We then correlate
these intermediary results with 3D geometry from a shape database at test time.
In a final pass, we propose a patch-based 3D shape synthesis method that
imposes the 3D geometry from these retrieved shapes as constraints on the
coarsely-completed mesh. This synthesis process enables us to reconstruct
fine-scale detail and generate high-resolution output while respecting the
global mesh structure obtained by the 3D-EPN. Although our 3D-EPN outperforms
state-of-the-art completion method, the main contribution in our work lies in
the combination of a data-driven shape predictor and analytic 3D shape
synthesis. In our results, we show extensive evaluations on a newly-introduced
shape completion benchmark for both real-world and synthetic data.


title: Flow polytopes with Catalan volumes

abstract:
  The Chan-Robbins-Yuen polytope can be thought of as the flow polytope of the
complete graph with netflow vector $(1, 0, \ldots, 0, -1)$. The normalized
volume of the Chan-Robbins-Yuen polytope equals the product of consecutive
Catalan numbers, yet there is no combinatorial proof of this fact. We consider
a natural generalization of this polytope, namely, the flow polytope of the
complete graph with netflow vector $(1,1, 0, \ldots, 0, -2)$. We show that the
volume of this polytope is a certain power of $2$ times the product of
consecutive Catalan numbers. Our proof uses constant term identities and
further deepens the combinatorial mystery of why these numbers appear. In
addition we introduce two more families of flow polytopes whose volumes are
given by product formulas.


title: Review on Hadron Spectroscopy

abstract:
  I review some of the lattice results on spectroscopy and resonances in the
past years. For the conventional hadron spectrum computations, focus has been
put on the isospin breaking effects, QED effects, and simulations near the
physical pion mass point. I then go through several single-channel scattering
studies within L\"uscher formalism, a method that has matured over the past few
years. The topics cover light mesons and also the charmed mesons, with the
latter case intimately related to the recently discovered exotic $XYZ$
particles. Other possible related formalisms that are available on the market
are also discussed.


title: Robust Optimization for Tree-Structured Stochastic Network Design

abstract:
  Stochastic network design is a general framework for optimizing network
connectivity. It has several applications in computational sustainability
including spatial conservation planning, pre-disaster network preparation, and
river network optimization. A common assumption in previous work has been made
that network parameters (e.g., probability of species colonization) are
precisely known, which is unrealistic in real- world settings. We therefore
address the robust river network design problem where the goal is to optimize
river connectivity for fish movement by removing barriers. We assume that fish
passability probabilities are known only imprecisely, but are within some
interval bounds. We then develop a planning approach that computes the policies
with either high robust ratio or low regret. Empirically, our approach scales
well to large river networks. We also provide insights into the solutions
generated by our robust approach, which has significantly higher robust ratio
than the baseline solution with mean parameter estimates.


title:
Galois level and congruence ideal for $p$-adic families of finite slope
  Siegel modular forms

abstract:
  We consider $p$-adic families of Siegel eigenforms of genus $2$ and finite
slope, defined as local pieces of an eigenvariety and equipped with a suitable
integral structure. Under some assumptions on the residual image, we show that
the image of the Galois representation associated with a family is big, in the
sense that a Lie algebra attached to it contains a congruence subalgebra of
non-zero level. We call Galois level of the family the largest such level. We
show that it is trivial when the residual representation has full image. When
the residual representation is a symmetric cube, the zero locus defined by the
Galois level of the family admits an automorphic description: it is the locus
of points that arise from overconvergent eigenforms for $\mathrm{GL}_2$, via a
$p$-adic Langlands lift attached to the symmetric cube representation. Our
proof goes via the comparison of the Galois level with a "fortuitous"
congruence ideal, that describes the zero- and one-dimensional subvarieties of
symmetric cube type appearing in the family. We show that some of the $p$-adic
lifts are interpolated by a morphism of rigid analytic spaces from an
eigencurve for $\mathrm{GL}_2$ to an eigenvariety for $\mathrm{GSp}_4$. The
remaining lifts appear as isolated points on the eigenvariety.


title:
Menu-Based Pricing for Charging of Electric Vehicles with
  Vehicle-to-Grid Service

abstract:
  The paper considers a bidirectional power flow model of the electric vehicles
(EVs) in a charging station. The EVs can inject energies by discharging via a
Vehicle-to-Grid (V2G) service which can enhance the profits of the charging
station. However, frequent charging and discharging degrade battery life. A
proper compensation needs to be paid to the users to participate in the V2G
service. We propose a menu-based pricing scheme, where the charging station
selects a price for each arriving user for the amount of battery utilization,
the total energy, and the time (deadline) that the EV will stay. The user can
accept one of the contracts or rejects all depending on their utilities. The
charging station can serve users using a combination of the renewable energy
and the conventional energy bought from the grid. We show that though there
exists a profit maximizing price which maximizes the social welfare, it
provides no surplus to the users if the charging station is aware of the
utilities of the users. If the charging station is not aware of the exact
utilities, the social welfare maximizing price may not maximize the expected
profit. In fact, it can give a zero profit. We propose a pricing strategy which
provides a guaranteed fixed profit to the charging station and it also
maximizes the expected profit for a wide range of utility functions. Our
analysis shows that when the harvested renewable energy is small the users have
higher incentives for the V2G service. We, numerically, show that the charging
station's profit and the user's surplus both increase as V2G service is
efficiently utilized by the pricing mechanism.


title:
The Proper Motions of the Double Radio Source n in the Orion BN/KL
  Region

abstract:
  We have extended the time baseline for observations of the proper motions of
radio sources in the Orion BN/KL region from 14.7 to 22.5 years. We present
improved determinations for the sources BN and I. In addition, we address the
proper motions of the double radio source n, that have been questioned in the
literature. We confirm that all three sources are moving away at transverse
velocities of tens of km s$^{-1}$ from a region in-between them, where they
were located about 500 years ago. Source n exhibits a new component that we
interpret as due to a one-sided ejection of free-free emitting plasma that took
place after 2006.36. We used the highly accurate relative proper motions
between sources BN and I to determine that their closest separation took place
in the year 1475$\pm$6, when they were within $\sim$100 AU or less from each
other in the plane of the sky.


title: When to Reset Your Keys: Optimal Timing of Security Updates via Learning

abstract:
  Cybersecurity is increasingly threatened by advanced and persistent attacks.
As these attacks are often designed to disable a system (or a critical
resource, e.g., a user account) repeatedly, it is crucial for the defender to
keep updating its security measures to strike a balance between the risk of
being compromised and the cost of security updates. Moreover, these decisions
often need to be made with limited and delayed feedback due to the stealthy
nature of advanced attacks. In addition to targeted attacks, such an optimal
timing policy under incomplete information has broad applications in
cybersecurity. Examples include key rotation, password change, application of
patches, and virtual machine refreshing. However, rigorous studies of optimal
timing are rare. Further, existing solutions typically rely on a pre-defined
attack model that is known to the defender, which is often not the case in
practice. In this work, we make an initial effort towards achieving optimal
timing of security updates in the face of unknown stealthy attacks. We consider
a variant of the influential FlipIt game model with asymmetric feedback and
unknown attack time distribution, which provides a general model to consecutive
security updates. The defender's problem is then modeled as a time associative
bandit problem with dependent arms. We derive upper confidence bound based
learning policies that achieve low regret compared with optimal periodic
defense strategies that can only be derived when attack time distributions are
known.


title:
Modified scattering for the quadratic nonlinear Klein-Gordon equation in
  two dimensions

abstract:
  In this paper, we consider the long time behavior of solution to the
quadratic gauge invariant nonlinear Klein-Gordon equation (NLKG) in two space
dimensions. For a given asymptotic profile, we construct a solution to (NLKG)
which converges to given asymptotic profile as t goes infinity. Here the
asymptotic profile is given by the leading term of the solution to the linear
Klein-Gordon equation with a logarithmic phase correction. Construction of a
suitable approximate solution is based on Fourier series expansion of the
nonlinearity.


title: Solitons and Quantum Behavior

abstract:
  In applied physics and in engineering intuitive understanding is a boost for
creativity and almost a necessity for efficient product improvement. The
existence of soliton solutions to the quantum equations in the presence of
self-interactions allows us to draw an intuitive picture of quantum mechanics.
The purpose of this work is to compile a collection of models, some of which
are simple, some are obvious, some have already appeared in papers and even in
textbooks, and some are new. However this is the first time they are presented
(to our knowledge) in a common place attempting to provide an intuitive
physical description for one of the basic particles in nature: the electron.
The soliton model applied to the electrons can be extended to the
electromagnetic field providing an unambiguous description for the photon. In
so doing a clear image of quantum mechanics emerges, including quantum optics,
QED and field quantization. To our belief this description is of highly
pedagogical value. We start with a traditional description of the old quantum
mechanics, first quantization and second quantization. We describe an intuitive
description of first and second quantization based on the concept of solitons,
pioneered by the double solution of de Broglie in 1927. Many aspects of first
and second quantization are clarified and visualized intuitively, including the
so called vacuum fluctuations.